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THE JESUP LECTURES
190a-1909
NEWTON
COLUMBIA UNIVERSITY LECTURES
LIGHT
BY
RICHARD C. MACLAURIN, LL.D., Sc.D,
PRESIDENT OF THE MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OF THE
UNIVERSITY
OF
Nefo
THE COLUMBIA UNIVERSITY PRESS
1909
All rights reserved
COPTBIGHT, 1909,
BY THE COLUMBIA UNIVERSITY PRESS.
Set up and electrotyped. Published June, 1909.
J. 8. Gushing Co. Berwick <fe Smith Co.
Norwood, Mass., U.S.A.
PREFACE
THESE lectures were given at the American Museum of
Natural History during the winter of 1908-9, when I had
the honor of occupying a chair of Mathematical Physics
at Columbia University in the City of New York. It is
not easy, in such a place, for a man of science to sit in
cloistered calm, far from the distractions of the busy
world of action, and to pursue research merely for self-
illumination or for the edification of a caste of intel-
lectuals. The throb of life is all around him, and it
impresses him with the duty of responding to the de-
mands of an active-minded people for reliable informa-
tion on the most recent developments of science. He is
expected to know ; but not only to know, but also to
communicate. And so, on being invited to give the Jesup
Lectures, I attempted to describe the salient features of
the modern theory of light within the narrow compass of
ten lectures, and undertook in doing so to avoid techni-
calities as much as possible. I have had specially in view
the man of intelligence who lays no claim to scientific
knowledge, but who wishes to know what all the talk of
science is about, and, in particular, why the physicists
make such strange postulates as ether and electrons, and
why they have so much confidence in the methods that
they employ and the results that they obtain. For this
purpose I have had to show him how wonderfully the
theory fits the facts, down to the minutest numerical
193277
yi PREFACE
detail; although, of course, the full force of the argument
is lost owing to the necessity of eschewing mathematics
and merely stating the results of theory without giving
the actual demonstrations, except in the simplest cases.
I hope, too, that the book may be found useful to the
large body of teachers of physics throughout the country.
They will find in it much that is scarcely touched upon in
the ordinary text-books, and their appreciation of the dif-
ficulties of presenting such a subject in non-technical lan-
guage will put them in that sympathetic frame of mind
that helps so much towards the understanding of a writer.
My thanks are due to Mr. Farwell for the care and
skill with which he conducted the experiments that illus-
trated the lectures, and to my colleague, Professor E. F.
Nichols, for reading the proof-sheets and displaying a
keen interest in the progress of the course.
R. C. M.
" A man of science does well indeed to take his views from
many points of sight, and to supply the defects of sense by a
well-regulated imagination; but as his knowledge of Nature
is founded on the observation of sensible things, he must be-
gin with these, and must often return to them to examine his
progress by them. Here is his secure hold ; and, as he sets
out from thence, so if he likewise trace not often his steps
backwards with caution, he will be in hazard of losing his
way in the labyrinths of Nature." Colin Maclaurin : An
account of Sir Isaac Newton's Philosophical Discoveries.
(1748.)
vii
CONTENTS
LBOTtTKl! PAGE
I. EARLY CONTRIBUTIONS TO OPTICAL THEORY . . 1
II. COLOR VISION AND COLOR PHOTOGRAPHY ... 24
III. DISPERSION AND ABSORPTION 47
IV. SPECTROSCOPY Y . .70
V. POLARIZATION . .... , . * 95
VI. THE LAWS OF REFLECTION AND REFRACTION . . 118
VII. THE PRINCIPLE OF INTERFERENCE . , . . 154
VIII. CRYSTALS . . . . . : ; V " .' . ' . . 175
IX. DIFFRACTION . . .* . . . . . .202
X. LIGHT AND ELECTRICITY . V . . . . 229
INDEX 249
LIGHT
EARLY CONTRIBUTIONS TO OPTICAL THEORY
"THEY tell us," said Matthew Arnold, "that when a
candle burns, the oxygen and nitrogen of the air combine
with the carbon in the candle to form carbonic acid gas.
Who cares?" I recall the story not with the object of
revealing flaws in the chemistry of the brilliant advocate
of sweetness and of light, but because it suggests an atti-
tude to science that is far from rare, even amongst people
of intelligence to-day. They tell you, sometimes frankly,
but more often by implication, that they care for none of
these things. Perhaps it is worth considering for a moment
to what this attitude is due. Doubtless it springs from a
variety of causes, according to the infinitely varied con-
stitutions of the minds and hearts of the different thinkers ;
but in nine cases out of ten its origin can, I think, be
traced either to misconception or to ignorance. Men are
engrossed in other affairs; they know of science only by
scraps, an occasional lecture, perhaps, or a magazine article
read to lessen the tedium of a railroad journey. At the
best they get a sight only of a portion of any one science,
never a clear view of the whole structure. Now modern
science is an elaborate work of art, and to be thoroughly
appreciated it must be looked upon as a whole. Who that
B 1
2 LIGHT
has any eye and mind for the beautiful, and that finds
himself in the presence of a great master, such as Rem-
brandt, will rest content with so distant a view or so hur-
ried a glance that he can see only the outline of a hand or
the contour of a cloak? The mind that can really carry
out the process suggested by the phrase ex pede Hercukm
is not only rarely gifted, but must have been trained with
unusual care. In a million, not ten that see only the foot
will have anything but the vaguest vision of the whole man
Hercules. The rest will turn aside with apathy and mur-
mur, "Who cares?' 7
Bearing these facts in mind in this course of lectures on
Light, I shall try to give you something more than a glimpse
or two of single portions of the great scientific structure.
Our view must necessarily be very incomplete, for to visit
every portion of the building and study it with thoroughness
would require the devotion of a lifetime. At the best I
can take you along the corridors and let you see into some
of the principal rooms. Enough, I hope, to enable you to
grasp the main features of the plan and to put you in a
position to appreciate the genius of the architects, and to
realize something of the patience and endurance required
to overcome so many obstacles and to build so solidly and
well. If, however, there is any here, as I sincerely hope
there is, who craves for more than this, and, not content
with general outlines, wishes to probe into the very heart
of nature, then, although I wish him all joy and success
in his quest, I think it right to warn him that he must not
expect very much from such a course as this. As Euclid
said to the Egyptian king inquiring for a short cut to the
mastery of geometry, "Sire, there is no royal road
thereto." Indeed, hard is the road and narrow the way,
EARLY CONTRIBUTIONS TO OPTICAL THEORY 3
and to follow it to the end requires a clear head, and above
all a stout heart. At the best I can put you on the way.
I have suggested that some men turn away from science
through the mere scrappiness of their knowledge, but this
is not the only thing that renders its pursuit unattractive.
Many poetic natures find it cold and inhuman. Recall
the query of Keats :
" Do not all charms fly
At the mere touch of cold philosophy ?
There was an awful rainbow once in heaven ;
We know her woof and texture. She is given
In the dull catalogue of common things."
The complaint seems to be that science, with its cold
analysis, robs us of the pleasing sense of awe and mystery ;
but if you dig deep, you will find still enough of mystery
left to satisfy the keenest yearner after half lights and the
obscure. At the best, science only replaces one mystery
by another of grander order.
As to the alleged inhumanity of science, the charge is
probably made by way of protest against the attitude of
some who, in the generation just past, made exaggerated
claims in the name of science. They professed to worship
Nature and to worship her so jealously as not to tolerate
the worship of any other gods besides. They disparaged
those human studies that have occupied men's minds
throughout the ages, and were so far from believing that
"the proper study of mankind is man " as to give the im-
pression that that was the one kind of study not worth
pursuing.
Such extreme opinions are naturally resented by the
Humanists, who hold that "man hath all which Nature
4 LIGHT
hath ; but more, And in that more lie all his hopes of good."
The controversy is fortunately dead by this time, when
science has become more genial, and it is seen to be absurd
to make an arbitrary separation between man and nature.
Apart from this, it is an obvious truism that a science such
as that of light is a purely human study; it is taken up
with discussions as to what man has thought of one of the
most impressive of his sensations, so that the study of
its history proves of intensely human interest. Here we
watch the race grappling with great intellectual difficul-
ties, and we see the spectacle of her champions painfully
but surely overcoming countless obstacles. Each of their
victories is a genuine victory of the spirit, each of their
defeats a spiritual chastisement.
Others who stop short of charging science with inhuman-
ity, think that its study robs men of their natural powers
of appreciation. They point to the pathetic case of Darwin,
but it would tie easy to quote many great names to show
that Darwin's experience, even if it has not been misunder-
stood, is extremely unusual. It would indeed be a terrible
price to pay for our exact knowledge of optics, if it robbed
us of our due joy in color and in light. Fortunately,
however, there is not the slightest reason why, after pon-
dering over the laws of light, we should appreciate less the
brilliance of a New York sky or the glory of the autumn
tints in the woods around us. Our study should rather
increase our interest and our capacity for appreciation and
enjoyment. It is strangely true, however, that artists
have often an antipathy to the science and this in spite
of the fact that the problems that they have to face require
for their solution an accurate knowledge of many optical
laws. Few men knew better than Ruskin that between
EARLY CONTRIBUTIONS TO OPTICAL THEORY 5
wise art and wise science there is essential relation for each
other's help and dignity, and yet even he seems doubtful
as to the benefit of scientific knowledge to the artist. His
lecture on the relation to art of the science of light is un-
usually diffuse (it deals almost as much with snakes as with
either art or science), so that it is difficult to gather here
anything relevant to the present discussion. In another
place, however, he says plainly that scientific knowledge
may be positively harmful to the artist. "The knowledge
may merely occupy the brain wastefully and warp his
artistic attention and energy from their point. As an
instance, Turner, in his early life, was sometimes good-
natured, and would show people what he was about. He
was one day making a drawing of Plymouth harbor,
with some ships at the distance of a mile or two, seen
against the light. Having shown this drawing to a naval
officer, the naval officer observed with surprise, and ob-
jected with very justifiable indignation, that in the picture
the ships of the line had no port-holes. 'No/ said Tur-
ner, ' certainly not. If you will walk up to Mt. Edge-
comb, and look at the ships against the sunset, you will
find that you can't see the port-holes.' ' Well, but/ said
the naval officer, still indignant, 'you know the port-holes
are there.' 'Yes/ said Turner, 'I know that well enough;
but my business is to draw what I see, and not what I know
is there.'" This is doubtless true enough, but its chief
application in Ruskin's mind had reference to the science of
anatomy, the study of which, he thought, had spoilt many
a good artist by giving him the "butcher's view." It
can scarcely, however, be applicable to Light, for that
artist has yet to arise who is so imbued with optical theories
as to distinguish blue from red by drawing ether waves
6 LIGHT
of the different lengths that science postulates. Probably
the repulsion of the artist to the science of light is due, at
least in part, to the feeling that the splendor of light and
color has little to do with the mechanical concepts of
optical theory ; but although modern science is accustomed
to speak hi the language of mechanics, it is quite prepared
to admit that the artist's feeling may be entirely an affair
of the spirit. It would like to see all artists walking in
its ranks. Of course no one would seriously suggest that
the study of optical science will make you an artist. If,
however, you have the artistic spirit, you will understand
that the science of Light is really a work of conscious and
premeditated art. Your intelligence will urge you to know
at least something about the subject, and you may even
agree with Ruskin that "whatever it is really desirable
and honorable to know, it is also desirable and honorable to
know as completely as possible."
If you will permit me one word more of an introductory
character, I should like to say that it will be my endeavor
to present the subject with all possible simplicity. This,
I hope, needs no apology ; at any rate you will not suppose
that I underrate your powers if I try to make things as
easy as I can. Of course it is true, as Ruskin says, that
"no study that is worth pursuing seriously can be pursued
without effort" ; but it is needless to make the effort painful
merely for the sake of preserving our dignity. And while
I shall avoid technicalities as much as possible for the
sake of lucidity, for the sake of art I shall equally avoid
any attempt at word-painting. The subject is too great in
itself for anything but a studied simplicity in its treatment.
The theory of light has, in these latter days, achieved
so many successes, and been worked up into so nearly
EARLY CONTRIBUTIONS TO OPTICAL THEORY 7
perfect a form, that there is a temptation to forget the
labors of the great men of the past who have done so much
to make these modern victories possible, and to present the
theory in the form it bears to-day as if no other had been
thought of. It is a temptation to be rigorously withstood.
In science no less than in other branches of human activity
we must not allow ourselves to forget that the roots of the
present lie deep in the past. By so doing we neglect a
valuable aid to the thorough understanding of the present,
and we rob ourselves of the pleasure and the illumination
that comes from tracing the development through the ages
of a great idea. Unfortunately, in the present lectures we
shall have no time for this, but we can scarcely avoid dip-
ping a little into the past, even in the most cursory examina-
tion of optical theory.
Doubtless thoughtful men of various races must have
pondered over the phenomena of light, but amongst the
earliest references in literature to anything that can, by the
utmost stretching of terms, be dignified by the name of a
theory of light, are the speculations of some of the philoso-
phers of Greece. The Greek mind is so often and so justly
held up as an object of admiration that it is with something
of a shock that we read the puerilities of its greatest thinkers
when dealing with physical science. In the field of optics
they seem mainly to have been occupied with the question
whether objects become visible by means of something
emitted by them, or by means of something that issues from
the seeing eye. Five centuries B.C. Pythagoras and his
school held that vision is caused by particles continually
projected into the pupil of the eye; while later, Empedocles
maintained that to excite the sense of sight there must
be something emitted from the eye, and that this must
8 LIGHT
meet with something else proceeding from the object seen.
Listen to and get what enlightenment you can from
Plato's explanation of an act of vision:
"The pure fire that is within us the gods made to flow
through the eyes in a single smooth substance, at the same
time compressing the center of the eye so as to retain all
the denser element, and only to allow this to be sifted
through pure. When, therefore, the light of day surrounds
the stream of vision, then like falls upon like, and there is a
union, and a body is formed by natural affinity, according to
the direction of the eyes, wherever the light that falls from
within meets that which comes from an external object.
And, everything being affected by likeness, whatever touches
and is touched by this stream of vision, their motions are
diffused over the whole body, and reach the soul, producing
that perception which we call sight. But when the external
and kindred fire passes away in night, then the stream of
vision is cut off; for, going forth to the unlike element, it is
changed and extinguished, being no longer of one nature
with the surrounding atmosphere, which is now deprived
of fire : the eye no longer sees, and we go to sleep ; for when
the eyelids are closed, which the gods invented as the pres-
ervation of the sight, they keep in the eternal fire." So
much for his explanation of vision. Hear next his theory
of colors. "There is a class of sensible things called by the
general name of colors. They are a flame that emanates
from all bodies, a flame that has particles corresponding to
the sense of sight. Of the particles coming from other
bodies that fall upon the sight, some are less, some are
greater, and some are equal to the parts of the sight itself.
Those that are equal are imperceptible, or transparent, as
we call them, whereas the smaller dilate, the larger contract
EARLY CONTRIBUTIONS TO OPTICAL THEORY 9
the sight, having a power akin to that of hot and cold bodies
on the flesh, or of astringent bodies on the tongue. Those
that dilate the visual ray we term white, the others black."
Aristotle, of course, objected to this as to most of Plato's
science. He came, in a vague way, nearer to the modern
view, as he regarded light not as material at all, but as
the influence of a medium on the eye. He says : " Vision
is the result of some impression made upon the faculty
of sense, an impression that must be due to the medium
that intervenes. There exists something which is pellucid.
Light is the action of this pellucid, and whenever this
pellucidity is present only potentially, there darkness also
is present. Light is neither fire nor substance, but only
the presence of fire, or something like it, in that which is
pellucid." This is, I think, the clearest account we have in
Greek philosophy of the nature of light. I will not venture
to say that it is obscure, but perhaps I may be permitted
to use Aristotle's own phraseology, and suggest that "its
pellucidity is present only potentially."
However, I must not weary you further with the specu-
lations of Greek philosophers or medieval thinkers. It is
not until the seventeenth century of our era that we get
any really great advance, when Snell discovered the law of
refraction and Newton made his classical experiments on
color. We may well pause just for a moment to consider
why in all those ages the world of science stood so still.
Certainly it was not due to any lack of intellect. No one
who looks into the matter can fail to recognize that there
really were giants of old. Indeed it would be a hazardous
thing to assert that within the last two thousand years there
is any evidence of human advancement, if you measure man
merely by the intellectual power of the greatest of his kind.
10 LIGHT
Talk with an ancient or medieval philosopher on matters
of science, and he appears like a child; but take him on
his own ground, and you will have to wrestle hard indeed to
overthrow him. No, it is not in mind but in method that
the race has advanced ; and where we are superior to our
forefathers is in the fact that we have learned at any
rate in science first to lay a solid foundation of fact before
we begin to theorize.
If you search in the field of optics, you will find that the
only general facts known before the seventeenth century
could all be stated in a few minutes. They were these :
(1) Light travels in straight lines a partial truth that
proved to be more misleading than a lie. (2) The fact
and the law of reflection. (3) The fact of refraction
not its law. (4) The fact of total reflection. These things
are probably familiar to most of you; but for the sake of
those to whom they are not, it may be well to direct your
attention to a few simple experiments, so that all may
realize clearly how much and how little was known in the
good old days. In the first place, " light appears to move
in straight lines." This is familiar to every one who has
looked at a shadow and noticed that its contour is deter-
mined by drawing straight lines from the source of light past
the edges of the object that casts the shadow. The light
goes straight past the edge and does not bend round corners,
so that we are tempted to lay down the law that " light moves
in straight lines." The one objection is that it is not true.
As we shall see later, this is a case in which we are misled
by our senses. Light does bend round corners, but under
ordinary circumstances the bending is so slight that the eye
is unable to detect it. So much for one of the four general
principles known before the seventeenth century. The
EARLY CONTRIBUTIONS TO OPTICAL THEORY 11
other three can all be demonstrated by slight modifications
of the same experiment. Darken your room as much as
possible, and let light from the sun stream in through a
single chink. (If you prefer to work at night, you can make
an artificial light take the place of the sun.) Let this
light fall on a tumbler of water in which are two or three
drops of milk. Blow in a little smoke to show the path of
the ray, or scatter a little powder, if you object to smoke.
You will observe that the ray, when it strikes the surface
of the water, is bent back into the air. This is the fact
of reflection. Its law is that the incident and reflected rays
are equally inclined to the surface of the water, and this also
you can verify. If you are interested only in reflection,
it will be better to use an ordinary mirror rather than the
water to produce reflection, as thereby you will get more
light reflected, and will have less difficulty in seeing the
reflected beam distinctly. The advantage of the water is
that it enables you to observe the other phenomena, to
which reference has been made. You will see that not all
the light is reflected, but that there is a bright beam in
the water. This beam is not in the same direction as the
incident one ; it looks as if the beam were broken at the sur-
face. This is the fact of refraction; the law that enables
us to predict exactly how much it will be broken was not
yet known at the time of which I speak. In this experi-
ment you have allowed the light to strike the water from
above. By means of a reflecting mirror it is easy to make
it reach the water surface from below. If you do this, you
will again get the phenomena of reflection and refraction;
but as you vary the angle at which the ray strikes the sur-
face, you will come to a region where the refracted ray
disappears. All the light is then reflected. This is the
12
LIGHT
phenomenon of totd reflection, and here again the fact, but
not the law, was known before the seventeenth century.
Before making these experiments, it may be well to look at
Fig. 1, which indicates what is to be expected.
FIG. 1
The line SBS' represents a section of the surface of the
water in the glass tank that stands upon this table. AB
is a beam of light from the lantern, and when this strikes
the water at B, part of it is reflected along BC and part
refracted along BE. The line A'B'C'D' represents the
path of the beam when things are arranged to exhibit the
phenomenon of total reflection. A beam A 'B' from the
lantern is reflected along E'C' by a plane mirror at B 1 '.
When the angle at which it strikes the water surface SS'
is properly chosen, the whole of the light is reflected along
C'D'.
I will now ask Mr. Farwell to show you these experi-
ments, not because they are novel or beautiful, but partly
because they deal with fundamental facts, and partly be-
cause I want to bring home to you the striking fact that
the results of human thinking over the phenomena of light
for thousands of years before the seventeenth century of our
era can all be presented in a single minute. How little
these thinkers really knew ! To those of you who are
familiar with the immense field of modern optics, the omis-
EARLY CONTRIBUTIONS TO OPTICAL THEORY 13
sions will appear enormous. The one that I wish to em-
phasize to-night is the absence of any exact knowledge
and any feasible theory of color. Its absence is the more
striking, as color is an attribute of light that impresses
not only the artist and the man of science, but every
normal human being. The man who unlocked this secret
was he who is everywhere hailed as the greatest of all
physicists, the man whose achievements so changed the
current of men's thoughts as to form the Great Divide, in
the realm of science, between the ancient and the modern
world Isaac Newton. You know that his greatest
achievements were in other fields, yet even in the domain
of optics I must to-night confine myself to a very small por-
tion of what he did, but that portion was epoch-making.
I hold in my hand his little book on "Opticks." Turn
over its pages, and you will be struck by the style. The
writer has evidently been brought up in the strict school
of the geometers, with Euclid for his model. Here is no
collection of obscure musings and hazy speculations, but
clear statements of what is to be proved and the manner
of proving it. After some preliminary definitions, the book
proceeds thus :
"Proposition I. Theorem I. Light which differs in
color differs also in degrees of Refrangibility." Then
follows the proof. "Prop. II. Theor. II. The light of
the Sun consists of Rays differently Refrangible." And
so on. Notice most carefully that he does not tread the
old high a priori road. He is not content, like many a
philosopher before and since, to sit in an obscure study and
think. He also observes. Listen to the first sentence of
his book. "My design in this book is not to explain the
properties of light by hypotheses, but to propose and prove
14 LIGHT
them by reason and experiments." That is the combination
that tells reason and experiment. Neither is of much
use without the other. We have seen where reason alone
landed the greatest thinkers of the ancient world, and
experiment alone would have been equally futile. To
advance science by experiment is no haphazard process,
as some imagine. It is a supreme effort of the mind, re-
quiring imagination and a working hypothesis to make it
effective. Without this the experimenter does not know
what questions to put to Nature. Compare a skilful cross-
examiner in the law courts with a novice. The latter asks
questions at random, in the hope (generally a vain one)
that he may hit on something relevant. The former has
a theory and a consequent method.
The experiments that Newton describes to prove his
various propositions are very numerous. As time is short,
we must to-night select a very few. Those of you who are
really interested will doubtless repeat most of Newton's
experiments for yourselves. I expect that you could buy
the necessary outfit at one of those marvels of New York
a ten-cent shop. The apparatus is certainly wonderfully
simple, consisting usually of little more than a glass prism,
and this fact may suggest the query why, in this wiser age,
such costly machinery is required to produce much less
epoch-making results. The answer is that, by the labors of
men like Newton and their followers, science has advanced so
rapidly and has become so much more exact that instruments
of precision, generally costly, are needed to move forward,
where rougher tools would have availed before. Newton's
first proposition is that " Lights that differ in color differ
also in degrees of refrangibility." The fact of refraction
has already been brought before you. You have seen that
EARLY CONTRIBUTIONS TO OPTICAL THEORY 15
when a ray of light goes from air into water or glass, the
ray is bent. Newton states that the amount of bending
depends on the color of the incident ray. His proof, as
usual, is by experiments. The first one is as follows:
Taking a piece of paper, he draws a straight line
across the middle and paints one half of the paper a
bright red and the other a vivid blue. The paper is laid on a
table before a window and viewed through a prism of glass
held with its edges horizontal. If the wedge-shaped part
of the prism is held upwards, the paper appears to be
lifted upwards; but the two halves are not lifted equally,
the blue being raised much more than the red. He con-
cludes that blue light is more refrangible than red, and by
varying the colors it is easy to extend the observations
so as to convince yourself that color and refrangibility
are intimately related. Mr. Farwell will show you this,
with the modifications required by the facts that he is
working at night, while Newton used sunlight, and his
experiment must be seen by a large audience and not by
a single observer. The second proposition of Newton is
that "The Light of the Sun consists of rays differently
refrangible." The proof by experiment was made by dark-
ening a room and making a small circular hole in the window
shutter, through which the light could stream. This light,
falling on some white paper on the opposite wall, produced
a light circular spot quite free from color. He then inter-
posed a glass prism in the path of the sunlight, and looking
at the paper on the wall, found, instead of a circular color-
less spot, a brilliant display of color what he called a
spectrum no longer round, but about five times longer
than it was broad. The fact that it was not round proved
the falsity of the current rules of "Vulgar Opticks," as he
16 LIGHT
called them. The arrangement of the colors in the spectrum
showed a difference of refrangibility in agreement with his
first proposition; whilst the presence of so many colors
indicated what a highly complex mixture sunlight really is.
Mr. Farwell will repeat the experiment.
This proposition of Newton, which sets out the composite
character of sunlight, is his most important one. If you
really grasp it, you are on the way to understand most of the
phenomena of color. It establishes the paradox that you
produce color by suppressing it. With all possible colors
mixed, you have colorless sunlight; take out one or more
of its elements, and color is the result. Newton, of course,
realized the importance of his proposition, and so he set
himself, even more rigorously than usual, to establish the
principle that he thus enunciates, "The Sun's light is an
heterogeneous mixture of rays, some of which are constantly
more refrangible than others." He changes the conditions
of his experiments in various ways, subjects the sunlight
now to reflection and now to refraction, in some cases from
natural bodies, in others from those artificially constructed
in all cases the results agree in establishing his main
contention. There is no time to describe these different
devices a single variant from that already shown must
suffice. We have seen that a ray of light in water or glass
will as a rule be partially reflected and partially refracted
when it comes to the surface separating the water or glass
from air. However, at a certain angle of incidence, an angle
that is called the critical angle, there will be no refraction,
and the light will be totally reflected. Now Newton saw
that if different colored rays were differently refrangible, the
critical angle would be different for each, and consequently
that if sunlight were composite, the phenomenon of total
EARLY CONTRIBUTIONS TO OPTICAL THEORY 17
reflection would occur at different incidences for the
different constituents. To test this, he took two similar
right-angled prisms of glass and held them together, but
not quite in optical contact, so that their cross-section
formed a square. Under most circumstances the light
from the sun falling perpendicularly on such an arrange-
ment would pass through without change. Owing, however,
to the film of air separating the two prisms, the angle of
incidence at this separating surface might lie, for any color,
within the range of total reflection. Such a color could
not get through the double prism, being totally reflected at
the common boundary of the two prisms. Thus, in the
beam 'that emerged, some of the color would be suppressed,
and the light would no longer be white like sunlight. To
test its exact character, the emergent beam had to be ana-
lyzed, and the simplest instrument for this purpose is a
prism which separates the different constituents by re-
fracting them all differently. Newton therefore placed a
prism behind his double prism, and watched what happened
as the latter was slowly turned round so as to change the
angle of incidence on the air-space between the two right-
angled prisms. He found that just when the film of air
met the rays from the sun at the critical angle for blue, the
blue disappeared from the spectrum produced by his last
prism, and that as the revolution was continued, all the
colors disappeared in succession, as the critical angle for
each was reached. This I shall now ask Mr. Farwell to
show you. The arrangement of the apparatus is indicated
in Fig. 2.
P 1 and P 2 are the right-angled prisms referred to. A
strip of tissue paper keeps them from actual contact, and
they are held together by an elastic band. The light from
18 LIGHT
the electric lantern is focussed so as to fall as a parallel
beam A B on the layer of air between the prisms, and if it
fall at the right angle, the corresponding ray will be totally
reflected along BC, and so will not enter the second prism,
P 2 . L is merely a focussing lens, P 3 is the analyzing prism,
and $!$ a the screen on which the phenomena are observed.
Fia. 2
Thus far I have dealt with only two of Newton's propo-
sitions. Of the many others that he lays down I can
refer to but a few. Proposition V: "Homogeneal light
is refracted regularly without any dilatation, splitting, or
scattering of the rays." We have seen that when a beam
of sunlight traverses a prism, its different constituents are
differently refracted, so that, instead of a narrow, colorless
band, we see a broad one brilliantly colored, and instead
of a white, circular spot representing the sun, we have a long-
drawn-out image with all the colors of the rainbow. The
"explanation" of this phenomenon current in Newton's day
was that the prism had the power of shattering the rays,
an " explanation" typical of medieval science, which was
generally satisfied with a mere name. Newton sounded
the death-knell of this theory by showing that if the light
employed were pure, " homogeneal ' ' was his phrase, or if
OF THt A
UNIVERSITY ]
OF fl
IBUTIONS TO OPTICAL THEORY
it were red, or green, or blue, and not a mixture of different
colors, then there was none of this spreading out of an
image, or dispersion, as we call it, so that the prism could
not be endowed with any mystic power of shattering a ray.
His method of proving this was as follows : He allowed a
ray of sunlight to stream into a darkened room. This he
FIG. 3
intercepted with a prism, and so produced a spectrum with
all the colors on a wooden screen behind the prism. This
screen was pierced with a hole that allowed light to stream
through and fall on a parallel screen behind it. The second
screen also contained a hole, and by turning the prism round,
Newton could sift out light from any part of the spectrum,
and arrange that the light going through the two holes
in the screens should be approximately homogeneous. He
then allowed this homogeneous light to pass through a
prism and make an image on a screen behind it. He
found that there was no appreciable spreading out or
dispersion of the homogeneous beam. Mr. Farwell will
show this to you, and Fig. 3 will serve to give you a picture
of the arrangement of Newton's apparatus.
Another experiment devised to serve the same end, and
one that you can very easily try for yourselves, is thus
20 LIGHT
described by Newton: "In the homogeneal light I placed
flies, and such like minute objects, and viewing them
through a prism, I saw their parts as distinctly defined
as if I had viewed them with the naked eye. The same
objects placed in the sun's unrefracted heterogeneal light,
which was white, I viewed also through a prism, and saw
them most confusedly defined, so that I could not dis-
tinguish their smaller parts from one another."
In the second part of the first book of "Opticks," his
second proposition is as follows: "All homogeneal light has
its own proper color, answering to its degree of refrangi-
bility, and that color cannot be changed by reflection and
refraction." He proved by experiment that " if any part of
red light was refracted, it remained totally of the same red
color as before. No orange, no yellow, no green or blue, no
other new color, was produced by refraction." And as these
colors were not changeable by refraction, so neither were
they by reflection. For all white, gray, red, yellow, green,
blue, or violet bodies, such as paper, ashes, red lead, indigo,
gold, silver, copper, grass, violets, peacocks' feathers and
such like, in red homogeneal light appear totally red, in
blue light totally blue, in green light totally green, and so
of other colors. "From all which," he concludes, "it is
manifest that if the sun's light consisted of but one sort of
rays, there would be but one color in the whole world, nor
would it be possible to produce any new color by reflections
and refractions, and by consequence that the variety of
colors depends upon the composition of light."
Time will not permit me to do more than mention two
other important propositions of this book. Proposition
IV: "Colors may be produced by composition that shall be
like to the colors of homogeneal light as to the appearance
EARLY CONTRIBUTIONS TO OPTICAL THEORY 21
of color, but not as to its immutability. " Proposition V:
" Whiteness and all gray colors between white and black
may be compounded of colors, and the whiteness of the
sun's light is compounded of all the primary colors mixed
in a due proportion."
Having unlocked these secrets of Nature, he applies the
principles thus established to explain the colors made by
prisms, the colors of the rainbow, and the permanent colors
of natural bodies. And he shows generally that "if the
reason of any color whatever be required, we have nothing
else to do than consider how the rays in the sun's light
have, by reflections or refractions, or other causes, been
parted from one another or mixed together."
Unless you know something of modern physics, you will
not realize the full significance of Newton's conclusions,
but I hope you will see that, having regard to all that had
gone before, they were epoch-making. By the aid of so
cheap an instrument as a prism, but with a priceless mind,
Newton revealed the true nature of color. Those of you
who have visited the English University of Cambridge,
have probably been in the Ante-Chapel of Trinity College,
and if you had any knowledge of science, you must have
looked with interest, if not with admiration, on a marble
statue of Newton standing pensively with a prism in his
hand. Long after Newton's day there came as an under-
graduate to the same old university the poet Wordsworth,
and he tells us how, looking from his rooms in a neighboring
college, he could behold
" The antechapel where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind forever
Voyaging through strange seas of Thought, alone."
22 LIGHT
What epoch-making voyages were his ! The one that
we have dwelt upon to-night would have been enough to
make the reputations of a score of men, but as you are
doubtless aware, it is one of the smallest of his achieve-
ments. His contributions to mechanics, celestial and
terrestrial, and his introduction of the greatest engine of
advancement in scientific investigation (the calculus) far
outweigh in most men's minds what he did for optics.
We need not attempt to estimate the relative values of these
various products of his genius. It is enough to recognize
him, as does the whole scientific world, as the greatest man
of science that has yet appeared. The impression that he
makes on the minds of all who have the capacity to under-
stand him is of a being almost superhuman. You feel that
you are in the presence of no ordinary master. All seems so
great, and yet done so simply and without apparent effort.
How came these mighty powers to such a man ? Is genius
hereditary, and was Newton's thus acquired? His fore-
bears were commonplace enough, and there was none of
eminence within the immediate circle of his relatives, so
that he seems a sport of Nature. What natural advantages
did he have ? Was he born rich as the world counts riches,
or with the greater riches of a fine physique ? His father
was a mere yeoman and, at his birth, his mother a poor
widow. He was a sickly infant, not expected to live for a
week. What of his education? He went to an obscure
school at Grantham, where I am sure they knew little of
what are now the most approved methods of pedagogy,
and afterwards to the University of Cambridge, where they
cared less. Nature rarely seems to trouble much about the
education of her favorite children, and after all that you
can say, the wind of genius blows where it listeth.
EARLY CONTRIBUTIONS TO OPTICAL THEORY 23
Finally, what of his character ? It comes as a shock to
find a grave moral weakness in a great man. One thinks
of Bacon and the cutting description of him, doubtless
somewhat exaggerated, as "the greatest, wisest, meanest
of mankind." Fortunately, amongst the leaders of modern
physics, there has been no such unhappy combination.
To speak only of the dead, such men as Faraday, Maxwell,
Helmholtz, Fitzgerald, and Stokes were men whose moral
dignity everywhere commanded respect. And I am glad
to say that this was true of Newton in a preeminent degree.
His was a nature of unusual dignity and calm, absolutely
free from the petty ambitions of lesser minds, and modest
to a degree. As an old man, worshiped by the intellect of
Europe as the greatest of his race, these were his words :
"I know not what the world will think of my labors,
but to myself it seems that I have been but as a child play-
ing on the sea-shore, now finding some pebble rather more
polished, and now some shell rather more agreeably varie-
gated than another, while the immense ocean of truth ex-
tended itself unexplored before me."
Just one word more. How often, when all else about a
man is satisfactory, his mere look disappoints! On the
screen is thrown a portrait of Newton, and in contempla-
tion of that beautiful face perhaps I may appropriately
leave you.
II
COLOR VISION AND COLOR PHOTOGRAPHY
As the arrangement of this course is not entirely hap-
hazard, it is of some importance that at each lecture you
should recall the main results reached in what has gone
before. Apart from the simple laws of reflection and re-
fraction, our chief concern in the last lecture was the
phenomenon of color, and the most important conclusions
were two : first, that there is an intimate relation between
color and ref rangibility ; and second, that sunlight is not
a simple thing, but a compound of numberless constituents.
I would have you remember that all the results were
based on experiments that you actually saw performed.
Of course the facts are one thing, and the language in which
you choose to describe them is another. Science has her
own language, unfortunately a highly technical one in these
latter days. I remember the regret expressed by a distin-
guished scholar of my own university for the good old
days, when men of science could express themselves in a
pleasing Latinity that every scholar could understand.
The change is, for many reasons, to be deplored. I do not
refer merely to the obvious loss that comes from the aban-
donment of a universal language, but rather to the evils
that ensue from the splitting up of scientific language by
repeated specialization, so that a chemist no longer under-
stands a physicist, and neither has anything but the faintest
conception of what a botanist is talking about.
24
COLOR VISION AND COLOR PHOTOGRAPHY 25
For good or evil, a physicist likes to make use of me-
chanical terms, and feels that, when he does so, he knows
his own language and can express himself with precision.
How, then, is he to describe the phenomena of light?
He does it with the aid of terms that naturally suggest
themselves when dealing with the familiar experience of
wave-motion. Waves in some form or another we all know
well, whether in air or water or the solid earth. When I
speak, a wave of sound spreads into the room, and at every
point where my voice is heard there is a to-and-fro motion
of the air, a periodic disturbance, as it is called, that con-
stitutes the essential feature of a wave-motion. At sea
the wind disturbs the water and sets up a to-and-fro mo-
tion that rocks you and the ship in which you lie, gently
or otherwise, in the cradle of the deep. Some great up-
heaval in the earth itself originates a to-and-fro motion
which spreads as an earthquake wave around the globe
with havoc in its trail. In all these cases you have a to-and-
fro motion in a medium the media being air, water,
and the earth. According to modern physics, light is due
to just such a to-and-fro motion a wave, if you prefer the
term in a medium that we call the ether. This ether is an
abstraction; that is, it is conceived of by abstracting or
picking out certain qualities of air and earth and water,
and refusing to abstract some others. Why should we
perform this curious feat? Because it helps us to do
wonders, to coordinate with simplicity and ease countless
optical phenomena that no mind could otherwise grasp
and no memory retain; while, without it, all seems
chaos.
In the to-and-fro disturbance that we call wave-motion
there are two elements of special importance : the magni-
26 LIGHT
tude of the disturbance, amplitude is the technical term,
and the frequency.
Watch a cork floating on the smooth surface of the
Hudson River, and then observe it bobbing up and down
as a wave advances over it. The greatest height it rises
is the amplitude, the number of times it moves upwards
in a second is the frequency. On these two elements,
amplitude and frequency, more than on anything else,
will depend the damage that the wave does if it strikes a
movable object. If the wave be very high, it will have great
capacity for work, useful or destructive ; under such cir-
cumstances, it is said to be of great intensity. But what
it effects will also depend very largely on the frequency.
I shall have to emphasize this so much in the next lecture
that now I need do no more than state the fact.
I have said that, according to modern theories, light is
to be regarded as due to waves in the ether. The effect
of these, as of any other waves, will depend on what they
strike. Light, of course, may shine on a stone, but the
stone will certainly not see light. Hence, if we are to under-
stand the phenomena of light, we must know something of
the mechanism, the eye, that receives the impress of the
ether waves. According to our theory, the waves in the
ether beat upon the eye in much the same way that waves
in the sea dash themselves on a rock-bound coast. The
analogy, however, would be closer and more instructive
if we took the case of waves dashing on something that is
itself movable. Think of the waves striking a ship at
sea ; their effect depends mainly on their height and on their
frequency. So it is with waves of light beating against the
eye. Great height corresponds to great intensity, a brilliant
light; frequency is the clue to color. If the ether waves
COLOR VISION AND COLOR PHOTOGRAPHY 27
strike on a normal eye 450 million million times per second,
then no matter what their intensity, they produce the sensa-
tion of red; if 550 million million times per second, they
produce the sensation of green; if 600 million million times
per second, the sensation of blue. If the eye be abnormal,
the color sensation may be quite different.
At this stage the interesting and important question arises :
Can the sensation of blue (or similarly of any other color)
be produced in any other way than by the regular impact
of ether waves striking the eye, and setting up periodic
disturbances therein, at the rate of 600 million million per
second ? The answer is that it can. Newton knew this,
and stated it in one of his propositions quoted in the last
lecture, and long before Newton's time the artists had learned
it from experience. To paint, it is not necessary to have
every color on your palette, for although it may be con-
venient to have quite a number, you can produce almost
any effect by the proper mixture of a few. By pondering
over these facts, a theory of primary colors was evolved,
a primary color being one that cannot be formed by the
mixture of any other colors. The artists, working with
impure colors, decided that the primary colors were
three red, yellow, and blue ; had they been able to effect
a mixture of pure colors, they would have fixed on red
and green and violet. This important fact is sometimes
enunciated in an algebraic form, what is called a color
equation, and may be thus expressed:
Any color = aR + bG 4- cV,
provided the coefficients a, b, c be properly chosen.
It may interest and amuse you to test this statement
for yourselves. Nothing but the simplest apparatus is
28 LIGHT
required, a common top, a stiff piece of paper, and pig-
ments that give the three colors, red, green, and violet.
Cut out a circular disk from your paper and divide it into
sectors by drawing lines from the center. Paint three
sectors with the three different colors, place the disk on
the top, and spin it. As it spins, you will perceive a definite
color due to the mixture of the three in the proportions
that you have chosen, and by varying those proportions
(i.e. by altering the size of the sectors), you will learn to
produce any color that you may desire.
Before proceeding farther, I wish to impress on you the
fact that I am not now presenting any theory, but merely
stating certain facts of observation. All the colors that
we know can be produced by suitable mixtures of these
three, Red, Green, and Violet. This is the great, though
certainly not the only, fact that any theory of color vision
has to account for. These theories deal with the mechanism
of the eye, and their object is to suggest a mode of working
that will fit in with all the facts. Of various rival theo-
ries, only two are worth considering to-night. The first was
clearly stated by Young, and afterwards developed by
Maxwell and Helmholtz, all men of the first rank as physi-
cists, so that their ideas naturally commend themselves to
men trained in physical science. The other is more modern
in its origin ; it was suggested by Hering, and being couched
in physiological language, finds more favor with the physi-
ologists than with the physicists.
As far as the perception of color is concerned, it is agreed
that the most important part of the eye is that inner wall,
the retina, which is connected with the brain by the optic
nerve. Close to this wall there is arranged a curious layer
of what are known as rods and cones, some three million
COLOR VISION AND COLOR PHOTOGRAPHY
29
of the latter in an average eye. It is suggested that these
rods and cones are the chief part of the mechanism which,
when disturbed by an incoming ether wave, transmits the
sensation of color to the brain. According to the Young-
Helmholtz theory, these little cones can be separated into
three classes, Red, Green and Violet, according to the sensa-
A D yC D
H
FIG. 4
tion that they are capable of transmitting, or more accurately
according to the color to which they are most sensitive.
If, for convenience, we call them the R, G, and V cones,
the V cone is most sensitive to violet, the G to green, and the
R to red. It must be understood, however, that each cone
is more or less sensitive throughout a considerable range of
frequency. Perhaps it will tend to clearness if we repre-
sent the state of affairs on a diagram.
The three curves in the figure show the sensitiveness of the
R, G, and V cones when they are stimulated by waves of differ-
ent frequencies. The frequencies are indicated by distances
measured horizontally across the page and also by the
numbers set out below the line AH. These are the number
of million million vibrations in a single second, so that
395 at A indicates that, corresponding to this point in the
30 LIGHT
diagram, the incoming wave is oscillating to and fro 395
million million times each second.
The distances measured at right angles to the line AH
indicate the corresponding sensitiveness of the three differ-
ent cones, the scale being chosen so that when the three
cones are equally stimulated, a sensation of white is pro-
duced. One very important fact indicated by this diagram
is that the range of frequencies that stimulate the eye
at all is finite. In the figure it extends from B to a, i.e.
from 437 to 775 million million vibrations per second.
There are many means of setting up vibrations having
frequencies outside these limits, but they produce no sen-
sation of light in a normal eye. However, the special
purpose of the diagram is to indicate the relative sensi-
tiveness of the different cones to a stimulus of given fre-
quency. The V cones are sensitive only in the range afi,
that is, for frequencies lying between 775 and 550 million
million, and are most sensitive when the frequency is about
650 million million. The G cones are sensitive from G
to 7, when the frequencies lie between 696 and 450 million
million, and are most affected when the frequency is about
550 million million. Lastly, the R cones are sensitive in
the range H to B, where the frequency varies from 755 to
437 million million, and they are most violently affected
when the incoming wave tosses the ether to and fro about
520 million million times per second. Just one more point
before we dismiss this diagram: the color anywhere in
the spectrum may be regarded as made up of not more than
two sensations, with a dash of white. You will see from
the figure that it is only in the region GyS that more than
two of the cones are stimulated simultaneously. At any
point of this region, such as p, if we draw the line pqrs, the
COLOR VISION AND COLOR PHOTOGRAPHY 3t
parts qr and qs show that the R and G cones are stimulated
so as to give the sensation of red and green, while the part
pq shows that, to this extent, all three, R, G, and V, are
equally stimulated, and this equal stimulation corresponds
to the sensation of white.
So far we have dealt only with the Young-Helmholtz
theory of color vision. The rival theory of Hering is
based on the observation that in most of the changes that
take place in living subjects, two main phases present them-
selves. In the first, we have a constructive phase, when an
organism appears to be built up out of lower forms, while
in the second a destructive process sets in that decomposes
the organism into lower elements. Hering supposes that
there exists in the retina a visual substance that has three
different constituents. The first we may call the Red-
green, the second the Yellow-blue, and the third the White-
black constituent. When an ether wave falls on the Red-
green substance, it may not affect it at all ; but if it has the
right frequency, it may set in motion the constructive ma-
chinery, and so give the sensation green; or, on the
other hand, it may start the destructive process, and red will
be seen. (Some find support for this theory from their ex-
perience that red is a tiring color to look at long, while
green is not.) The same sort of thing may happen to the
other constituents; for example, to the Yellow-blue one.
A certain frequency may set up the process of destruction,
and we have yellow ; whereas a differently timed stimulus
induces construction, and a sensation of blue is the result.
We shall not have time this evening to enter into a com-
parison of the merits and demerits of these rival theories.
They must be tested, of course, by their correspondence
with the facts of experience. As far as the few facts hitherto
32 LIGHT
marshalled are concerned, either theory would do, as in fact
would almost any other that suggested a mechanism sensitive
to three or four different kinds of impressions. No such
theory explains anything as far as color is concerned.
The facts as to color are known; the object of the theory
is to go from the known facts to the unknown mechanism
of the eye that perceives. But although we have no time
to discuss these theories further, we may perhaps just in-
dicate the direction in which we must go if a decision as to
their relative merits is to be reached. We must, of course,
look at all the facts, but we should pay special attention
to those that are likely to tell us most about the mechanism
of the eye. You will have observed that it is generally
when a machine goes wrong that you begin really to under-
stand how it works or should work. When all is running
smoothly, you sit comfortably in your automobile and
care little how it works. There is nothing to think about
except, perhaps, to decide by the mere turn of a handle
whether a humble pedestrian is to be your victim or not.
Let, however, something go wrong that brings you to your
proper position under the machine ; then you begin to really
know its mechanism. So it is with most machines ; the study
of their defects and shortcomings is the surest road to a
mastery of their working. Now the eye is not a perfect
machine, and one of its defects, and by no means an un-
common one, produces color blindness. Some see no red,
others no green, and a few no violet, whilst now and then
a person is found who sees neither red nos violet. It is
by the careful study of such abnormalities that we may
best hope to test the merits and defects of any theory
of color vision.
And now, as time is short, I must pass somewhat abruptly
COLOR VISION AND COLOR PHOTOGRAPHY 33
to consider that other subject announced for discussion
at this lecture the subject of color photography. You
will see at a glance that the two subjects of color vision
and photography are not quite strangers to each other. It
is obvious that the methods of giving to the eye the impres-
sion of the colors of a landscape must depend in some
way, intimate or remote, on the mechanism of vision. At
the same time it soon appears that we can progress with
color photography without coming to a complete under-
standing as to the true theory of color vision. Whether
we accept the Young-Helmholtz theory, or lean towards
the rival one of Hering, or prefer some modification of
either, will not much affect our grasp of the principles of
color photography or our skill in its art. To understand
these principles, the one thing needful is the full realization
of the fact, already emphasized as crucial, that any color
can be produced by a proper combination of a finite number
of colors, for example, by a mixture of pure red and green
and violet.
It is sometimes thought that color photography is a
thing of yesterday ; in reality it has occupied men's minds
seriously for about seventy years. To trace the develop-
ment throughout that period and to indicate the means
adopted to overcome the countless difficulties that have
arisen, would be a fascinating study of ingenuity and pa-
tience. For this, however, we have no time this evening,
but must hasten to a brief description of a few of the more
recent methods. The problem has been attacked in two
totally distinct ways, which it is usual to distinguish by the
adjectives direct and indirect. The aim of the direct method
is to prepare a surface that is sensitive to light and that is
so affected by the different colors that it reflects blue if it
34 LIGHT
has been touched by blue, red if it has been touched by red,
and so for all the other colors. By far the most important
step in this direction was taken in 1891 by Lippmann,
although since then his process has been much improved
by others. It would be impossible to explain the process
intelligibly without some reference to the Principle of
Interference, an optical principle of great importance that
must be dealt with in a later lecture. Perhaps, then, it
will be advisable to postpone any further reference to this
method until. the principle of interference has been dis-
cussed. I may say here, however, that up to the present
no direct process has been so successful as the indirect, and
that in this contest, as in others, it has been found that a
flank movement is more effective than a frontal attack.
To those who know in any measure the immense debt
that modern science, and particularly the science of light,
owes to Maxwell, it is interesting to recall the fact that it
was he that found the clue to the indirect method that in
later days has proved so effective. As long ago as 1855,
in a paper contributed to the Royal Society of Edinburgh,
he wrote as follows: "Let it be required to ascertain the
color of a landscape by means of impressions taken on a
preparation equally sensitive to rays of every color. Let
a plate of red glass be placed before the camera, and an
impression taken. The positive of this will be transparent
wherever the red light has been abundant in the landscape,
and opaque where it has been wanting. Let it now be put
in a magic lantern, along with the red glass, and a red pic-
ture will be thrown on the screen. Let this operation be
repeated with a green and a violet glass, and by means of
three magic lanterns let the three images be superposed on
the screen. The color of any point on the screen will
COLOR VISION AND COLOR PHOTOGRAPHY 35
depend on that of the corresponding point of the landscape,
and by properly adjusting the intensities of the lights,
etc., a complete copy of the landscape, as far as visible color
is concerned, will be thrown on the screen." Here you
have a clear indication of the path that will lead to the
desired summit; but it is one thing to point out the way
(a very useful thing, of course) and quite another to actually
do the climbing. Difficulties of all sorts, some expected,
others unlooked-for, may be encountered. Let us see
something of the difficulties that have arisen in trying to
follow Maxwell's directions.
Before attempting this, it may be well to recall to your
minds the process of ordinary photography, now so familiar
to everybody, and to describe it in the language of the
modern theory of light. A photographic film or plate is
coated with a substance, which, like every ordinary piece of
matter is, according to the generally accepted theory, made
of molecules each molecule being a group of smaller
parts, the atoms. When a wave of light beats upon such
a plate, it shakes up the molecules more or less violently,
and tends to shatter them to pieces. It does not destroy
them; but, if its action be forceful enough, it so disturbs
the atoms as to alter their relative positions and thus to
constitute new groups or molecules. The new molecules
have different chemical properties from the old, and the
change is usually described by saying that a chemical action
has taken place, or that light may affect things chemically.
Whether any such action takes place depends chiefly on
two things : the intensity and the frequency of the wave of
light. A difficulty sometimes arises in the minds of thought-
ful amateurs when they hear or read such statements
as these. They emphasize the shortness of the exposure
36 LIGHT
required to affect a photographic plate, and ask how a little
wave of light can do so much in one-tenth or one-hundredth
of a second. To understand this, you must bear in mind
the enormously high frequencies of a wave of light. The
frequency depends upon the color, but we have seen that in
round numbers and within the visible spectrum it lies between
400 and 800 million million. Imagine that you are watching
a log floating in the sea, and that it strikes against a pier as
it rises and falls with the waves, say once in six seconds
a not unusual state of affairs. What length of time would
correspond to the exposure of a photographic plate to violet
light for one-tenth of a second ? It is a simple question of
arithmetic.
800 x 1Q12 vibrations = 8 x 10 13 x 6 seconds
o v ini3 v a
= OX1U xo years = 2 - 1 X 10 8 years,
60 x 60 x 24 x 365 J
or more than two million years. The log might do something
to the pier in that time, and so it is not altogether surprising
that, in an exactly corresponding time, the light does some-
thing to the photographic plate.
Let us suppose, then, that light from the various points of
a human face beat upon a photographic plate for one-tenth of
a second. The light from different parts will have different
intensities, as there will be gradations of light and shade.
The more intense light will batter the molecules more
violently than the feebler light, and so will produce greater
chemical action, which will show itself by greater blackness.
Thus the lighter the object the blacker will be its image
on the plate. In this way is produced the familiar negative,
the gradations of light and darkness in the face correspond-
ing exactly to those of darkness and light in the negative,
COLOR VISION AND COLOR PHOTOGRAPHY 37
and it is by the gradation of light and shade that the whole
picture is presented to the eye. If now we place this nega-
tive in front of a paper that is sensitive to light, and allow
the light to stream through the negative on to the paper,
you realize at once that the blacker parts of the negative
will let through less light than the lighter parts, and thus
that the parts of the paper underneath very dark portions
of the negative will scarcely be affected at all, while those
below bright portions will be battered and blackened. In
this manner is produced a positive, and the gradations of
light and shade in this will correspond to those in the
original object, and thus present a more or less perfect like-
ness. Of course some means must be employed to fix the
negative and the positive, so that they will not be sensitive
to light after exposure. It would be out of place to discuss
such problems here ; I am merely recalling to you the main
features of what I hope is familiar ground. Now if you
have had any experience, you will realize that there are
many places where you may go wrong and that to produce
a first-class photograph you must know with precision
many things; e.g. how long to expose your negative,
under what conditions and for what time to develop it,
how best to fix it, and so with the positive. It is sometimes
said that in producing a photograph there are only two
operations, making the negative and the positive, but of
course each of these is complex, and if you go wrong in
any one of at least half a dozen different operations, you
spoil the photograph. With color photography, as prac-
tised until very recently, the difficulty is just this, that there
are so many operations requiring precision and skill, and
consequently so many possibilities of marring the final
result.
38 LIGHT
The fundamental idea of most processes in color pho-
tography is to obtain different photographs of the different
colored parts of the object and superpose them. Watch
a chromo-lithographer at work, and you will see him make
a great many pictures. One represents the dark red portion
of the object, another a different shade of red, then there
may be several blues, and so on. When all these are super-
posed, we get a picture more or less like the original. If
the color scheme is at all complex, many separate pictures
must be made before they can be combined, so that if we
applied the same principle to photography we might need
20 or 30 different photographs to unite into a single pic-
ture. Were this the case, the problem of color photography
would be practically hopeless, as each photograph involves
so many processes, each with its pitfalls. Owing, however,
to the cardinal fact already emphasized, that any color
can be made by a suitable mixture of a few, viz. Red and
Green and Violet, the process is greatly simplified. At
most, three separate photographs are needed; hence the
term, three-color photography.
Even with this simplification the process is difficult enough.
Many are the methods that have been suggested, but it
will probably make for clearness if I describe in outline a
single one, and as far as principles are concerned, to under-
stand one is to understand all. It is convenient to sepa-
rate three different steps in the process: (A) the analysis
of the complex colored light into three constituents and
the production of three corresponding negatives; (B) the
making of three positives from these negatives; (C) the
recomposition of the three colored elements so as to com-
pletely represent the original object.
(A) The analysis is done by means of light filters, an
COLOR VISION AND COLOR PHOTOGRAPHY 39
arrangement either of colored liquid or of films of colored
gelatine interposed between the object and the photo-
graphic plate. Thus, if a vessel containing red liquid be
placed before the lens, all but the red rays will be filtered
out, and only the red part of the picture will impress itself
on the plate. We have now such a variety of coloring
materials at our disposal that we can get a filter of almost
any color that we want; but the exact filtering qualities
of any substance are determined by other things than mere
color, and these are things that the unaided eye is not
competent to detect. After many thousands of experi-
ments, an immense amount of knowledge has been garnered
in this field. The light that shines through two liquids
may appear of exactly the same color to the eye, but it
may affect similar photographic plates differently in the
two cases. However, different plates are differently sensi-
tive to the same light, and it was the discovery that plates
coated with different chemicals are differently affected by
the light, that really made color photography possible.
By this time we have learned how to prepare a plate A,
that will be sensitive to light that comes through filter a,
and be little affected by the light from filters 6, c, and d }
while plate B is sensitive to the light that filters through b
and is not much influenced by the others, and so for all the
series.
It must be noted, however, that we need to know not
only that a plate is sensitive, but the character of its sen-
sitiveness. How long are you to expose is an important
question in ordinary photography, and it is peculiarly so
in three-color work, for if you make the reds too deep, or
the greens too faint, you will utterly mar the effect. Hence
you must know with some precision the relative sensitive-
40 LIGHT
ness of the different plates employed in the process. Of
course, having obtained the negatives, they must be devel-
oped and fixed as in ordinary photography.
So much for (A), the analysis of the light and the pro-
duction of the negatives. Now turn to (J5), the making of
the three positives. Here the main point to bear in mind
is that an almost perfect agreement between the three
colored elements is essential. Color is so delicate a
creature that the slightest discord will jar. Hence the sen-
sitive paper used for obtaining the positives requires
unusual care in its production and treatment. The paper
must be as nearly as possible inextensible, and the sensitive
film of uniform thickness. The positives may then be
obtained from the negatives by the ordinary process, and
thus three colorless images are formed, each made up of
reliefs in gelatine. These films are then put into baths
that give them respectively the three colors corresponding
to the original analysis by the light filters. It should be
noted that if, as in the process we are now describing, the
three pictures are not placed side by side and composed
into one by some optical device, but are merely superposed,
and if further, as in this process, pigments are used to give
the colors in the positives, then the light filters must not
be red and green and violet, but rather red and yellow and
blue. The difference arises from the fact, well known to
every student of color, that you get a different effect by
mixing lights and by superposing pigments of the same
hues as the lights. If you mix lights, as in the process of
stippling, you add one thing to another. Red and green
and violet waves each strike upon the eye and produce
a color sensation of definite quality, depending on the
relative intensities of the different lights. If, on the other
COLOR VISION AND COLOR PHOTOGRAPHY 41
hand, you mix pigments, you subtract one thing from another.
Superpose violet on green and this on red. To estimate the
resultant influence on the eye, you have to consider how
much of the red is taken out by the green and how much
more of these two is subtracted in the passage through the
violet. The process is seen to be subtractive, and you would
expect the result to be different from the additive one that
takes place when lights are mixed. Experiment shows
clearly that there is a difference, and it was because the
artists used a subtractive and not an additive process that
they concluded, as we have seen, that the primary colors
are red and yellow and blue instead of red and green and
violet.
The last phase (C) of the process has still to be referred
to, the recomposition of the three elements of the final
picture. This is done by superposing the three colored
films obtained as already described. The process, how-
ever, is much less simple than it appears at first sight.
When the three films are superposed, some defect in one
or other of the monochromes is almost sure to be revealed :
the red may be too intense or the violet too faint, or there
may be local faults. It is therefore necessary to super-
pose the films provisionally in order that such defects may
be revealed, and then to have resort to various expedients
for removing the defects. When the best has been accom-
plished, the films must be very carefully placed on top of
one another so as to fit as exactly as possible, and thus
you have a color photograph mounted on glass or on paper,
according as you wish to view it as a transparency or not.
You will have realized, no doubt, that a process such as
that described requires no ordinary care and skill. Many
of the operations can only be satisfactorily performed in
42 LIGHT
a physical laboratory, with the instruments of precision
and the skill in using them that such a laboratory affords.
Under such circumstances, color photography could never
become a popular art. Recently, however, a process due
to the brothers Lumiere of Paris has come into vogue, and
this is so much more easily carried out that it may yet
become quite popular. It is no longer necessary for the
photographer to concern himself with the complex problems
that have just been referred to ; most of these problems
have been solved for him by the maker of the autochrome
plate, as it is called. The user of the plate has little more
to do than expose and develop it, as he would in the pho-
tography with which we are all familiar.
The materials employed are simple. The plate is care-
fully coated with a paste made from potato starch. The
starch is composed of fine grains, and these are separated
into three sets and dyed respectively red and green and
violet for the process, as we shall see, is essentially an
additive one. When mixed together in equal proportions,
the grains form a powder not quite white, but of an olive-
gray tint. This powder is scattered on a glass plate on
which is an adhesive, and the surplus powder removed until
there is left only a single layer of starch grains some four
million to the square inch. This layer is coated with var-
nish, and when covered with a sensitive emulsion of the
right kind, constitutes the autochrome plate.
How does such a contrivance enable us to reproduce the
colors of a landscape? The explanation, after what has
been said already, is simple enough. The starch grains
act as light filters ; we may say approximately that the red
grains filter out all but red, the green all but green, and the
violet all but violet. The red light from any part of the
COLOR VISION AND COLOR PHOTOGRAPHY 43
landscape will filter through the red grains only and reach
the sensitive emulsion behind the starch. If this emulsion
be sensitive to red, it will be acted upon chemically, and
there will be a black spot behind each red grain, through
which the light has come. Suppose, then, that light were
now to shine from behind the emulsion, it would be stopped
by the black spots, and wherever red was present in the
original there would be darkness on the plate. In other
words, the blackened emulsion constitutes a negative of the
red part of the landscape. This negative may be turned
into a positive by processes similar to those employed in
ordinary photography. Wash away the black spots and
leave them colorless, so that there is now a clear space be-
hind the red grains that were originally affected. If now
light shines through from behind, we should have a positive
of the red part of the picture. What is true of the red is
true also of the green and violet, and as we have already
seen that any color can be represented by suitable com-
binations of these three, we are in a position to understand
why the autochrome plate can give us by a single exposure
a perfect picture, however complex be the scheme of color.
One feature of the process may require some comment.
As the three constituent colors, red and green and violet,
are, in this process, necessarily taken together, the emul-
sion must be as nearly as possible equally sensitive to these
three colors. You must know that this is certainly not
the case with the plates you use in ordinary photography.
Such plates are highly sensitive to violet, and scarcely
sensitive at all to red and very little to green. The fact
that they are insensitive to red enables you to carry on the
development in a red light, and so to see clearly what you
are doing. The Lumiere emulsion is sensitive to red and
44 LIGHT
green about equally, but it is much more sensitive to violet.
To overcome this difficulty, at least in part, a yellow screen
is inserted in front of the plate. This cuts out some of the
violet light, and by diminishing its intensity compensates
in a measure for the plate's supersensitiveness to violet.
With this device the plate is rendered approximately pan-
chromatic. As it is sensitive to all colors, you must work
with it only in complete darkness.
In a moment I shall show you a large collection of color
photographs taken by various processes, amongst others
by that just described. I owe them to the courtesy
of a student of Columbia University, who has made
a special study of the subject. Before showing these,
however, a few further remarks with reference to the Lu-
mieres' latest process may not be out of place. (1) As
it stands to-day, the process is useless except for trans-
parencies. The starch paste is not quite transparent, and
absorbs so much light that the picture, when viewed by
reflection, appears almost black. (2) The process will
not give us photographs on paper. (3) The plate that is
exposed is the same that afterwards presents the colored
transparency. Hence a separate exposure is required for
each picture, and there can be no multiplication of the
same photograph, as there is in ordinary photography.
(4) The process does not as yet lend itself to the art of
the retoucher, nor permit any liberties to be taken.
[A large collection of color photographs was here exhibited.]
After seeing such pictures as these, the question naturally
arises, What are the relations of color photography at its
best to art ? Will it aid the art of painting, or is there any
chance that it may seriously rival that art, and possibly
COLOR VISION AND COLOR PHOTOGRAPHY 45
even supersede it? Before attempting any answer, we
must remember that color photography is still in its
infancy, and we must make reasonable allowance for
the improvements that are sure to come in the future.
But what are its outstanding defects to-day? Several are
suggested, but the one most generally emphasized is that
a color photograph is still somewhat hard and metallic,
that it lacks the softness and the charm of a real work of
art. Your view as to this must be largely a matter of taste,
and perhaps it is the wisest course to accept the maxim
de gustibus non est disputandum. Personally, I am inclined
to doubt whether a color photograph is necessarily hard,
although, of course, I admit that it often is so. If, however,
this hardness really exists as a necessity, and not as a mere
accident, it is not easy to see to what it is due. There
can be no doubt that a color photograph is capable of giv-
ing a faithful reproduction of each detail of the original, and
if this be so, why should not the whole be faithful, and
thus as soft and charming as the original? The answer
is that, possibly, the final result may be marred by an
excessive faithfulness in detail. In looking at a landscape,
the eye takes it in as a whole and not by separate parts.
Every color is modified by the presence of all the others
so that the actual appearance of a single leaf is somewhat
different from what it would be were you to isolate the leaf
and examine it alone. Now the photographic plate sees
by isolating, and it presents the exact intensity of each con-
stituent color as it is, unmodified by the presence of the
rest. It may be the failure to allow for the subtle influences
of neighboring colors that produces a sense of harshness
and a consequent lack of charm. But, you object, the eye
looks at the photograph as a whole, and why, then, should
46 LIGHT
not the colors in the photograph react on one another
and produce the same effect as they do in the original?
Perhaps they do for some, but it may not be so for every
eye. We must remember that there is an important dif-
ference between the photograph and its original : the one
is seen as a flat surface, the other in perspective. The
artist may be able to surmount the consequent difficulties
by taking liberties with the details of the color, while the
photographic plate is fettered by being bound too closely
to an absolute truth of detail.
However, even if this be so, and color photographs be
thus doomed eternally to a certain harshness, there can, I
think, be little doubt that some day they will form a seri-
ous rival to all but the highest art. Such art can never be
endangered. It will always hold, unchallenged, the great
field of imaginative painting that appeals so powerfully
to the heart and mind, whilst in the realms of portraiture
and landscape painting there must always be moods and
phases that only a great artist can seize upon and express.
This will be the work of the few, those greatest of our race
who show us aspects of things that otherwise we should
wholly miss, and delight us by expressing clearly what we
only indistinctly feel.
Ill
DISPERSION AND ABSORPTION
IN the first lecture of this course I showed you that it was
possible within the compass of a single minute to summarize
all the knowledge of optical principles gained by man from
the dawn of his intelligence until Newton appeared in the
seventeenth century of our era. One of the few general
facts known in pre-Newtonian days was the fact of Refrac-
tion, the fact, namely, that a beam of light is bent in passing
from one medium to another, as, for example, from air to
water. By considering carefully the amount of bending,
Newton was led, as we have seen, to a clear enunciation
of the relation between refrangibility and color and to a
revelation of the composite character of a beam of sunlight.
The white beam is a coat of many colors, and each color
is bent differently in crossing a refracting surface. Thus,
when a parallel beam of sunlight strikes the water, the
different elements are spread out in the water. This is the
fact of dispersion. It has already been brought before your
notice by experiments. Our object to-night is to scruti-
nize it somewhat more closely and try to gain a clue as to
the reason of the spreading out in other words, we seek
a theory of dispersion. Before setting out in the search, it
is well to look another fact in the face, at first sight a
very different one, although a closer examination reveals
a strong family likeness between the two. This is the
47
48 LIGHT
fact of absorption, and particularly the fact that a substance
may be transparent for one kind of light and opaque for
another it may freely transmit blue and absorb most of
the red. The explanation of this involves a theory of
absorption, and it is with theories of absorption and dis-
persion that we are to deal exclusively in this lecture.
I have already stated that a modern physicist prefers
to speak in the language of mechanics, so that it should
cause no surprise that in dealing with absorption and dis-
persion we take certain mechanical principles as the basis
of our theories. One of these principles is so important
that I must state and illustrate it as fully as time will per-
mit, for unless you grasp it firmly, you cannot hope to under-
stand the theories that will be presented to you; whilst if
you do understand it, at least the main outlines of these
theories should be easily and clearly seen. Suppose that
you have a system of bodies at rest, and that you disturb it
slightly from its position of equilibrium. If that position
be stable, the system will oscillate to and fro like a ship
rocking on the ocean, with a definite frequency that de-
pends entirely on the arrangement of the system and the
forces that act upon it. This frequency, i.e. the number of
oscillations per second, may be called the natural frequency,
as it depends entirely on what happens when the system
is allowed to move naturally, without any interference from
without. Suppose, next, that by outside action you force
an oscillatory motion on the system. The frequency of this
outside action is entirely at your disposal ; you can make
it what you will, and may find it convenient to style it the
forced frequency. Now the mechanical principle that I
wish to emphasize is this: the disturbance produced in a
system depends on the frequency of the oscillation forced
DISPERSION AND ABSORPTION 49
upon it, and is very much greater when there is coincidence,
or nearly coincidence, between the forced and the natural fre-
quencies than when this is not the case. Perhaps the most
familiar illustration presents itself in the problem of giving
a child a swing. You can scarcely have failed to observe
that the magnitude of the swing depends very largely on
how your pushes are timed.
If you push at random, you
will sometimes help the swing
and sometimes retard it, and
the work that you do will be
much the most effective if you
always push when the swing is
in the same phase of its to-and-
fro motion, i.e. if you arrange
that the forced frequency
should coincide with the natu-
ral one. Here is a simple de-
vice that will illustrate the
same principle. It consists, as
you see (Fig. 5), of two pen-
dulums, A and B, fastened by FlG ' 5
strings to a not very rigid support, CD. By swinging
either pendulum, you see that its natural frequency
depends upon its length, that the frequencies of the two
pendulums are the same when the lengths are the same,
and that by varying the lengths you can get almost any
frequency that you may want. Now suppose I set A in
motion and swing it at right angles to the plane A CD,
so that it does not get entangled with the other pendulum.
As A moves to and fro, the pull in the string AC will set up
a vibration in the support CD, and this will be communi-
50 LIGHT
cated to the string BD. When the lengths AC and BD
are very different, you will observe that, in spite of the
vibration communicated to BD, the pendulum B remains
practically at rest ; you see no signs of its motion. When,
however, the lengths AC and BD are nearly equal, B be-
gins to show signs of unrest, and it moves very perceptibly
when the strings are equally long, i.e. when the forced and
the natural frequencies coincide.
As another simple illustration of the same important
principle, consider the motion of water in a bucket. If
it be at rest to begin with, and you slightly disturb it, the
water will oscillate backwards and forwards with a natural
frequency that is easily observed. Now take the bucket
by the handle and carry it off. As you step along regularly,
each time that your foot goes down you will give a slight
jerk to the handle of the bucket, and this will be communi-
cated to the water. Thus forced oscillations will be set
up, their frequency depending on the rate at which you walk.
If, by design or by accident, you time your treads so that
their frequency coincides with the natural frequency of the
water, very much greater disturbance will take place than
would otherwise be the case, and if the bucket be nearly
full, a good deal of the water will flop over the edges.
Other illustrations might be drawn from various fields,
for the principle is wonderfully far-reaching, and enters
into the explanation of countless phenomena, from the
trivial one just mentioned to some of the most stupendous
and awe-inspiring catastrophes that human history records
or the study of celestial mechanics reveals. To-night we
have no time to enter further into the matter, except to
bring before you one more simple experiment as a final
illustration of the same underlying principle. A (Fig. 6)
DISPERSION AND ABSORPTION
51
is an organ-pipe, the end of which is closed by a thin film,
formed by dipping the pipe into a soapy solution. If the
air within the pipe be disturbed in any way, it will oscillate
to and fro with a natural frequency that depends on the
form and dimensions of the pipe. These oscillations will
B
FIG. 6
cause the film to pulsate, and the character of these pulsa-
tions is revealed by allowing a beam of light to be reflected
from the film on to a screen at S. By watching the move-
ment on the screen, you can judge whether there is much
throbbing of the film or not. Now let us force oscillations
on pipe A by means of vibrations in another organ-pipe
B, and vary the frequency of these vibrations by altering
the length of this second pipe. You will observe that the
disturbance revealed by looking at the screen is enormously
more violent when the forced and natural frequencies
coincide than when they are widely different. Here, as
before, you see that for many purposes the magnitude of a
shake is less important than its frequency, and that a small
52
LIGHT
A t
frequency
FIG. 7
vibration rightly timed may set up far more disturbance
than a large one with a different frequency.
Bearing this principle in mind, imagine that you are
watching a fleet of ships upon the ocean, and that, to begin
with, all is calm. Then suppose that each is slightly dis-
turbed, as by the shifting of machinery or cargo. Each
ship will rock to and fro, with a natural frequency depend-
ing on the shape of the
vessel and the arrange-
ment of its cargo. If all
the ships be similar, they
will all rock with the
same frequency. Now
D % imagine a series of waves
to come along and strike
upon these moving ships.
They will continue to rock, and if the frequency of the in-
coming waves be very different from the natural frequency of
the ships, there will be little change in the motion. Suppose,
however, the frequency of the waves is gradually changed.
As it approaches that of the natural frequency of the ships,
the motion will be much more violent, and will be most
marked when the natural and forced frequencies are the
same. Once this stage is passed, and the forced frequency
begins to differ largely from the natural one, the oscillations
will die down, and in time you will return to calmness and
to comfort. If you care to represent things graphically,
you may indicate the forced frequencies by distances
measured horizontally along the line ABODE of Fig. 7,
and the corresponding disturbances by lines drawn ver-
tically. You then get a figure such as is here presented,
where C corresponds to the natural frequency of the
DISPERSION AND ABSORPTION 53
ship's oscillation; and most of the disturbance is confined
to a somewhat narrow range, BD, in the neighborhood of C.
In the region where the disturbance is considerable, the
ships are rocking violently, and are therefore capable of
doing a large amount of work. In technical language,
they have great energy. This energy must come from
somewhere, and its only possible source is the motion of
the sea waves. Under these circumstances, a great deal
of energy must be absorbed from the water waves, so that
in the region beyond the ships you would observe a com-
parative calm. You have only to apply the same principles
to the waves in the ether that give us the sensation of light
to understand how a substance may absorb most of the
light of one color, and be practically transparent to every
other kind of light. In this case the ships are replaced
by the atoms of matter, or rather, according to modern
views, each atom is a whole fleet of ships. The old atom of
chemistry is now replaced by a group of electrons, which
move about like the stars in a cluster, and could they be
seen, might appear as the Pleiades ''glittering like a swarm
of fireflies tangled in a silvery braid." If the ether waves
have a frequency nearly coincident with the natural fre-
quency of the electrons, they do so much work in disturbing
these electrons that their energy is almost all spent. They
have not enough left to stimulate the optic nerve, and we
see no light. On the screen is thrown the familiar spectrum
caused by sending a beam of white light through a trans-
parent prism of glass. There is no appreciable absorption
for any color ; the spectrum is continuous, with every color
of the rainbow represented. Now let the same light pass
also through this chemical solution, and observe the change
in the spectrum. A portion of the yellow is cut out and
54 LIGHT
replaced by absolute blackness, so that this kind of light is
absorbed by the solution, while all other kinds come through
just as before. Are we not justified in concluding, in view
of all that has gone before, that the natural frequency of
the electrons in the solution is the same as the frequency
in the ether waves corresponding to this portion of the
yellow ?
In the case that we have considered, where there is a
single moving object, such as a ship, there may be only
one natural frequency, but with a more complex mechan-
ism the natural frequencies may be many. If you regard
the principal planets of the solar system as forming a single
mechanism, each of the eight constituents goes through
regular periodic movements with a definite frequency.
Thus, in their motion round the Sun, they observe a strict
and invariable law, Mercury taking 88 days (in round num-
bers), Venus 225, the Earth 365, and so on to Neptune,
with the lengthy period of 60,127 days. Imagine, then, a
mighty system of waves running across the solar system.
If the frequency were such that the waves oscillated once in
88 days, most of the energy of the waves would be absorbed
in dashing the planet Mercury to and fro, while the other
planets would be comparatively little affected. If, how-
ever, the waves oscillated once in a year, our earth would
be responsible for the absorption of energy, and similarly
for other frequencies. Suppose, now, that the impinging
waves had all possible frequencies. They would all pass
through the solar system practically unmodified, except
the eight with frequencies corresponding to the periodic
movements of the planets. These eight would have their
energy absorbed in disturbing the planets, and they would
be relatively small and insignificant in the region of space
DISPERSION AND ABSORPTION 55
beyond the solar system. In exactly the same way will
light be absorbed by a substance, those colors being
cut out that correspond to frequencies identical with the
various natural frequencies of the complex group of elec-
trons composing the substance. In Fig. 8 you will see how
many dark bands there are in the spectra of some simple
substances, and if you realize that each of those dark lines
Nitrous fumes
Illlll
II
Vapour of Iodine
FIG. 8
indicates a different natural frequency, you will understand,
in a measure, how complex must be the motions going on
within the atom, and how formidable the task of the man
of science who tries to master its mechanism.
Here you get a glimpse into a field of great interest and
promise. The principle of fundamental importance is
that the position of the absorption bands in the spectrum
of any substance gives us information, and very definite
information, as to the frequencies of the vibrations that go
on within its atoms. If we knew the nature of those atoms,
we could, were our mathematics sufficiently developed,
calculate the frequencies of the vibrations. At present
we are trying to reverse the process, and seek tne unknown
from the known, and the time may yet come when we can
speak confidently of the minutest movements within the
56 LIGHT
atom. That time is certainly not yet, and probably for
long we must devote ourselves with patient labor to ac-
cumulating facts that bear upon the problem. Much has
already been done, and the positions of the absorption bands
for many substances have been accurately observed over a
wide range of frequencies. Let me call your attention to a
few of the suggestive results that have thus been reached.
(1) The lines in the spectrum are not arranged at random,
but accorcfeig to laws which are more or less simple with
different elements. The simplest case is that in which the
relation between the frequencies corresponds exactly to the
relation between a fundamental note and its harmonics.
Strike the middle C of a piano, and you set up a to-and-fro
motion in the air, there being 256 vibrations in a second,
so that the frequency is 256. If you strike exactly an octave
higher, you double the frequency. It is found that the
lines in the spectra of some substances are arranged so that
the frequency corresponding to one line is exactly double
that of the other. If, however, you take all the lines into
consideration, the relation between them is much more
complex. One of the best-known examples is afforded
by the spectrum of hydrogen. In 1885 Balmer showed
that the frequencies corresponding to the different lines were
all given by the formula, frequency = a (1 4/n 2 ), where a
is a constant and n any integer greater than 2. At this
time only 9 lines had been observed, but as the number
was extended beyond 30, it was found that Balmer's law
still fitted the observations admirably. Thus, hydrogen
seemed to present a unique example of simplicity, all the
lines in its spectrum being connected by the same simple
law. However, the later speculations of other physicists,
particularly Rydberg, Kayser, and Runge, made it seem
DISPERSION AND ABSORPTION 57
probable that other lines existed, although they had not yet
been observed. This was confirmed in a striking way by
Pickering in 1896, while examining the spectrum of a star
that shows the hydrogen lines strongly. He found a new
series of lines related to the old ones in just the way that had
been anticipated.
(2) It is found that with several elements the lines in
the spectrum are arranged in groups of twos or threes,
forming doublets or triplets, as they are called, and that
the difference in the frequencies of the two members of a
doublet is the same for each group, with a similar law for
triplets.
(3) Where the lines are not arranged in doublets or
triplets, they often appear in two different series. There
is a series of sharp lines connected by one law, and another
series of diffuse lines connected by a different law.
(4) The regularity in the spectra of some elements, e.g.
tin, lead, arsenic, antimony, bismuth, and platinum, con-
sists in the recurrence of certain constant differences of fre-
quency between the lines.
(5) In what are known as band spectra, when the fluted
spectrum is resolved by higher dispersion into groups of
fine lines, it is often found that the frequencies obey a very
simple law. They form an arithmetical series, i.e. each fre-
quency differs from its predecessor by a constant difference.
On careful examination, it appears that the spectrum is made
up by repetitions of similar groups of lines, and it seems
probable that the number and distribution of the lines in
each group depend on the number and distribution of the
atoms, or of the electrons that compose these atoms.
(6) Lastly, various relations have been suggested between
the atomic weights of different substances and their natural
58 -"'-. LIGHT
frequencies. Kayser and Runge have concluded that in the
case of elements of the same chemical family which show
a series of doublets in their spectra, the constant difference
of frequencies between the two members of the doublets
is very nearly proportional to the squares of the atomic
weights. Marshall Watts has shown that with the class of
elements that contains mercury, cadmium, and zinc, the
ratio of the difference between the frequencies of certain
lines of one element to the difference between the frequen-
cies of the corresponding lines of the other element is the
same as the ratio of the squares of their atomic weights.
Morse, of Columbia University, has found that if you take a
series of carbonates with different chemical bases carbon-
ates of magnesium, of calcium, of iron, of zinc, and so on, you
discover a very simple relation between the atomic weight of
the base and the frequency that is determined from the
position of the absorption band, and that there is a similar
law for the nitrates and the sulphates of the different bases.
These various facts that have been marshalled are, as I
have said, highly suggestive, and they will inevitably be
made the basis of many future speculations as to the nature
of the atom. One thing at least they show us very clearly,
namely, that in the little kingdom of an atom, just as in
the mighty realm of the Sun, law is supreme. In many
cases we have found the law, but there is much yet to be
done to fit it into our other knowledge. At present we have
only glimpses as to how this may be accomplished ; but we
see enough to give us hope that somewhere in the future the
foundations of a new chemistry will be firmly laid. Then
we shall know the movements of the atoms and the laws
that govern them as definitely as now we know the orbits of
the planets and the forces that confine them there.
DISPERSION AND ABSORPTION 59
Having delayed so long over absorption, I must hurry
on to deal with dispersion, the theory of which I undertook
to discuss at the beginning of this lecture. One aspect of
that theory is simple enough : it is the aspect usually pre-
sented exclusively in elementary text-books on light.
They tell us that dispersion is due to the fact that where
there is no matter present, waves of light all move with the
same speed, whatever be their frequency (or color), but
that they move with different speeds in any material such
as glass or water. This is true and very important, but it
is no explanation. It does not go deep enough, for we want
to know why these facts should be as stated. Before
entering upon this, however, it will be well to see clearly
that the fact of different speeds for different frequencies
necessarily leads to dispersion. A simple analogy may help
you to understand the phenomena. Suppose that you
watch a column of soldiers marching steadily at the rate of 4
miles an hour, and that when they cross a certain line they
come upon ground that is so much rougher that they ad-
vance at the rate of only 3 miles an hour. What would be
the effect of this on an observer looking from a distance,
and fixing his attention on the front of the column? Let
ST in Fig. 9 represent the line that divides the smooth
from the rough ground, and E, F, G, H, and similar letters,
the positions of different soldiers at different times. If the
front of the column was at E Q F Q G Q H Q at any time, then
an hour later it would be at EFGH, where E Q E is 4
miles. An hour later than this H would be at HI (4
miles from H), but E would have covered only 3 miles
on the rougher ground, and would be at E l where EE l is
3 miles. F and G would be at F lt and G ? 1 , as shown in
the figure, having walked partly over smooth and partly
60
LIGHT
over rough ground. The front of the column would be rep-
resented by the line E 1} F l} G ly H v This is not parallel to
EFGH, so that the column would have changed its front,
and instead of moving in the direction EE 1} it would appear
to be making along the direction ER, where ER is at right
angles to the front. If then you were describing the direc-
tion in which the column was tending, you might say that
this direction was broken or refracted in crossing the line
ST. It is not difficult, but I have no time for this now, to
show that a similar result would be looked for with a ray
of light on the theory of wave-motion. I trust that you can
supply this step in the argument, and convince yourselves
of the fact that refraction is at once accounted for by a
change of velocity on crossing from one medium into the
other. The step to dispersion is immediate and obvious.
The amount that the column changes its front depends, as
DISPERSION AND ABSORPTION 61
you see, on the speed with which the men walk on crossing
the boundary line ST. If they meet with even rougher
ground than before, so that they move more slowly, the
change of front will be greater than before. Thus, suppose
that the column is composed of two sets of men, one in
blue and the other in red uniforms, and that until they reach
the rough ground they advance together at the same rate.
(This corresponds to the fact that in free space, where there
is no matter, waves of light of all colors have the same
velocity.) After crossing the line ST, let the red men walk
at 3 and the blue at 2 miles per hour. The latter will
separate from the former, and will form a new column,
whose front is in the direction E 2 F% <7 2 H v in the figure, and
which therefore appears to be moving in the direction EB.
The columns will disperse in different directions, EH and
EB, and if you apply similar reasoning to the case of
waves of light, you will understand how dispersion is
accounted for, provided only you can see that waves of
different frequencies may have different speeds in the same
medium.
This dependence of the speed of a wave on its frequency,
on which we have just seen that any explanation of dis-
persion must be based, is no simple or obvious thing. It
has occupied the minds of leading physicists for nearly
a century and, in spite of all their labors, I am not sure
that even now we thoroughly understand it. There is an
initial difficulty that is very formidable. Think of a beam
of light passing through water or a piece of glass. The
water and the glass look thoroughly homogeneous, and
even if you examine them with the most powerful mi-
croscope, you will get no direct evidence that one of the
smallest parts differs in any essential way from another.
62 LIGHT
Now if waves of any kind are propagated in a homogeneous
medium, it is difficult, if not quite impossible, to see how
their speed can depend on their frequencies. However, we
have to face the fact of dispersion, and this, if nothing else,
would drive us to consider the possibility of matter, such
as glass or water, being other than homogeneous. In its
ultimate analysis we shall take it to be coarse-grained, and
see how this will help us. The grains, or atoms, we shall
regard as obstacles in the path of the waves affecting their
progress. Some insight into the matter might be obtained
by thinking of a column of soldiers marching through a for-
est ; their rate of progress would obviously depend in some
measure upon the distance between the trees. A far
more instructive study for our purposes would be to observe
carefully the rate at which waves were propagated in water
in which floats are placed at regular intervals. If you do
this, you will find that the speed of the wave depends upon
its frequency, and that if you keep the floats always at
the same distance, but modify the frequency, you alter
the speed of the wave. This is just what you want for dis-
persion, and you may naturally think that you have found
the key that unlocks the secret. So, no doubt, thought
Cauchy when, early last century, he took up the problem
and hit on this idea. But the way of the physicist is hard,
and his lot is made peculiarly difficult by the duty that he
has imposed upon himself of living up to a very high stan-
dard. He is not content with mere descriptive theories,
he strives to state them in the strict language of mathe-
matics and to obtain therefrom a formula. From such a
formula definite numerical results can be calculated and a
close and accurate comparison made between theory and
observation. The object of a dispersion theory is to build
DISPERSION AND ABSORPTION 63
up from some rational basis a formula that will enable us
to calculate the velocity of light for waves of different fre-
quencies, and to obtain results that agree as closely as pos-
sible with what is derived from experiment. Instead of
calculating the velocity directly, it is convenient for some
purposes to estimate the ratio of the velocity of light-waves
in free space to that of waves of the same frequency in the
matter under consideration, e.g. glass. This ratio is called
the refractive index of the matter, and we shall denote it
by the symbol n. As light has the same velocity for all
frequencies in free space, and this velocity is known,
the velocity corresponding to any frequency in a material
such as glass is at once obtained by dividing the known
velocity in free space by the refractive index of the glass.
The refractive index (n) will depend on the frequency (/),
and any dispersion formula gives the relation that exists
between n and / on the basis of the theory considered.
Cauchy 's theory led him to a dispersion formula of this
kind :
where K, a, b, . . . are constants in any given material, but
change if we pass from one material to another, as from
glass to water. On putting this formula to the test of
comparison with experimental results, Cauchy and his
immediate followers found that it stood the test well, so
that the problem of dispersion seemed to be solved. And
yet to-day the position occupied by Cauchy has been
wholly abandoned, and you may well ask why. I have
time to touch on only three reasons to account for the fact
that it has been necessary to look for some other theory of
dispersion than the one that we are now discussing.
64 LIGHT
(1) In the first place, it must be noted that the obser-
vations were confined to a somewhat narrow range of fre-
quencies. They were all in the neighborhood of the vis-
ible spectrum, the frequencies varying in round numbers
from 400 to 800 million million. Such frequencies are
specially interesting, from the fact that they alone produce
in the human eye the sensation of light. But waves of
other frequencies are easily set up and their influence
detected. If their frequencies be high, they are specially
active in affecting a photographic plate, while if low, they
show themselves in the form of radiant heat. There is, of
course, no reason why waves of such frequencies should
be subject to any different law from that which holds
for frequencies that give the sensation of light. Thanks
to the patience and the ingenuity of modern physicists, we
have by this time immensely extended the range of ob-
servation of refractive indices. In a few moments I
shall refer you to such indices accurately observed
for frequencies varying from about 13 million million to
over 600 million million. Over such a wide range Cauchy's
formula proves to be extremely ill adapted to represent
the facts.
(2) The second objection to Cauchy's formula arises
from a careful examination of his fundamental idea. That
idea, as already stated, is that the velocity of a wave must
be affected by the relation between its frequency and the
distance between neighboring molecules. Assuming this,
and noting the values of the constants in Cauchy's formula
that are required to make it fit as well as possible with the
observed facts, we can estimate approximately the distance
between consecutive molecules in any substance. Now
there are other and much surer ways of estimating these
DISPERSION AND ABSORPTION 65
distances, and it is found that Cauchy's formula separates
the molecules far too widely. In a given length it would
place only one where we have good reason for supposing
that there are about thirty molecules.
(3) Thirdly, Cauchy's theory gives us no clue to the con-
nection between absorption and dispersion, and these, from
many points of view, we now see to be intimately related
phenomena.
I have not time to do more than indicate the character
of more modern theories of dispersion that endeavor to
avoid these difficulties. The fundamental idea with
them all is that the molecules, or, according to the more
recent theories, the atoms, are complex structures, the parts
of which can vibrate to and fro with definite natural fre-
quencies. Thus in the group of electrons constituting an
atom, each member may, under normal circumstances,
move steadily in an orbit, like a planet round the Sun.
When a wave strikes such a system, its speed will be affected
just as in Cauchy's theory, mainly by two things: first,
the displacement that the wave produces in the moving
member; and second, the magnitude of the force that
tends to restore that member to its orginial position.
When dealing with absorption, we had reason to emphasize
the fact that the displacement produced by the impinging
wave would depend very largely on the relation between its
frequency and the natural frequency of the moving system.
Well-established dynamical principles lead us easily to a
formula for the displacement corresponding to any given
frequency, and the only matter about which we are in
doubt is the character of the force that tends to restore a
disturbed element to its original orbit. We find that if
the frequency (/) is not very close to any of the natural
66 LIGHT
frequencies (/i/ 2 "0 of the system, then the refractive index
(n) should be given by the formula
,
/"-/a 2
Here a, K, A lf and A 2 are constants for any given material,
the value of a depending on the nature of the intermo-
lecular forces as to which we are, as yet, more or less in
ignorance. The following table will show you how this
formula fits in with the facts as observed in the case of
rock-salt, a substance chosen because we know its refractive
indices over an enormous range of frequencies. You will
observe that throughout the whole range, theory and ob-
servation agree within the limits of experimental error.
It must be understood that the six constants ^4. 1; A 2 ,f v
/ 2 , a, K are determined so as to make the formula fit the facts
for six arbitrarily chosen values of the frequency (/), and
that the formula is tested by noting how close is its agree-
ment with the remaining 60 observations, there being 66
of such observations in all. But there are other collateral
tests. The constants / x and/ 2 , calculated, be it remembered,
from observations of refractive indices alone, denote the
natural frequencies of parts of the molecule. We have
seen, in the discussion on absorption, that these frequencies
determine the position of the absorption bands of the sub-
stance. Now the frequencies corresponding to the absorp-
tion bands can be determined by direct experiment, and
it is found that they agree as closely as could be desired
with the values calculated from the above formula. Again,
if you look at the formula, you will observe that when the
frequency is zero, so that/ = 0, we have n 2 = K. If the fre-
quency is zero, that means that there are no vibrations per
DISPERSION AND ABSORPTION
/
(in million
millions)
n
(theory)
n
(observation)
/
(in million
millions)
n
(theory)
n
(observation)
617
1.5533
1.5533
255
1.5303
1.5303
609
1.5526
1.5526
250
1.5302
1.5301
607
1.5525
1.5525
238
1.5297
1.5297
602
1.5519
1.5519
228
1.5294
1.5294
580
1.5500
1.5500
202
1.5285
1.5285
578
1.5499
1.5499
193
1.5582
1.5281
569
1.5491
1.5491
183
1.5278
1.5278
558
1.5482
1.5482
170
1.5274
1.5274
542
1.5469
1.5469
145
1.5265
1.5265
530
1.5458
1.5458
137
1.5263
1.5262
525
1.5455
1.5455
133
1.5261
1.5261
521
1.5452
1.5452
127
1.5258
1.5258
518
1.5450
1.5450
96
1.5241
1.5240
512
1.5445
1.5445
92
1.5237
1.5237
509
1.5443
1.5443
89
1.5235
1.5235
491
1.5430
1.5430
83
1.5229
1.5229
469
1.5414
1.5414
79
1.5224
1.5224
457
1.5406
1.5406
73
1.5216
1.5216
436
1.5393
1.5393
64
1.5200
1.5197
417
1.5381
1.5381
57
1.5183
1.5180
394
1.5368
1.5368
52
1.5155
1.5159
375
1.5358
1.5358
44
1.5123
1.5121
356
1.5348
1.5348
42
1.5103
1.5102
339
1.5340
1.5340
40
1.5086
1.5085
332
1.5336
1.5336
37
1.5063
1.5064
308
1.5325
1.5325
35
1.5030
1.5030
302
1.5323
1.5323
30
1.4952
1.4951
297
1.5321
1.5321
25
1.4809
1.4805
289
1.5317
1.5317
21
1.4625
1.4627
285
1.5315
1.5315
19
1.4415
1.4410
277
1.5312
1.5312
17
1.4152
1.4148
271
1.5310
1.5310
15
1.3736
1.3735
263
1.5307
1.5306
13
1.3407
1.3403
68 LIGHT
second, and therefore none at all. In the final lecture of
this course we shall deal with some relations between light
and electricity, the connection between which, according
to modern views, is most intimate. Then we shall be in a
better position to understand that when there are no vi-
brations, so that you have a steady electric field, the square
of the refractive index must be identified with what has
long been known as the specific inductive capacity of the
material. This quantity K can be determined by suitable
electrical measurements, and when the value so obtained
is compared with that derived as indicated above from our
formula, there is an excellent agreement between the two
measures.
Just one more point and I have done. I have said that
the formula gives the refractive indices for frequencies (/),
which are not very close to any of the natural frequencies
(/! and / 2 ...)- If / be close to/ x or / 2 , there will be con-
siderable absorption, and the formula must be modified.
Instead of troubling you with symbols, I shall indicate by a
figure the nature of the change that occurs in the neigh-
borhood of an absorption band. Let us represent fre-
quencies (/) by distances measured along the horizontal
line CDF... in Fig. 10, and the corresponding refractive
indices (n) by distances measured at right angles to this
line. The dotted curve in the figure indicates how the re-
fractive index varies with the frequency, when we are not
near one of the natural frequencies. You will observe that
the curve rises steadily to the right, indicating that the re-
fractive index increases with the frequency ; orange is more
refracted than red, and blue more than orange. Next, sup-
pose that we are dealing with a substance that has a natu-
ral frequency at D. Then our theory would lead to a formula
DISPERSION AND ABSORPTION
69
connecting n and /, which is graphically represented by
the continuous line of the figure. You will notice a strik-
ing contrast to the previous case. The refractive index
no longer rises steadily as the frequency increases. As the
FIG. 10
natural frequency is approached, the refractive index rises
abnormally, and it begins to fall and to fall rapidly when
the natural frequency is passed. In the special case that I
have chosen, orange is more refracted than either red or
blue, and blue is even less refracted than red. The order of
the colors in the spectrum is thus quite different from the
ordinary, and it appeared so lawless when first observed,
that the phenomenon was branded with the name anoma-
lous dispersion. We now see that there is nothing lawless
about it, and that the same theory that enables us to ex-
plain ordinary or normal dispersion gives us also the law
(of course a different law) for this apparent anomaly.
IV
SPECTROSCOPY
IN the last lecture we were occupied a good deal with
discussions as to the structure of an atom and a molecule.
We saw that, according to the most recent speculations,
an atom is no longer regarded as a hard, rigid mass, but as
a throbbing, palpitating mechanism, almost a living thing.
Such a mechanism is capable of vibrating in various dif-
ferent modes, each with its natural frequency. In any
given substance in a given physical condition, the num-
ber of the possible modes of vibration and the values of
the corresponding frequencies must be perfectly definite.
Any periodic movement in the atom or the molecule will
tend to set up disturbances in the ether, and these will
be periodic and have the same frequencies as those of the
vibrations that originate them. Whether such vibrations
set up in the ether will produce the sensation of light or
not, will depend on their frequency. In round numbers
this frequency must lie between four hundred and eight
hundred million million per second, as vibrations that are
either slower or faster than this do not affect our sight,
although their influence may easily be detected in other
ways. Let us suppose, for example, that under any given
circumstances the molecule is so constructed that it can
vibrate in two different ways, with frequencies of five hun-
dred and six hundred million million respectively. These
vibrations will set up light of two different colors, and
70
SPECTROSCOPY 71
if the substance be viewed through a circular hole (as
in Newton's experiment referred to on p. 15) and the light
passed through a prism, we shall see two circular colored
patches in different positions, one of them blue and the
other orange. If the diameter of each patch be very
small, it may be possible to distinguish the two patches
easily and clearly; but if the two frequencies be chosen
more closely together, the circular patches will almost
inevitably overlap, and it will be difficult to distinguish
clearly between the two. This overlapping of the different
colors would prove a very serious defect if accurate measure-
ments were aimed at, and, had it not been possible to
remove the defect, the modern science of spectroscopy
would have been impossible. The simplicity of the change
required in Newton's arrangement is a striking example
of the occasional importance of small things for achieve-
ment in science. All that is needed is to replace the circular
hole by a narrow slit parallel to the sharp edge of the prism.
Then, instead of two circular patches of light on the screen,
we have two narrow lines parallel to one another, and unless
the two frequencies be nearly coincident, these lines will
be clearly distinguished and their positions easily deter-
mined with precision and accuracy.
To understand the principles of spectroscopy, you must
bear in mind that different lines in the spectrum indicate
different frequencies, and each frequency corresponds (as
a rule) to a different mode of vibration. Of course much
may be going on within the molecule that does not influence
our sight (as we have seen, the range of sensitiveness of
the eye is limited), and again it may require a stimulus of a
special kind, such as a high temperature, to set any particu-
lar mode of vibration in action. Thus a substance may be
72 LIGHT
vibrating in many modes, with frequencies too high or too
low for us to see, and we may at one time observe lines in
the spectrum of an element which are not visible at all
under different circumstances. The important point for
violet indigo blue green yellow orange
Lithium
Calcium
Strontium
FIG. 11
us at present is that, if we are right in regarding a substance
as vibrating with definite natural frequencies, we should
expect that its spectrum, viewed under proper conditions,
would not be a continuous band of color, but a series of
isolated bright lines, each of a color corresponding to the
frequency. And as a matter of fact this is so, as you will
see from the experiment to be made immediately, or from
Fig. 11, which indicates the position and color of the bright
lines in the emission spectra of various elements. It is
important to observe that these all represent the spectra
of elements that are in the form of gas or vapor. If the
substance is in the solid or liquid state, its spectrum no
longer consists of a series of isolated bright lines, but is
continuous. This difference in the aspect of the spectrum
SPECTROSCOPY 73
of a substance gaseous in one case, liquid or solid in the
other is of fundamental importance in the theory of
spectroscopy, and it may be well to get a glimpse of the
reason for the difference. According to the generally
accepted view as to the nature of a gas, the molecules of
such a substance are in constant motion. Collisions be-
tween neighbors are therefore to be expected, the frequency
of these collisions depending, amongst other things, on the
distance between the neighbors, or on the density of
the population. If the gas be not very much compressed,
the distance between neighboring molecules will be large
enough to allow them "to move fairly freely and to execute
their natural vibrations without being disturbed by con-
stant collisions. Suppose, however, that the gas is com-
pressed enough to liquefy it, or that further changes
are made until a solid is obtained. Clearly the condi-
tions of the molecules have been greatly modified. In-
stead of being fairly free to move, each is now cabined,
cribbed, and confined and, as a consequence, collisions be-
tween neighboring molecules are almost constantly taking
place. Thus, instead of a few definite modes of vibration, we
have vibrations of almost every possible frequency, and the
spectrum is continuous. Here in this electric arc you have
a solid hot enough to send out a brilliant light. Pass the
light through the prism to analyze it, and you see a brilliant
spectrum on the screen. You observe that it is perfectly
continuous, no sign of a break or an isolated patch of bright-
ness as your eye passes from red to violet, through all the
familiar colors of the rainbow. Now place a piece of so-
dium in the arc. The heat is intense enough to turn it
instantly into vapor, and you see at once, in addition to
what was seen before, a bright line in the orange. The
74 LIGHT
solid carbon pencil gives a continuous spectrum, the gaseous
sodium an isolated line or series of lines.
You have seen, then, that a substance in the form of
a vapor or gas will, if viewed under proper conditions,
exhibit a spectrum crossed by certain bright lines. The
science of spectrum analysis rests, in the main, on two facts
with reference to these lines. In the first place, the position
of the lines is always the same for the same element in the same
condition, and in the second place, the arrangement of the
lines is different for different elements. Once this is grasped,
there can be no difficulty in understanding how the study
of spectra enables us to detect the chemical nature and the
condition of various substances, whether they be in our
laboratories, or in the Sun, over ninety million miles away,
or in some star away in the measureless abyss of space.
For purposes of investigation, we need an instrument that
will enable us to see these bright lines clearly and measure
their relative positions accurately. An instrument specially
designed for this purpose is called a spectroscope. It is a
wonderful instrument, for, although constructed on the
simplest principles, it has revolutionized astronomy and
done great things for chemistry and physics. We want
some means of separating the light that arises from the
different natural vibrations with different frequencies ; in
other words, we want dispersion. The simplest instrument
for producing this is that employed to such good purpose
by Newton, the prism. Figure 12 shows four such prisms
(P) mounted between two telescopes, A and B, so as to
make a spectroscope of the simplest type. The light from
the substance to be examined passes through a narrow slit
into telescope A, and after being bent and dispersed by
the prisms, it enters telescope B, and impresses itself on
SPECTROSCOPY 75
an eye looking through this telescope. The instrument
may have only a single prism, but this will not produce
great dispersion, and may not separate the various lines as
widely as is desired. To increase the dispersion, two or more
prisms are employed, the light passing through one after
another and being more dispersed at each passage. This
FIG. 12
arrangement has the defect that a considerable amount of
light is lost by reflection and absorption, and the loss may
be so great that the fine lines are not clearly visible. To
avoid this serious defect, the more modern spectroscopes
employ another means of producing large dispersion. The
prism is replaced by a grating, a contrivance for dispersing
light, the principle of which will be dealt with in a later
lecture on diffraction. Two distinct forms of grating have
been invented. The first was made by ruling a series of fine
lines on glass or speculum, and was perfected by Rowland
of Baltimore ; the second, the echelon spectroscope, due to
Michelson of Chicago, consists of a series of thin glass
76 LIGHT
plates piled on one another like a flight of steps. To a
spectroscope of any of these forms a photographic apparatus
may be attached so as to obtain a permanent record on
a plate instead of a passing impression on the eye. Such
an arrangement is called a spectrograph, and it is one of the
most important instruments in an.astrophysical observa-
tory.
On looking through a spectroscope at a luminous object,
you see its spectrum. If the spectrum be continuous, you
know that you are looking at a solid or a liquid hot enough
to emit light; whereas, if the spectrum be discontinuous,
you are looking at a gas. Thus a mere glance through a
spectroscope enables you to tell in a moment something
of the physical condition of an object, and this whether
the object be near or far. In this way we know that
comets are mainly glowing gas, and so are many nebulse.
In all the wonders of the heavens, few things are so impress-
ive as the gigantic cloudlike forms, such as the great nebula
in Orion. Is each of these a vast collection of stars like the
Milky Way, or is its structure quite different from this?
After much difference of opinion among astronomers, the
question was finally settled by Sir William Huggins, one of
the pioneers of spectroscopy. " On the evening of August
29, 1864," he says, "I directed the spectroscope for the
first time to a planetary nebula in Draco. I looked into
the spectroscope. No spectrum such as I had expected !
A single bright line only ! . . . A little closer looking
showed two other bright lines on the side towards the blue,
all three lines being separated by intervals relatively dark.
The riddle of the nebulae was solved. The answer which
had come to us in the light itself read : Not an aggregation
of stars, but a luminous gas"
SPECTROSCOPY 77
Thus the spectroscope tells us something of the physical
condition of a substance. It shows whether it is gaseous
or not. But it does much more than this; it reveals the
chemical constitution. This is settled by noting carefully
the positions of the various lines in the spectra, and com-
paring them with the positions of lines in the spectra of
known elements. A glance at Fig. 11 will serve to recall
the fact that the spectra of no two different elements are
the same, so that if we see in the spectrum of any substance
the characteristic lines of any element, e.g. hydrogen, we
can be certain that the substance contains hydrogen. A
more careful examination of the various spectra makes it
evident that the chance of confusing two elements is
extremely small. We now possess very carefully made
maps of the spectra of the elements, and these greatly
facilitate the process of identification. This spectroscopic
method of examining the chemical constitution of a sub-
stance is a very simple and a very valuable one. Its extreme
delicacy enables us to detect the presence of minute quan-
tities of a substance that no ordinary chemical process could
possibly detect. Morever, the fact that a different series of
lines in the spectrum indicates a different element shows that
if we find spectra differing from any already known, we have
good ground for supposing that we are in the presence of
a new element. And so it happened that one of the first
fruits of the science of spectroscopy was the discovery of
new elements. Bunsen was the pioneer in this field. In
1860 he discovered in this way the elements C cesium and
Rubidium; in the following year Crookes discovered
Thallium, and there has been a long list of similar dis-
coveries since then.
This spectroscopic method of distinguishing one substance
78 LIGHT
from another by the positions of the lines in their spectra
has, during the last half century, become one of the common-
places of chemistry. In recent years, however, the attention
of physicists has been directed to other features of the lines
than their mere positions. Even a slight examination reveals
the fact that there are various differences between the lines,
e.g. one is much broader, or much brighter, than another.
In these latter days each line is subjected to the most minute
examination, the pioneer in this field of investigation hav-
ing been Michelson of Chicago. By means of an ingen-
ious instrument of his own invention, the interferometer,
an instrument the explanation of which depends on the
principle of interference that is dealt with in a later lecture,
he observes certain features of the lines, and records the
results of his observations graphically in the form of what
he calls visibility curves. If you look at those curves for
different substances, you will see that one line differs very
markedly from another. Here, for example, in Fig. 13,
are the curves for different lines in the spectra of various
substances: (a) for the red line of cadmium, (6) the red
line of hydrogen, and (c) the green line of mercury. From
the study of the form of these lines, Michelson makes
various interesting and important deductions as to the
character of the source that sends out the light radiation.
He concludes that (a) comes from a source of the simplest
possible character, a single vibrator sending out waves
that are almost perfectly homogeneous. The form of (&)
seems to indicate that the source is more complex than with
(a), and Michelson concluded that the radiation came from
two sources, differing ve 1 y slightly in frequency and in in-
tensity. His prediction as to the essentially double char-
acter of this line was afterwards confirmed by direct obser-
SPECTROSCOPY
79
vation. The curve (c) reveals a much more complex source ;
in this case, apparently, the radiation comes from a number
of vibrators differing both in frequency and in intensity.
The interest of such investigations centers entirely on the
light that it sheds on the fundamental problem of the struc-
(b)
(c)
FIG. 13
ture of the atom, as the vibrations must be due to motion
within that small kingdom.
Thus far we have spoken only of the positions and fea-
tures of certain bright lines in the spectrum, these bright
lines being separated by spaces that are relatively dark.
On looking at the solar spectrum with a good spectroscope,
a different phenomenon is revealed. The spectrum is seen
to be bright and all but continuous except that it is crossed
by a large number of fine dark lines. These lines were
80 LIGHT
first carefully observed by Fraunhofer in 1814, and are
still known by his name. In the intervening century they
have been studied with the greatest care, and the task of
mapping them accurately has been undertaken and carried
out with marvellous patience and skill. Thus Rowland's
map records the places of about tweny thousand of these
lines. What is their meaning, and why should we trouble
to record their positions with so much care? After the
last lecture on absorption, we should have no difficulty
in answering such questions. A vibrating system absorbs
the energy of waves that have the same frequencies as the
natural frequencies of the system. Look at the spectrum
of the vapor of sodium. You will see two bright lines (D)
close to one another in the orange, and the positions of these
lines depend upon the frequencies of the natural vibrations
of the sodium atom. If now a train of waves passes through
the sodium vapor, those waves will have their energy
extracted that have frequencies corresponding exactly to
those of these two D lines. Hence, if the light that falls
upon the sodium vapor come, let us say, from a glowing
liquid hotter than this sodium, the continuous spectrum
of the liquid will be crossed by two dark lines coinciding
in position with those D lines. This is the phenomenon
of reversal. It is no mere deduction from theory, but a fact,
verified, as you see, by the experiment that is being con-
ducted before you. The principle involved in the ex-
planation here given had occurred to Stokes and other
physicists in the first half of last century ; but it was re-
served for Kirchhoff in 1859 to set it forth clearly and test
it by experiment. From that date we may mark the rise
of what is often called the new astronomy an applica-
tion of spectroscopic methods to the study of the physi-
SPECTROSCOPY
81
cal condition of the heavenly bodies which has led to many
epoch-making results.
In Fig. 14 the phenomenon of reversal is exhibited by
showing side by side the bright lines of the emission spec-
tra, and the dark lines in the absorption spectra of a few
elements. The point to be specially noticed is the coinci-
Sodium
dence in position of the bright lines in one case with the dark
lines in the other. It may at first be thought that these
coincidences are only accidental. This might, indeed, be
so were there only a few coincidences, but the number ac-
tually observed puts the idea of chance out of the question.
Thus, in the case of the iron lines, Kirchhoff, on taking into
account the number of the lines, their distances from one
another, and the degree of exactness with which their posi-
tions could be determined, calculated that the odds were
at least a million million million to one against a mere
chance coincidence. We may thus feel practically certain
that, when we see dark lines in a spectrum coinciding in
82 LIGHT
position with bright lines in the emission spectrum of an
element, we are looking at the light from a hot source
shining through a cooler vapor containing the element
in question. It will be realized at once that this enables
us to detect the presence of elements in any body, be it near
or far, that is in a certain physical condition. What this
condition is should be carefully borne in mind. The body
must be hot enough to give a continuous spectrum, and it
must be surrounded by a cooler atmosphere. The spectro-
scope then enables us to determine the ingredients of this
atmosphere. Naturally, the method was first tried upon the
Sun, and the observation of the Fraunhofer lines and the
comparison of their positions with those of the bright lines
in the spectra of various elements have made a great ad-
vance in our knowledge of solar chemistry possible and
easy. In this way a very large number of familiar elements
have been discovered in the Sun, so many that it may be
simpler to mention a few that have not been found there,
such as gold, arsenic, mercury, nitrogen, and sulphur.
There are still a great many unidentified lines in the solar
spectrum, some twelve thousand having been registered that
are as yet without chemical interpretation. Clearly, the
method here sketched is not confined to the Sun but is ap-
plicable to any body whose spectrum can be examined.
Thus, for example, we now know with certainty that many
of the stars are made up of much the same material as our
earth, and that they are in much the same condition as the
Sun, that is, they are hot bodies surrounded by a gaseous
atmosphere.
Turning, for a moment, from stellar chemistry to more
mundane matters, we may observe that the careful study
of absorption spectra may yet help us to solve many funda-
SPECTROSCOPY 83
mental problems in molecular physics and chemistry. In
this field much useful work has already been done by
Hartley and others in the examination of the absorption
spectra of various organic compounds. These compounds
are formed by grouping different elements round a carbon
atom, and a fundamental question is : How are the atoms
arranged ? if you could see them, what would be their rela-
tions to one another in space ? Such questions can some-
times be answered, with more or less assurance, by the care-
ful study of the nature of the chemical reactions of the
substance under different circumstances. But often this
method fails, and Hartley shows that the study of absorp-
tion spectra may help us out of the difficulties, and enable
us to say, for example,
that in a certain com- A ~ #
pound the hydrogen atom " J " v
is linked to the nitrogen
and not to the oxygen. A mere change of linkage, that
is, a change of grouping, can modify the spectrum, and the
study of such changes bids fair to give us an insight into
the actual arrangement of atoms in the group.
In dealing with so extensive a subject as spectroscopy
in a lecture such as this, it must soon be realized that there
is not sufficient time to do more than speak of its funda-
mental principles and point out a few of its most striking
achievements. Some of the latter have already been in-
dicated ; let us glance at a few more. Spectroscopy enables
us to discover not only the physical condition and chemical
nature of various heavenly bodies, but also, in certain circum-
stances, the speed at which they are moving. To understand
this, suppose that you are sitting in a canoe at A (Fig. 15), and
that you set up a series of waves by dipping your paddle
84 LIGHT
into the water once a second. If V be the speed with which
the waves move over the surface of the water, the first wave
will reach B at a time , and the second at a time 1-f
- , both times being measured in seconds from the mo-
ment when your paddle first touched the water at A. The
interval of time between the two waves reaching B is one
second. This will be the case whatever be the velocity
V, so that a change of velocity does not affect the time in-
terval between the waves that strike upon B] in other
words, it does not affect the frequency of the oscillations at
B. But now suppose that you paddle your canoe toward B
with velocity v. The first wave reaches B at the time
as before. The second wave again starts one second
later, but it has not so far to go in reaching B. It goes only
the distance CB = AB v, so that it arrives at B at the
,. (AB v) AB , - v r . , , - ..
time 1 + y - -y- + 1 y. The interval of time
between the first and second waves that reach B is thus
changed from 1 to 1 (and it would be easy to show in a
similar way that the interval would be changed to 1 + ^ if
you paddled in a direction away from B instead of towards it).
This change of interval means, of course, a change of fre-
quency in the oscillations observed at B. You will see that
there is nothing in the argument that limits its application
to water waves ; if true at all, it should apply equally to
waves in water, or any other medium, such as air or ether.
The only difficulty in its application to light is that a care-
ful scrutiny reveals some rather delicate questions as to the
SPECTROSCOPY 85
relative motion of ether and matter, questions that it would
be out of place to discuss on this occasion. The principle
itself was first clearly stated by Doppler in 1843, and was
tested two years later by observations on sound from loco-
motives. The theory of sound shows that the pitch of a
note depends on the frequency of the oscillations in the air
that strikes upon the ear. Hence, according to Doppler's
principle, the pitch of a note should change in a definite
way, as the source of sound approaches and recedes from
an observer. The general character of the change can be
observed by any one who cares to listen carefully to the
sound of the bell when a bicycle passes him in the street.
The object of the experiments referred to was to test the
principle in a more thorough fashion by exact* measure-
ments of the pitch, and the results showed clearly that the
principle was well grounded in fact.
To understand the application of Doppler's principle
to spectroscopy, you have only to recall the fact that the
positions of the lines in the spectrum depend upon the fre-
quency of the vibrations. Consequently, a change of fre-
quency should reveal itself by a shift in the positions of the
spectral lines, and a measurement of this shift gives us the
means of calculating the velocity of the source of light (say
a star), or rather the component of its velocity in the direc-
tion of the line of sight. Many interesting results have been
obtained by this mode of research. Thus, for example, it
has enabled us to estimate the speed of different parts of
the Sun, such as the mighty currents of gas in the neigh-
borhood of a Sun spot, or those awe-inspiring tongues of
flame (the prominences) that shoot up from the central
fire of the Sun, in some cases at the rate of about seven
hundred miles per second. Similarly, it has made it pos-
86 LIGHT
sible to determine the speed of many stars that are far too
distant to have their velocities gauged by any other method.
As is to be expected, the velocities are found to be very
different for different stars. Some are moving relatively
to the Sun at about one mile per second, others at nearly
a hundred miles. The majority on one side of the heavens
have a general relative motion towards the Sun, those on the
opposite side a similar motion away from the Sun. The
inference, of course, is that the Sun itself is not stationary,
but is sweeping through space with his attendant train of
planets. Another interesting achievement of this mode of
research is that it has enabled us in many cases, in a sense,
to see that which is invisible. In general, no star can be
seen unless it be hot enough to emit light, and yet, though
unseen, its presence may be none the less distinctly felt.
Whether hot or cold, it will still have weight, and will have
the mystic power of gravitation, of attracting all neighbor-
ing bodies towards itself. If heavy enough, it will compel
its neighbors to move round it in definite orbits, like the
planets round the Sun. If we see a star moving round an
orbit, we may be certain that it has a companion that
attracts it, whether this companion be visible or not, and
the principles of celestial mechanics may enable us to de-
termine various facts about this dark companion for
example, its weight. Now the observation of the shifting
of the lines in the spectrum of various stars, when conducted
over a long period, often shows that the stars are not moving
uniformly in a definite direction, but are circling round an
orbit, and so from the knowledge of the visible we are led
to infer the presence of the invisible. The application of
Doppler's principle also occasionally gives us information
as to the structure of the heavenly bodies. Among the
SPECTROSCOPY 87
most striking objects to be seen with a good telescope are
the beautiful rings of Saturn. What is the structure of
these rings? This was a question long debated, until
Maxwell in 1859 showed by means of mechanical principles
that the rings could not possibly be solid, for in such a
state they would be unstable and would fly to pieces. The
argument convinced all those who were not afraid of the
highroad of mathematics and mechanical science, but it
was not till 1895 that we had ocular demonstration that
Maxwell was right. In that year Keeler showed, by a care-
ful study of the spectra of the light reflected from the rings,
that the inner edge is moving faster than the outer, which
of course would be impossible with a solid. As Maxwell
had indicated, the ring is a group of meteorites, each mov-
ing as a separate planet round Saturn as its central Sun.
So much for Doppler's principle and its applications;
let us turn to some other phases of the modern science of
spectroscopy. We have had occasion to refer to the solar
prominences, those mighty tongues of flame that shoot
outwards from the Sun to distances, sometimes, of several
hundred thousand miles. Huge and brilliant as they are,
they are not to be seen under ordinary circumstances with
the naked eye, for their brightness is overpowered in the glare
of the sunlight. And so, until forty years ago, they were
thought of only as an eclipse phenomenon, and were looked
for eagerly on those rare occasions when at any given place
the Sun is seen in total eclipse. All this was suddenly
changed by an epoch-making application of the spectroscope
an application due to the ingenuity of Janssen, Lockyer,
and Huggins by means of which the prominences may
be seen on any day. The principle of the arrangement is
very simple. A spectroscope disperses the sunlight that
88 LIGHT
passes through it ; it spreads out the image of the narrow
slit from, say, one-thousandth of an inch to many feet.
This dispersion, as we saw in an earlier lecture, is due
entirely to the different refrangibility of the various con-
stituents that go to make up the composite thing that we
call sunlight. Homogeneous light, light of a definite re-
frangibility, is not dispersed. Now it so happens that the
solar prominences are made up mainly of homogeneous
light, such as the light from hydrogen or helium or calcium.
Consequently, while the light from the Sun is spread out
by the spectroscope, that from the prominence is not.
Hence, by employing a spectroscope of sufficient dispersive
power, it is possible to spread out the sunlight so much that
the prominence looks bright in comparison with the Sun,
and may be plainly seen on any day of the year, without
the tedium of waiting for a total eclipse.
That was an ingenious and important device; but even
more so was the later development due to Hale (now of the
Mt. Wilson Solar Observatory). This device enables us not
only to see the prominences at any time, but to photograph
them, and thus obtain a permanent record of their features.
The form of spectroscope specially designed for this purpose
is known as a spectroheliograph. Let us see how it works.
A special feature of the solar prominences is the presence
therein of quantities of the vapor of calcium, the spectrum
of which is characterized by two bright lines called H and K.
Suppose that we present the slit of the spectroheliograph
to a prominence, so as to allow the light from the promi-
nence to stream through the instrument. In this way we
look, as through a narrow window, at a section ABCD (Fig.
16). The light from this section, if passed through a prism
or other dispersing apparatus, would be drawn out into a
SPECTROSCOPY
spectrum, and if you were to put your eye in the position
of the line K, you would be in a position specially favorable
to receive impressions from light that came from the vapor
of calcium. As this vapor is an important ingredient in the
prominence, the portion BC of the section that you were
observing, would appear much brighter than the portions
AB and CD that lay outside the prominence. In this way
the cross-section BC
of the prominence
would stand out more
or less distinctly, and
by moving the slit up
and down, you could
thus observe various
cross-sections, and so
map out the whole
prominence. To obtain
a permanent record, it
is necessary to replace
the eye by a photographic plate, in front of which a second
slit is placed in such a position that it catches the light
from calcium vapor, but no other kind of light. A suit-
able mechanism moves the slits so as to give a succession
of photographs corresponding to different cross-sections of
the prominence.
The method here sketched was first tried with complete
success by Hale in 1892. He saw at once that it could be
applied to the study of other solar features. If, for example,
there were a cloud of calcium vapor anywhere in the Sun's
surface, the same method would enable the observer to
pick it out and photograph it. Hale did this in 1892, and
his more recent photographs of calcium floccvli reveal the
FIG. 16
90 LIGHT
fact that these beautiful clouds are specially striking in
the neighborhood of Sun spots. Then, of course, there is
no reason to confine the method to photographing clouds
of calcium. Other elements may be dealt with similarly.
In this way, working with one of the hydrogen lines, Hale
found that great masses of this gas are concentrated in
clouds on various parts of the Sun's surface, and photo-
graphs of these hydrogen flocculi show them to be so nu-
merous as to make the bright face of the Sun present a
distinctly mottled appearance.
We have seen that the spectroscope enables us to detect
the presence of familiar chemical elements in the Sun and
stars, to measure the velocities of such distant bodies, and
to photograph many otherwise invisible features on the face
of the Sun. We have also seen that it may give us an in-
sight into the physical condition of various heavenly bodies.
A continuous spectrum indicates a glowing solid or liquid,
while a discontinuous spectrum reveals a gas. But we can
often tell more than that the object of our interest is a great
mass of gas. We may learn something of its temperature
and of its pressure. It is found by observation that the rela-
tive intensity of different lines varies with the temperature
of the source of light. For example, in the spectrum of
magnesium, there are two lines, a and 6, say; of these two,
a is brighter than b at the temperature of the electric spark,
but b is brighter than a at lower temperatures. This may
serve to indicate how the relative intensity of the lines in
the spectrum may serve as a clue to the temperature of
the glowing gas. Moreover, the character of the spectral
lines is altered by a change of pressure. If the pressure be
increased, the lines broaden, so that an observation of
their width tells us something of the pressure of the gas,
SPECTROSCOPY 91
It is even possible to take a photograph (by means of a
spectroheliograph) of the calcium vapor at 1 the base of the
calcium flocculi in the Sun, without being troubled by the
lighter vapor above. To do this, it is merely necessary to
set the second slit of the instrument near the edge of the
broad K bands, so that the light from the rarer vapor
cannot enter the spectroscope, and is thus debarred from
affecting the photographic plate. Such a device has made
it possible to learn a good deal of the structure of these
flocculi, by examining sections of them taken at various
levels.
The last point that there is time to touch upon is the
contribution that spectroscopy has made to our knowledge
of the trend of stellar evolution. This idea of development,
or evolution, if you prefer the term, has become a common-
place of modern thought in almost every field of speculation
and of knowledge. It is an old idea, brought, as you all
know, into a precise form that immediately appealed to
man's imagination by Darwin in his Origin of Species
that epoch-making book that was published in the same
year in which Kirchhoff laid the foundations of the science
of spectroscopy. Long before Darwin's day, the idea of
stellar evolution had been broached, the idea that the
heavenly bodies have not been always as they are to-day,
but that they have been and still are going through a gradual
process of change. To unravel this secret of the universe
and get some insight into the earlier history and later
destiny of the worlds around us is one of the grandest
problems that the pygmy man has been bold enough to
attack. Kant, the great philosopher, made some sugges-
tive speculations, and Laplace, the great mathematician,
developed them into a definite working hypothesis. But
92 LIGHT
all such thinking was somewhat premature. If you wish
to trace the development of anything, you must know as
accurately as possible its physical condition at various
stages of its growth. People are naturally somewhat
skeptical when they are asked to believe that their remote
ancestors were probably arboreal in their habits ; but they
are really not in a position to judge of the merits of such
a theory unless they have made a careful study of the dif-
ferent stages of human development. And so with the
problem of stellar evolution it is necessary to begin by
rinding out all that can be known of the actual physi-
cal condition of different members of the heavenly host.
Spectroscopy is making the solution of the problem possible ;
it cannot be said to have solved it yet. By means of this
science we now know a good deal as to the physical condi-
tions of a very large number of heavenly bodies. We can
thus arrange these bodies into groups, the members of each
group having certain properties in common, and it may be
that these groups represent different stages in a general pro-
cess of development. Suppose we put them into six groups,
and look at each very briefly. First, there are the nebulae.
Many of these are enormous clouds of glowing gas, the
bright lines in their spectra indicating the presence of
hydrogen and helium, and of an unknown element which
has been given the name nebidum. Out of these cloud-
like masses we might expect various forms to be evolved,
through the action of gravity and other forces, and in view
of certain speculations as to the mode of their evolution it
is interesting to observe that of 120,000 nebulae that have
been examined, more than half have a spiral form. They
look like mighty Catherine wheels in the very act of whirl-
ing. Second, we have the special class of nebula; that con-
SPECTROSCOPY 93
stitute the Orion type. Their spectra exhibit no bright
lines except those of hydrogen and helium, and these lines
are very broad and faint. Third are the white stars, such
as Sirius. Their spectra show broader lines of hydrogen,
with narrow and faint dark lines of iron, sodium, magnesium,
and a few other elements. Their atmospheres are still very
rare, much rarer than that of the Sun. Fourth come the
yellowish stars like the Sun. They have far more dark lines
in their spectra than their predecessors, and there is evidence
of much greater density. Fifth, we have the red stars, of
which An tares is a type. They are beginning to fade into
invisibility. Their spectra are much more complex than
those of the previous groups, and contain a great many lines,
and not a few dark bands or flu tings. Last come the dark,
invisible stars. They are too cold to give any light, and
can be detected only, as already indicated, by the shifting
of the lines in the spectrum of a neighboring bright star.
Here, at any rate, we have food for thought. We may
feel certain that some process of development is in prog-
ress, for nothing that we know well stands quite still.
But what is the exact order of the development, whether
that order is everywhere the same, and whither it all
tends are questions we may hesitate to answer. Here,
probably the better part of valor is discretion. Later
researches have revealed many difficulties in Darwin's
theories, and put many a stumbling-block in the path of
him who is too eager to embrace the nebular hypothesis
of Kant and Laplace as to the mode of stellar evolution.
The leaders of thought in this field must work with patience
and endurance perhaps for many a generation before there
is anything like a final concord in answering these great
questions. I leave them with you as food for speculation
94 LIGHT
and, if vastness attracts you, here you have some problems
preeminently to your taste. You are not asked to decipher
the history of man, nor to tell the tale of the "solid" earth,
which is the scene of all his thinking and activity, but
to describe the birth, the struggles, and the end of the uni-
verse.
POLARIZATION
E C
C' L
FIG. 17
LET me direct your attention to an experiment that you
may all repeat without difficulty. I take a sheet of ordi-
nary glass, ACB (Fig. 17), and hold it between my eye, E,
and the light, L, so that EL is perpendicular to the plane of
the glass. As I turn the glass round, keeping unmoved,
and the plane of the glass
always at right angles to
EL, the light maintains a
uniform brightness. Now
I put in a second sheet of
glass, A'C'B', and hold it
parallel to the first. The
light does not look quite as
bright as before, but it is still true that its intensity is un-
changed by any turning of the first piece of glass in the
manner that has been described. Next let us modify this
experiment by substituting for the glass a substance almost
as transparent. Here is some Iceland spar made into the
form of a Nicol's prism. On putting it before the light of
the lantern, you see how transparent it is by observing how
brilliantly the screen is illuminated by the light that
streams through the prism. Another prism similar to the
first is now introduced, and you observe that as this prism
is turned round, exactly as was the glass with which we
began, the brightness of the screen is no longer constant,
95
96 LIGHT
but is varying continuously. Now the screen is exceed-
ingly bright, and now that I have turned the prism a greater
way round through ninety degrees, there is no light at all
on the screen. Further turning gradually restores the light
until a full half turn has been made, when the screen is as
brightly lit up as ever, and so the cycle goes on until again
all the light is extinguished. This is certainly a curious
phenomenon, the cutting off of light by means of a trans-
parent substance merely by holding it in the right position.
The explanation of the phenomenon involves the discus-
sion of the polarization of light, a subject interesting in
itself and of the first importance in the development of
optical theory.
You have already been reminded that light is to be re-
garded as due to a to-and-fro oscillation, a wave-motion
propagated in a medium that is called the ether. Let us
suppose that such a disturbance enters this room by the
north wall and that, at any instant of time, every element
of ether on that wall is moving similarly. We should speak
of this wall as the wave-front, and in due time, as the dis-
turbance was passed on from element to element, this wave-
front would move across the room and reach the south wall.
So far we have said nothing as to the direction of motion of
each element in the wave-front; we have merely said that
the motion is of a vibratory character, each point moving
to and fro and returning to its original position with a
definite frequency. It now becomes necessary to specify
more definitely the character of this motion, and the first
point to bear in mind is that, for reasons that will be in-
dicated almost immediately, we must think of all the ele-
ments in a wave-front as moving entirely in that plane.
In the case just referred to, if we could see the ethereal
POLARIZATION 97
elements as the light entered the north wall of the room,
each of these elements would be moving in a little orbit,
every point of which would be
on the north wall. Of course
this restricts the possible
movements of the ether very
much; it confines them all
to the wave-front, but there
is still a great deal of freedom. Orbits of all sorts might
be described, some elements might be vibrating to and fro
along a line, some in circles, others in ellipses, and others
in more complex orbits always with the restriction that
the plane of these orbits
must be the wave-front.
ooo
00
OOO Such a s Y s tem of multiform
(*\ orbits is depicted in Fig.
18, the plane of the paper
representing the wave-
FlG - 19 front, and if such a condi-
tion of things existed, the light would not be polarized. The
peculiarity of polarized light is that all these orbits are
similar. If they are all circles, as in Fig. 19, the light is
said to be circularly polarized. The circular orbits may
be described in two different
senses, clockwise and coun- /^ f\ f\
ter-clockwise, and these are \_/ \J \J
usually distinguished as right- S\ S~\ s\
handed and left-handed polar- T J f J f J
ization. Again, the orbits may FIQ 20
be all similar and similarly
situated ellipses, as in Fig. 20, and this constitutes elliptical
polarization. Or all the elements of the ether may vi-
98 LIGHT
brate backward and forward along a series of parallel lines.
This is rectilinear polarization, or what is more generally
called plane polarization. The plane at right angles to
the wave-front and through the direction of displacement
is called the plane of polarization. Fig. 21 represents two
cases of plane polarized
light, the planes of polari-
, , zation being at right angles
/ T > to one another.
The case last dealt with,
that of plane polarization,
FIG. 21 . / . i . ,. ., ;
is one of special simplicity
and special importance. The vibrating elements are all
moving backward and forward along a series of parallel
lines. This type of motion is well illustrated by look-
ing at a string, AB (Fig. 22 a), which is held taut, with
its ends fixed at A and B. If the string be plucked
aside very slightly at C, its elements will vibrate to
and fro in the plane ACB, the various points moving
along lines at right angles to AB. In this case ACB
is the plane of polarization, and it should be noted that,
as the wave of disturbance progresses along the string, the
motion of each point is in the
wave-front at right angles (a) A Li ^~ -B
to the string, the vibrations r ,
f,\A _^ _^ C V
being of the type described as ^ ' ~* FIG 2 J*
transverse vibrations. If the
vibrations be longitudinal instead of transverse, we have an-
other important type, whose leading features can be illus-
trated by the motion of an elastic string, AB, which is kept
taut as before. If now a point C be moved to C" (Fig.
22 6) along the string, instead of at right angles to it,
POLARIZATION 99
a longitudinal wave will move along the string, and the
various elements will vibrate to and fro in the direction
AB. These two types of vibrations differ in one very
important particular, the ' transverse can be polarized,
the longitudinal cannot. The peculiarity of a polarized
vibration is that each of the moving elements is con-
strained to move in a similar orbit, and it is evident
that this can be done with the string vibrating tranversely.
With the longitudinal vibrations, on the other hand, only
one direction of motion is possible, and if this be stopped,
there can be no vibration at all. Hence it follows that
if light can be polarized, the vibrations must be of the trans-
verse and not of the longitudinal type ; the displacements in
the ether must be in the wave-front, and not at right angles
thereto. We shall see presently that the experiment made
at the outset of this lecture with the Nicol prisms is easily
explained if we recognize the possibility of polarization, but
otherwise it is inexplicable. It is for this reason that this
experiment is crucial in the theory of light. The idea of
accounting for optical phenomena by ascribing them to
motion in the ether is an old one, but in the earlier days
this ether was always thought of as an extremely rare
medium, a sort of idealized gas rarer than anything of
the kind that we know of by experience. Now a gas can
not propagate vibrations except those of the longitudinal
type, such as the waves in the air that produce the sensa-
tion of sound. To transmit transverse vibrations, a medium
must be able to resist certain changes of shape; it must
have some rigidity, like a piece of steel. This proved a
great stumbling-block to many, even to such leading men
of science as Arago and Fresnel, when the phenomena of
polarization seemed to force upon them the idea of
100
LIGHT
transverse vibrations in the ether. Fresnel admitted that
he "had not courage to publish such a conception"; but
Young and other men were bolder, so that the idea of
transverse ethereal vibrations is now a commonplace,
and the notion of an ether with some rigidity has lost its
terrors.
We have already made use of a vibrating string to illus-
trate the meaning of a plane polarized wave, and we may
FIG. 23
use it also to throw some light on the experiment with the
Nicol prisms at the outset of this lecture. I have here a rope,
and as I move one end of it, you observe a wave of disturb-
ance passing along the rope, and the rope being quite free,
the displacements may be in any directions at right angles
to "the rope. Next I pass the rope through this simple
wooden structure P of Fig. 23. You will observe that it
is a box divided up into narrow compartments by a series of
parallel partitions that are just wide enough apart to allow
the rope to pass freely between two consecutive partitions.
The effect of passing the rope through this apparatus is to
polarize the wave of displacement that passes along the rope.
If the partitions are vertical, the displacements are all con-
POLARIZATION
101
fined to a vertical plane, so that we have a plane polarized
wave, the plane of polarization being vertical. Now if I take
a second box, A, similar to the first, P, and hold it with its
partitions vertical (i.e. parallel to those of the first box), you
will observe that when the rope is passed through A as well as
P, the disturbance that gets through P is freely transmitted
through A also. Suppose, however, I turn A somewhat,
so that its partitions
are no longer parallel to
those of P, then you will
observe that A destroys
some of the motion in
the rope after it has been
transmitted through P,
and that when A is
turned so that its parti-
tions are horizontal, and
therefore at right angles to those of P, then, however vio-
lently I move the end of the rope, there is absolutely no dis-
turbance that gets through both boxes. Now we shall see
in a later lecture, when dealing with crystals, that a crystal
acts upon a beam of light somewhat in the same way that
this apparatus acts upon our rope. It will not permit
vibrations to pass through it, unless they are confined to
one or other of two planes at right angles. The effect is the
same as if we had a number of obstacles symmetrically
arranged, as are the shaded portions of Fig. 24. Any one
setting out from could not proceed along a straight line
(such as Oa) for any distance without being stopped by an
obstacle, unless they moved along one or other of the two lines
Ox and Oy, which are at right angles to one another. A to-
and-fro motion along these directions might be maintained
FIG. 24
102 LIGHT
indefinitely, but in no other direction would it be possible.
The Nicol's prism used in our experiment is a simple and
ingenious instrument made of the crystal Iceland spar,
and so arranged that of the two waves that might be prop-
agated (each plane polarized at right angles to the other)
one is got rid of by total reflection. Thus a Nicol's prism
acts upon light in such a way that the only light that can
get through the prism is plane polarized in what is known
as the principal plane of the prism. If, then, we hold two
Nicols with their principal planes parallel, this corresponds
exactly to the case of the two boxes with their partitions
parallel, and the light that comes through the first is freely
transmitted by the second. On turning the second Nicol, a
change is made, and if it be turned so that the two Nicols
are crossed, that is, if their principal planes be at right
angles, we have a state of affairs similar to that with the
boxes, the partitions of one being vertical and of the other
horizontal. Under such circumstances we have seen that
no disturbance in the rope can be propagated through
both boxes, and no light gets through both Nicols.
I hope that enough has been said to make clear the mean-
ing of polarization, and particularly of plane polarized light.
Now when a beam of plane polarized light passes through a
solid like glass or a liquid like water, its plane of polariza-
tion on emergence is the same as it was at entrance. This,
however, is not the case with all substances, a large number
being so constituted that the emergent light is polarized in
a different plane from the incident. Under such circum-
stances the plane of polarization has been rotated through
a certain angle, and this phenomenon is consequently
spoken of as the rotation of the plane of polarization of
light, or more briefly as rotatory polarization. If you care
POLARIZATION 103
to see the phenomenon, it is very easily exhibited with
the apparatus before you. You will observe that after
a little adjustment these two Nicols are now "crossed/'
with their principal planes at right angles, so that no light
can get through them both. Now I place between the
Nicols this plate of quartz, and you see at once that the
screen is illuminated. However, on turning one of the
Nicols gradually, you see that we reach a position where
darkness once more reigns, and a very little consideration
will show you that this is what we should expect if the
quartz has the power of rotating the plane of polarization
of the light that passes through it, and that the amount of
this rotation is measured exactly by the angle through which
it was necessary to turn the Nicol to produce darkness
again after the quartz had been introduced. This phenome-
non of rotatory polarization is a very interesting one ; we
shall be occupied with it exclusively during the remainder
of this lecture. It will be advisable, however, to postpone
the consideration of the very important case when the rota-
tion is effected by the influence of magnetism, as that case
will be taken up more appropriately when we are dealing
with the relations between light, electricity, and magnetism
in the concluding lecture of this course.
Substances that are endowed with the power of rotating
the plane of polarization of light may differ as to the direc-
tion as well as the magnitude of the rotation that they
produce in any given circumstances. Some may rotate the
plane as if you were turning an ordinary screw to the right,
while others rotate it to the left. Such substances are dis-
tinguished by various names, such as right-handed and left-
handed, or dextro-rotatory and laevo-rotatory, and wher-
ever they have the rotatory power at all, they are spoken
104 LIGHT
of as optically active. There are two main classes to be
considered : in the first class are certain crystals, and in the
second certain organic substances in solution. In both cases
experiment proves that the angle of rotation is proportional
to the thickness of the active medium traversed by the
light, so that the rotation produced by a given thickness
may be taken as a measure of the rotatory power of the
substance.
The most obvious thing about a crystal is that it differs
from a non-crystal in having a definite structure. It is
not a formless thing like a piece of glass. If you could
watch the process of crystallization, you would see a definite
form being built up as if by the unerring hand of a skilful
artist. You might expect, then, that this fundamental
difference between crystalline and non-crystalline media
would have something to do with the explanation of rota-
tory power. And there can be no doubt that it has, the
only doubt being as to the actual arrangement of the mole-
cules in any crystal, and the mode in which this arrangement
makes the crystal optically active. That there is an inti-
mate relation between structure and rotatory power was
shown long ago by Sir John Herschel. It was known that
some specimens of quartz rotate the plane of polarization
to the right, while others rotate it to the left. Herschel
found that this difference went hand in hand with certain
differences of crystalline form. In the quartz of one class
certain facets of the crystal were found on minute examina-
tion to lean all in one direction, to the right, say,
whilst with the other class the corresponding facets leaned
to the left. The first class was dextro-rotatory, the sec-
ond IsBVO-rotatory. And had there been any doubts that
rotatory power is due to structure, these must have been
POLARIZATION
105
removed by the consideration of the fact that the optical
activity of a substance disappears when its crystalline
structure is destroyed, as happens to quartz when it is
fused, or to camphor when it is dissolved.
Crystalline structure may produce rotation, but how
does it effect it? This is a question not easy to answer
Q'
FIG. 25
satisfactorily, especially within the limits of such a lecture
as this, but perhaps I may give you some glimpses of what
has been done to solve the mystery. It is first necessary
to realize that what looks like a plane polarized beam of
light may really be a combination of two equal and opposite
circularly polarized beams, the orbits of the two circles
being described in opposite senses. Suppose that we set
two particles off from C (Fig. 25 a) with equal speeds in
opposite senses in the circle, one going round clockwise
and the other counter-clockwise. After a time they will
arrive at the points B and A respectively, where B is just
as far above the level COC' as A is below it. Now if we
raise a point a distance BN by means of one motion, and
lower it an equal distance, AN, by means of the other t the
effect of the combined motions is to keep the particle at
the level N on the line COG'. Thus the combined effect of
two equal and opposite circular motions is exactly equiva-
106 LIGHT
lent to a vibration along the straight line COC f ; in other
words, what looks like rectilinear (or plane) polarization
may really consist of a combination of two opposite circular
polarizations. Let us suppose, in the next place, that the
two particles do not set out simultaneously from (7, but
that one starts from C and moves round the circle in a
clockwise sense, while the other goes in the opposite sense,
and starts from E (Fig. 25 6). It will be seen, as before,
that the combination of these two motions is equivalent
to a vibration along the straight line QOQ', which is such
that OQ bisects the angle EOC. Think next of a right-
and a left-handed circularly polarized wave moving through
a crystal, and that, owing to the peculiar structure of the
crystal, these two waves move through the crystal with
different speeds. The two waves will take a different
time to traverse a given thickness of the material, so that
one will get through the plate faster than the other. A
point in the left-handed wave (let us say) will, while the wave
has traversed the plate, have made a certain number of
complete revolutions and come back to its starting-point
C (Fig. 25 b) ; the corresponding point in the other wave
will have had more time when that wave emerges from the
plate, and will have arrived at E. Once through the plate
and into the surrounding non-crystalline medium, the two
waves will proceed at equal speeds, so that their combined
effect will correspond to that of two circular motions de-
scribed in opposite senses at the same rate, one starting from
C and the other from E. We have already seen that these
two are equivalent to a vibration along a straight line Q'OQ,
or to plane polarized light. However, the plane of polariza-
tion will now be Q'OQ, whereas it was C'OC on entering
the crystalline plate ; in other words, the crystal will have
POLARIZATION 107
rotated the plane of polarization through an angle repre-
sented by COQ.
It remains only to consider what structure would give
rise to different speeds for right- and left-handed waves.
An almost endless variety of such structures might be
suggested ; almost anything would serve the purpose that
would present a lack of symmetry to a clockwise and a
counter-clockwise circu-
lar motion. Suppose
that we could watch a
crystal being built up,
as it is when the solid
slowly crystallizes out of
the mother liquor. Each
molecule, or group of
molecules, when it fell -,
llG.
down, would take up its
place on the solid already formed, and it would do this not
in a random fashion, but according to some definite rule, as
if in obedience to some inexorable law of its being. Thus
each group might be shaped somewhat as shown in Fig. 26,
and the different groups piled on one another in the fashion
there depicted. Under such circumstances the crystal would
present a lack of symmetry as regards right- and left-handed
rotation. It is easy to imagine a great variety of patterns
that would be similarly unsymmetrical, and much ingenuity
has been displayed in building up artificial media in some
such way as this, and arranging them so as to endow the
structure with optical rotatory power. Thus Reusch
showed that by superposing thin films of mica according
to a simple law, the rotatory power of quartz could be
reproduced in all its details. More recently, under the
108
LIGHT
guidance of the electric theory of matter, it has become
common to estimate the influence, in rotating the plane
of polarization, of groups of electrons arranged in an un-
symmetrical manner. With certain simple assumptions
it is possible to express the ideas in the exact language of
mathematics, and so to test the theory in a quantitative way
by seeing to what extent it agrees with the most careful
measurements of rotation. There are two such tests of
any theory : first, it must indicate the relation between the
amount of rotation and the thickness of the medium that
is traversed; and second, it must show in what way the
rotation depends upon the color (or, in other words, the
frequency) of the light. Any theory such as has been
suggested above shows that whatever be the color of the
incident light, the amount of rotation should be propor-
tional to the thickness of the active substance through
which the light passes, i.e. it should be twice as great for
two inches as for one. The following table gives the rota-
tion produced by two plates of quartz, one being 1 milli-
meter, and two others 7^ millimeters in thickness, the rota-
tions being given in degrees for various colored lights :
THICKNESS
BED
CHANGE
YELLOW
GREEN
BLUE
INDIGO
VIOLET
1 mm. . . .
18
gj|
24
29
31
36
42
7.5 mm. . . .
135
161J
180
217
232
270
315
It will be observed that the amount of rotation with
each color follows the law of proportionality to the thick-
ness, just as the theory indicates. The theory also shows
that the relation between the amount of rotation and the
frequency of the vibrations in the light is, for a substance
POLARIZATION
109
like quartz, given by a formula of the type R = a/ 2 +
J
J ~~
when R is the rotation, / the frequency, and a, b,
and /! are constants depending on the nature of the sub-
stance. How closely this fits the facts is shown in the
following table, which compares the theoretical and the
observed natures of R for the case of quartz, R denoting
the rotation in degrees produced by a plate one millimeter
in thickness, and / being the frequency in million millions
per second :
f
140.12
1.57
1.60
169.41
2.29
2.28
206.80
3.43
3.43
277.65
6.23
6.18
447.01
16.56
16.54
456.89
17.33
17.31
508.82
21.70
21.72
517.85
22.53
22.55
519.74
22.70
22.72
R (theory) . .
R (observation)
f
549.09
25.51
25.53
589.57
29.67
29.72
609.92
31.92
31.97
624.70
33.60
33.67
687.97
41.46
41.55
740.98
48.85
48.93
871.53
70.61
70.59
1091.7
121.34
121.06
1367.1
220.57
220.72
R (theory) . .
R (observation)
So far we have been dealing with substances that lose
their rotatory power when they are brought into a liquid
state by fusion or solution. There exists, however, a large
number of substances that have this power although they
are liquids, and that retain it even when the liquid is
turned into a vapor. Thus, in 1815, Biot discovered that
turpentine is optically active, this important discovery, like
several others in science, being accidental, as it was made
when Biot was searching for something quite different.
Two years later the same physicist made a discovery that
is still more interesting from our point of view. He looked
for rotatory power in the vapor of turpentine, and actually
observed it. His most conclusive results were obtained
when working with vapor in a tube about fifty feet long, set
110 LIGHT
up in an old church at Luxembourg. However, although
he saw clearly that there was rotation of the plane of
polarization of the light that had passed through this tube,
he was prevented from measuring it accurately, as the
inflammable vapor ignited and destroyed his apparatus.
Science had to wait nearly half a century until the investi-
gation was resumed in 1864 by Gernez. He succeeded in
determining the rotations produced by various liquids and
in showing that their rotatory power is retained when they
are transformed into the state of vapor. This is a very
striking result, in view of what has been said as to the
probable explanation of optical activity. This power has
been ascribed to structural arrangement, and yet there
seems no possibility of permanent structure with the
molecules of a vapor which are in constant motion. This
seems to drive us to the hypothesis of structure not of the
molecules, but in the molecules themselves. The atoms of
which the molecules are built may be arranged in such a way
as to produce optical activity, so that the study of our
subject lures us into the rich and expansive field of Stereo-
chemistry. This is that fruitful department of modern
chemistry that concerns itself with the arrangement of
atoms in space and seeks to determine how, if you were
making a model of a molecule, you would place the different
atoms of which it is composed. We have time only for a
hurried glance into this field, enough perhaps to stimulate
our desire for further knowledge and to break down a por-
tion of the arbitrary boundary that has been set up between
chemistry and physics.
The first epoch-making work in the direction that has
just been indicated was that of Pasteur, who, in 1848, took
up the study of the rotatory power of different forms of
POLARIZATION 111
tartaric acid. He found it possible to separate this acid
into four different classes, all with the same chemical
constitution (i.e. made up of the same elements), but with
different physical structure and different optical power.
Two of the classes were optically inactive, and two had
rotatory power. One of the inactive acids had the pecul-
iarity that when it was crystallized, its crystals, on careful
examination, proved to be separable into two distinct types,
whereas, with the other inactive acid, the crystals were not
thus separable. The two types of crystals that have just
been mentioned as constituting together the inactive acid
of the first class, differed from one another in a simple yet
remarkable manner. Their points of resemblance and of
contrast were exactly like those of certain objects and their
images as seen in a plane mirror. Your right and left hand
have many points of likeness, but yet they are quite differ-
ent. They are not superposable ; twist the right hand
as you will, and it refuses to fit into a glove made for the
left. If you hold the right hand before a mirror, and look
at the image, you will see a left hand, so that the relation
between the two types of crystals under discussion might
be indicated by saying that one type was left-handed and
the other right-handed. Pasteur, after separating these
types from one another, formed a solution of each. The
right-handed type was found to have the same chemical
constitution as the original acid of which it formed a part ;
but instead of being inactive, it had rotatory power. It rotated
the plane of polarization, let us say, to the right, and so
was ctoro-rotatory. The left-handed type had also the
same chemical constitution, but it, too, was optically active
and too-rotatory. The presence of equal quantities of
these two types in the original acid explained its inactivity,
112 LIGHT
for each neutralized the other, the right-handed rotation
produced by the first type being exactly counterbalanced
by the left-handed rotation of the second. From the con-
sideration of these and similar phenomena, Pasteur was
led to make the general statement that all organic com-
pounds could be divided into one or other of two groups,
according to the form of their molecular arrangement. It
will be observed that not every object differs in appearance
from its image in a plane mirror ; in the case of a perfectly
regular figure, such as a cube or a regular tetrahedron,
object and image are superposable. On the other hand,
with such objects as a screw, an irregular tetrahedron, or
the hand, object and image are not superposable. Pasteur
suggested that when the arrangement of the atoms fell
into the first of these classes there would be molecular sym-
metry, and the substance would be optically inactive ; but
a group belonging to the second class would represent mo-
lecular asymmetry, and rotatory power would be expected.
After Pasteur's researches, the next great impetus to
work in this field was given in 1874 by the speculations
of Van't Hoff and Le Bel. The fundamental conception
here was a definite arrangement of atoms, the so-called
tetrahedral molecule, which has formed the basis of the
larger part of later speculations in stereochemistry. It is
now a commonplace of the text-books, and it would be
out of place to discuss it here further than is necessary to
give a general impression of the main ideas, in so far as
they throw any light on the problem of optical activity.
We have already remarked that the fundamental idea of
stereochemistry is that, in a given compound, the atoms
composing a molecule are arranged in a definite form, and
the fundamental problem is to determine that form for
POLARIZATION 113
different compounds. Now Van't Hoff's hypothesis is
that, in the case of organic compounds, the arrangement
is such that the different atoms, or groups of atoms, occupy
the four corners ABCD (Fig. 27) of a tetrahedron, the
carbon element being in the center. If this were so, it
would be convenient to separate carbon compounds into two
classes, in the first of which there is only one carbon atom
present, and in the second there are
two or more such atoms. In the
first class, if the four groups at the
corners of the tetrahedron were all
different, any arrangement and its
optical image would be different.
Thus every form would have its as-
sociate, and as each would be unsym-
metrical, they would both be optically
active, one rotating to the right and the other to the left.
A compound made up of equal parts of these two forms
would be neutral, and so optically inactive. Hence in this
class we should expect three modifications of any arrange-
ment : one dextro-rotatory, another Isevo-rotatory, the
third inactive. In the second class, where there were
more than one asymmetric carbon atom in the molecule,
the number of possibilities would be greater. The case of
tartaric acid has already been described. Here we have
four different forms one dextro-rotatory, another laevo-
rotatory, a third inactive, being compounded of equal pro-
portions of the first two, and a fourth also inactive, but
for a different reason. This inactive form differs from the
other in that it cannot be resolved into active constituents.
The molecule is built up of two similar halves, so that
there is optical compensation within the molecule itself.
114 LIGHT
A great deal of work has been done in this field since 1874,
and there has been much to give support to the main lines of
the theory here set forth. It has been found that there is
no rotatory power in any compound that does not contain
an asymmetric carbon atom, and that by introducing or re-
moving such atoms from a substance the power of optical
activity can be made to come or go. Many of the difficul-
ties that early presented themselves have been removed.
Thus, at the outset, several substances that contain an asym-
metric carbon atom were found to be inactive, contrary to
the theory; but later research has shown either that such
substances really possess some rotatory power (although a
feeble one), or that they consist of mixtures in equal quan-
tities of two oppositely rotating constituents, or that they
are made up of two similarly constituted halves, which,
although not separable, have oppositely rotating powers.
Of special importance in this domain have been the re-
searches of E. Fischer on the members of the sugar group.
If Van't Hoff's hypothesis be right, then it is a simple prob-
lem of permutations and combinations to predict the num-
ber of different modifications that should be possible with
a given group of atoms. If the mathematical problem be
too hard or too repellent, you may reach the answer by the
aid of models and a little patient trial. You have merely
to attach a series of differently colored balls to the corners
of a tetrahedron, and see how many different arrangements
it is possible to make. In doing this you may learn more
than the mere number of different forms in which the com-
pound could exist, for, by observing the salient points of
resemblance and contrast between different arrangements,
you may get hints as to the significance of these for chem-
istry and for optics. Thus, when Fischer was working on
POLARIZATION 115
the members of the sugar group, he made a careful examina-
tion of dextrose, and concluded from its chemical reactions
that the atoms in the molecule were arranged in a certain
way. The arrangement was not symmetrical, and the
substance was optically active of the right-handed rotatory
type. Fischer concluded that there might be expected to
exist another form, the arrangement of whose atoms would
be related to that just mentioned in the same way as an
object and its image in a mirror. He succeeded, after care-
ful trial, in actually isolating such a form, one that was
also optically active, but of the left-handed rotatory type.
Perhaps enough has been said to indicate that the hy-
pothesis of a definite arrangement of the atoms in the mole-
cules of a substance is not a mere idle speculation. It has
proved a very useful conception in modern chemistry, but
our interest in it here is mainly for the light it throws on the
problem of optical activity. We have seen that rotatory
power is always associated with an asymmetrical arrange-
ment of the atoms, and when dealing earlier with quartz
and similar active solids, we remarked that lack of sym-
metry would result in right- and left-handed circularly
polarized waves traversing the medium with different
speeds, and so would account for the rotation of the
plane of polarization. .
Apart, however, from all such speculations, it may be
well to remark that there is no doubt about the fact of
rotation, so that, whether these theories find favor or not,
we may make use of this fact in any way that seems good
to us. The facts that are simplest and most important
to bear in mind are as follows: Not every substance is
optically active, but many possess this power of rotating
the plane of polarization of a beam of light that passes
116 LIGHT
through them. The amount of the rotation is found to
depend on the temperature, and also on the color of the
light that is employed. For light of a definite color (e.g.
that of one of the sodium lines), the rotation varies directly
as the thickness of the substance traversed by the light.
In the case of liquids it depends also very markedly on the
strength of the solution, and this has given rise to a very
simple and very important plan for estimating the strength
of a given solution. It could be carried out with the ap-
paratus used in the experiment with which this lecture was
begun. Let light from a sodium flame pass through the
first of these Nicol's prisms. It issues, as we have seen, as
plane polarized light, and we can determine the plane of
polarization exactly by noting the position in which the
second Nicol must be placed in order to cut off all the light
from the screen. Now put a vessel containing an optically
active solution between the Nicols, and you will find that
the second Nicol must be turned through a certain angle
in order once more to completely cut off the light from the
screen. If you have a means of measuring carefully the
angle through which the Nicol was turned, you know ex-
actly the rotation of the plane of polarization that this
solution has produced. If, then, by previous experiment,
you have determined the strength of solution that produces
that amount of rotation, you realize that your problem is
solved. I have suggested the use of Nicols, but of course
other means of producing polarization may be employed. A
great variety of polarizing apparatus has been invented and
is constantly being used to determine the strengths of solu-
tions of such substances as nicotine, cocaine, starch, and
alcohol, and most important of all, considering the magni-
tude of the commercial interests involved, of sugar.
POLARIZATION 117
It may seem a curious ending to a lecture that deals
entirely with what seems almost painfully " unpractical/'
polarization, rotatory power, molecular structure, and
the like, to refer to means of measuring the strength of
alcohol or the value of a cargo of sugar. If, however, you
know anything of the history of science, you will not think
it strange at all, but will rather be inclined to regard it as
typical of almost countless similar cases. No wise man
would undertake to draw quite clearly the line between
" practical" and "unpractical," between "useful" and
"useless," knowledge. By all means let us be practical
and useful, but let us use these terms in no narrow sense,
nor suppose for a moment that the race will advance most
rapidly, even with material things, by sticking closely
to what is obviously "practical." If our ancestors had
always been sticklers for "practical" knowledge, we should
probably still be eating acorns.
VI
THE LAWS OF REFLECTION AND REFRACTION
IN the opening lecture of this course it was remarked
that man's knowledge of optical laws might be summed
up almost to Newton's day within the compass of a single
sentence. Of general principles all that was known was
the fact and the law of reflection (as regards direction only),
the fact of total reflection, and the fact of refraction. It
is difficult for any but a specialist to realize what enormous
advances have been made since then, both in observation
and in theory. We now have a great variety of instru-
ments of precision that enable us to observe most optical
phenomena with marvellous accuracy, and a theory has
been developed that enables us to group together the whole
mass of facts with the utmost simplicity and with almost
startling success. Few men are in a position to understand
the searching nature of the test that can now be applied
to optical theories, and to appreciate how well the modern
theory stands the test. Not until you have put yourself
in such a position can you understand the confidence of a
modern physicist in his theories. He is no longer content
with a mere descriptive theory which tells him in a general
way that such and such phenomena are to be expected.
His theory must enter into the minutest details and predict
quantitatively. It must tell him that if he measures this
or that with sufficient accuracy, he will find its measure to
be so and so. In the case of the modern theory of light,
118
THE LAWS OF REFLECTION AND REFRACTION 119
all the improvements and all the refinements of modern
instruments but tend to confirm the correctness of the pre-
diction. I have already given you instances of this (for
example, when dealing with dispersion) ; but, even at the
risk of wearying you with figures and with tables, I must
give you more of a similar kind to-night and in later lectures.
Let us look first at the simpler and more generally known
laws of reflection and refraction. These deal only with
the directions of the various
rays, and show how to de-
termine the directions of
the reflected and refracted
ray of light when that of
the incident ray is given.
In Fig. 28 AB represents
an incident ray which
strikes a reflecting surface
BK at the point B, in such
a way that part of the light is reflected along the ray BO,
and the rest refracted along BH. If EBF be drawn at
right angles to the reflecting surface, the plane containing
AB and BE is called the plane of incidence. The law
of reflection, which determines the direction of the re-
flected ray, states that BC is in the plane of incidence
and that the angle EBO is exactly equal to the angle
EBA, orr = i, with the notation indicated in the figure.
The law of refraction (sometimes called Snell's law,
having first been laid down by Snell in 1621) states that
the refracted ray BH is also in the plane of incidence,
and that the angle FBH is connected with the angle
A BE by the relation sin i = /A sin r', where /A is a constant
depending on the nature of the two media on each side of
120 LIGHT
BK, and known as the relative refractive index of these
media. (If the space above BK is a vacuum, then n is
the absolute refractive index, or simply the refractive index
of the medium below BK.) As it is impossible to find an
angle whose sine is greater than unity, SnelFs law shows that
r' could not be found if the angle of incidence i were such
that sin i were greater than n, the relative refractive index.
If the first medium be more highly refractive than the sec-
ond, for example, if the first be water and the second air, then
the relative refractive index //. is less than unity, and the
angle whose sine is equal to fi is called the critical angle.
Under such circumstances r' would be impossible if the
angle of incidence i were greater than the critical angle
so that we should expect that there would be no refracted
ray, and that all the light would be reflected. This is the
phenomenon of total reflection that was brought before your
notice in the first lecture, and the point to be noticed now
is that Snell's law indicates exactly the conditions under
which this phenomenon is to be expected.
All these laws with reference to reflection, refraction,
and total reflection have been verified experimentally with
the greatest precision. Of all the countless experiments
that have been made with reflected beams, no careful
measurement has ever suggested the slightest departure
from the law of equal angles, i = r. And the same may
be said of Snell's law of refraction. Of course there is
a possible error in all such measurements, for no amount
of care can make them absolutely exact. A considerable
part of modern science consists in estimating carefully
the probable errors of measurement. To test these laws
of reflection and refraction, it is necessary to measure cer-
tain angles, and this, with the wonderful instruments of
THE LAWS OF REFLECTION AND REFRACTION 121
to-day, can be done with great nicety, though of course
not with absolute precision. With very great care the
angles may be measured accurately enough to insure the
correctness of refractive indices to six places of decimals;
but even with the care and skill necessary to insure this
degree of accuracy, no one has found any departure from
Snell's law that was outside the limits of the probable errors
of experiment.
It will have been observed that these laws of reflection
and refraction are merely condensed statements of experi-
mental facts. No theory is involved in them ; they simply
sum up in a convenient form the results of a large number
of observations and so serve one of the great ends of science
to save labor and relieve our memories of the burden of
too many isolated facts. If, however, we are imbued with
the scientific spirit, we cannot rest content with such laws,
but must strive to fit them in with our other knowledge
and to get a view of optics that is comprehensive enough
to take in these laws and all else within the optical field
besides. To this end we need a theory of light, and for
about a century there has been little doubt as to the gen-
eral lines along which such a theory must be developed.
We need a wave theory of some kind, that is, we must think
of light as due to a periodic disturbance like a wave propa-
gated in a medium. Now, if we set out with any such wave
theory, and with the conception that a wave travels with
a definite speed in one medium (such as air), and with a
different speed in another (such as glass), we are led simply
and inevitably to just these laws of reflection and refraction
of which we have been speaking. These laws are required
to secure continuity at the interface between two media;
without them there would be a rupture there or a sudden
122 LIGHT
break. At present I cannot stop to prove such a statement,
although it is very easily proved; I must simply ask you
to believe that it is so, and that the relative refractive index
of which we have spoken is the ratio of the speeds of the
waves in the two media under consideration.
As far, then, as the mere directions of the reflected and
refracted rays are concerned, almost any wave theory will
account for the facts. But other things than these directions
must be considered. Suppose that you are studying the
effect of waves that you see running across the surface of a
lake. You may well want to know more than the mere
direction in which they are moving. If you wish to esti-
mate the damage that the waves will do when they strike
upon some object, you will want to know their height.
In an ether wave which, according to our theory, gives us
the sensation of light, each element of the ether vibrates to
and fro about some mean position. Its greatest displace-
ment from this position corresponds exactly to the height
in a water wave, and is technically known as the amplitude
of the wave. This you will wish to know if you are to meas-
ure the intensity of the light, for it may be proved that the
intensity depends on the amplitude, and is, in fact, propor-
tional to the square of this amplitude. Another important
element in a wave of water, or of anything else, is its phase.
Watch two waves, similar in height and shape, running
side by side along the surface of some water. The crest of
one may always be in line with the crest of the other. In
this case they could be described as being "in phase," or
"in the same phase." More probably, however, the crest
of one would lag somewhat behind that of the other. To
describe this we should say that there was a " difference of
phase" between the waves, and this difference might be
THE LAWS OF REFLECTION AND REFRACTION 123
a matter of much import. (As a matter of fact, it would
have great importance if we came to consider the effect
of combining the two waves, as we shall see in the next
lecture on Interference.) What, then, does a wave theory of
light tell us of the amplitude (or intensity) and the phase
of the reflected and of the refracted beams, and how do
the predictions of theory compare with the results of obser-
vation? These are very important questions. They are,
indeed, crucial in optical theory, for they enable us to dis-
tinguish one wave theory from another, and to say which
best fits the facts. This, of course, settles the question as
to which theory is to be preferred, for the whole end of a
scientific theory is to fit the facts ; if it fails to do this, it is
probably worse than useless. What, however, do we mean by
distinguishing one wave theory from another ? Any theory
of light that endeavors to coordinate its phenomena by
means of the conception of a to-and-fro motion propagated
in the ether may be called a wave theory; but before such a
theory can lead us to precise results, we must formulate defi-
nite ideas as to the nature of the ether. Here there is room
for difference of opinion, and so for different wave theories.
In any case the idea of an ether is an abstraction; it is reached
by taking away certain properties of ordinary matter and
endowing an ideal medium with all that remains. Without
such a process the ether could not be thought of at all, for
our mental conceptions are necessarily derived, more or
less directly, from our experience. Such abstract ideas
are common enough in scientific and even in ordinary
discussion. Thus we have the idea of an incompressible
substance. We observe that air is easily compressed, that
bread resists compression more strongly, and that water
opposes with tremendous force any attempt to diminish its
124 LIGHT
volume. It is an easy matter in thought to carry on the
process until we have abstracted completely the power of
yielding to compression, and so we reach the abstract idea
of an incompressible substance. If we were interested in
considering the motion of such a substance, we might well
apply accepted dynamical principles to aid us in the dis-
cussion, and so we might reason as to its behavior, even
although it would be impossible actually to point to a sub-
stance that was incompressible. Again, we have the idea
of a frictionless fluid. We observe that if w pull a spoon
through treacle, the treacle resists the motion, and we have
to exercise a considerable force to overcome this resistance,
or friction. If we replace the treacle by olive oil, the friction
is diminished, while with water it is scarcely perceptible.
Here, again, it is not difficult to abstract the viscosity, the
power of opposing motion by friction, and so to arrive at the
abstract idea of a frictionless fluid. In this case, also, we
might apply dynamical principles to aid us in discussing the
behavior of such a fluid, and we need not be hampered in
that discussion by the fact that no one has ever presented
us with a bottle of a frictionless fluid. Now the ether that
is spoken of so much in these latter days in various
branches of science is a similar abstraction. Let us begin
with ordinary matter, a piece of steel or jelly, say. It has a
definite density, and definite elastic constants which meas-
ure its powers of resistance. It resists a change of volume ;
it requires force to compress or expand it. It resists at-
tempts to twist it and change its shape. Such powers of
resistance can be measured on a definite scale and expressed
numerically by means of such elastic constants as com-
pressibility and torsional rigidity. It seems natural in a
wave theory of light to begin with an ether that has all
THE LAWS OF REFLECTION AND REFRACTION 125
these powers, and to see if, by a proper choice of the con-
stants representing density, compressibility, and rigidity,
it is possible to account for the phenomena of light. This
is the famous elastic solid theory of light. If a disturbance
is set up in a medium such as has been described, it is easy
to show that waves will be propagated with a speed that
will depend on the magnitude of the elastic constants.
Moreover, in passing from one medium to another with dif-
ferent elastic constants, reflected and refracted waves will
be set up, and, as has been indicated already, the directions
of these will correspond exactly to those laid down by the
laws of reflection and refraction that have already been
formulated and have been fully verified by experiment.
It would thus appear that we are on the right track; but
when we come to look carefully at the other features of the
waves, their amplitudes and phases, we begin to encounter
difficulties. There are other difficulties that I need not
refer to ; it will be sufficient to say that the only successful
way of overcoming them all is to abstract something from
our ordinary elastic medium. We have too much cargo and
must lighten the ship. Let us throw over all power of
resisting change of shape, except the power of resisting a
twist. The medium so obtained will possess the mobility
of a fluid with some of the rigidity of a solid. As it does not
resist a mere change of shape, it will allow bodies to move
freely through it like a fluid; but it objects to twisting of
its elements, and so has rigidity. A fluid like water, with
a number of little gyrostats spinning in it, and by their
momentum opposing any change of spin, might serve as
a rough model to bring to mind the peculiar properties of
this " rotationally elastic" ether. It might be impossible
to construct this model, but there is no great difficulty in
126 LIGHT
conceiving of such a medium by the process of abstraction
and of reasoning as to its behavior in obedience to general
dynamical laws. Such a medium, if disturbed, will transmit
the disturbance as a wave (i.e. a periodic displacement), and
this wave will not be of the longitudinal type, but of the
transverse kind that the phenomenon of polarization demands
from any theory of light. The speed with which the wave
travels will depend on the rigidity and the density of the ether,
and the ratio of the constants representing these quantities
must be chosen so as to fit in with the observed value of the
speed of light in vacuo where there is nothing but ether
to affect the speed. The presence of matter will modify
the effective rigidity, so that a wave will travel with a dif-
ferent speed in water or glass than in vacuo. In passing
from one of these media to the other, there will be reflection
and refraction, and provided that we assume that there is
no discontinuity of motion at the interface, no rupture at
the surface of separation, the general principles of dynamics
will enable us to calculate not only the directions of the
reflected and refracted waves, but also their amplitudes
and phases. When this is done, it becomes at once evident
that the condition of the reflected and refracted waves must
depend on the state of polarization, as well as on the direc-
tion, of the incident beam. Two important cases present
themselves : in one the light is polarized parallel to the plane
of incidence, and in the other at right angles to this plane
these cases being specially important, as the details of all
other cases can be immediately deduced from a considera-
tion of these two. Then it also appears, as might be ex-
pected, that the results depend on the nature of the tran-
sition from one medium to the other, from air to water, say.
In any case, actually presented in an experiment, this tran-
THE LAWS OF REFLECTION AND REFRACTION 127
sition may be absolutely sudden, or it may be more or less
gradual. Such a question cannot be decided offhand; to
the eye the transition may look quite sudden, but this
effect may be due to imperfections of our vision, and if we
could see things at close enough range, the idea of an abso-
lutely sudden transition might appear illusory. However,
the hypothesis of a sudden transition is probably the natural
one with which to begin, and it was on this hypothesis that
formulae from which to calculate all the details of the re-
flected and refracted waves were first obtained. In the
present course I have promised to eschew mathematics
as much as possible, so that here we must be content with
a graphical representation of the formulae. Instead of
looking at all the details, let us for a time concentrate our
attention on a single one, the intensity of the reflected beam
a quantity, as has been remarked, that is proportional
to the square of the amplitude of the reflected wave. In
Fig. 29 the curves marked R and R' represent the percent-
age of the incident light reflected from glass, whose refrac-
tive index is /* = 1.52, at different angles of incidence i.
The different angles of incidence are indicated by distances
measured across the page, and the corresponding percent-
age of reflected light by distances at right angles to this.
Both curves represent the formulae obtained from theory in
the manner just indicated, R' dealing with light polarized
parallel to the plane of incidence, and R perpendicular
thereto. It is specially worthy of remark that for the latter
case the intensity begins to diminish as the angle of inci-
dence (i) increases, that it goes to zero at the point marked
P, and then rapidly rises. The theory indicates that the
position of the point P is determined by the simple formula
tan i = /*. At this angle none of the light that is polarized
128
LIGHT
perpendicularly to the plane of incidence is reflected, so
that all the light that can be reflected at that angle is po-
larized parallel to the plane of incidence. This indicates
100
1
90
80
70
60
I
I
1
'
/
1
\
I
I
[ I
40
/
/
/
1
J
'
1
L
J
y
1
/
j
Percentage i
1 """ O C
x
R/
X
/
-
-
-
-
'
-
-~
^^
-
/
*
10 20 30 40 50 P 60 70 80 90
Angle of Incidence (t)
FIG. 29
that by simple reflection we have a means of producing
plane polarized light. We have merely to arrange that
light should fall on a reflecting surface at the proper angle.
This angle is given by the formula tan i = p, and is called
THE LAWS OF REFLECTION AND REFRACTION 129
the polarizing angle. It is just about a century since Malus
discovered that light could be polarized by reflection, and a
few years later Brewster deduced from a series of experi-
ments that the polarizing angle was given by the formula
tan i = p. The following table shows how the values of
the polarizing angles of different substances, calculated
from the theoretical formula tan i = /*, agree or disagree
with the angles actually observed :
i (theory)
53 7'
53 18'
55 33'
55 37'
58 13'
58 36'
i (experiment) .
53 7'
53 18'
55 33'
55 37'
58 12'
58 36'
i (theory) . .
59 41'
60 30'
63 33'
67 7'
67 32'
67 40'
i (experiment) .
59 44'
60 30'
63 34'
67 6'
67 26'
67 30'
It will be seen that the agreement is very close, but not
perfect, and we should find results of the same character
if we compared the theoretical and observed values of the
intensity of the reflected light, and, what are much more
readily measured with precision, certain phase relations. In
all cases the theory fits the facts very nearly, but not ex-
actly. We find, however, that all these minute discrep-
ancies disappear when we abandon the hypothesis of an
abrupt transition from one medium to another. A com-
parison of theory and experiment then gives us the means of
estimating approximately the thickness of the surface layer
within which the transition takes place. We find in many
cases that it is less than one-hundredth of a wave length, and
how extremely short that is for ordinary light will be made
apparent in a later lecture. Let us see how well our theory
fits the facts when we take into account the influence of
130
LIGHT
this transition layer. We shall consider first the intensity
of the reflected light, although the intensity cannot be meas-
ured so accurately as most of the other features with which
we have to deal. It is true that there has been a great im-
provement in photometric processes of recent years, but
these are still far from the stage of precision that has been
attained in other departments of optics. The following
table gives the percentage of the light reflected at different
angles of incidence (i), calculated from theory for the case
of glass, and compares the results with the most careful
observations of the amount of light actually reflected :
i
10
20
30
40
Percentage Reflected (theory) . .
3.78
3.78
3.90
3.92
4.39
Percentage Reflected (experiment)
3.78
3.78
3.77
3.92
4.37
i
50
60
65
70
Percentage Reflected (theory) . .
5.37
8.31
11.28
16.12
Percentage Reflected (experiment)
5.53
8.34
11.16
16.04
Some of you, who find numbers distasteful or hard to com-
prehend, may prefer to see these results exhibited in a form
that appeals to the eye. For this purpose they are ex-
hibited graphically in Fig. 30. As we shall have quite a
number of similar figures before our course is run, it may
be well to adopt a uniform mode of presentation and explain
it once for all here. You should bear in mind, then, that
in all such figures, the continuous curve corresponds to the
predictions of theory, while the crosses indicate the results
of actual experiment. Thus the agreement or disagreement
THE LAWS OF REFLECTION AND REFRACTION 131
between theory and observation is measured by the degree
of closeness with which the crosses lie along the continuous
curve. In this case it will be observed that the agreement
16
14
12
10
,. 10 20
Angle of Incidence (i)
40
60
Fio. 30
is very close, especially in the region where the incidence is
small, in which accurate measurements are most easily made.
An inspection of the figure will show that, in the case of the
most marked disagreement, it is more probable that the meas-
ure of intensity was rather too high, or too low, than that
132
LIGHT
the theory is in error. In nearly all cases the differences
between theory and observation are well within the limits
of the probable errors of experiment.
So much for the intensity of the reflected light. Next,
let us suppose that matters are so arranged that the in-
cident light has equal intensities when polarized parallel
and perpendicularly to the plane of incidence, and let us
measure the ratio of the intensity of the reflected light that
is polarized perpendicularly to the plane of incidence to
that of the reflected light that is polarized parallel to this
plane. The measurement of this ratio can be made far
more accurately than that of the intensity of any light. Its
value can be obtained without any photometric processes
at all, simply by ascertaining the position of the plane of
polarization of the reflected light, and the measurement
of the angle determining this position is an operation that
can be performed with great delicacy. The table that fol-
lows gives us the means of comparing the values of this ratio
in the case of reflection from diamond at various angles of
incidence and of estimating the degree of accuracy with
which the theory fits the facts :
i
60
61
62
63
64
65
Ratio (theory) . .
.0421
.0324
0234
.0166
.0104
.0056
Ratio (experiment) .
.0420
.0312
.0213
.0178
.0102
.0057
i
66
67
67 30'
68
68 30'
69
Ratio (theory) . .
.0028
.0009
.0006
.0007
.0013
.0020
Ratio (experiment) .
.0030
.0009
.0006
.0007
.0013
.0026
i
7O
71
72
73
74
75 .
Ratio (theory) . .
.0049
.0103
.0177
.0275
.0399
.0552
Ratio (experiment) .
.0054
.0106
.0184
.0296
.0469
.0576
Qi- j nc.
UNIVERSITY j
OF /
OF REFLECTION AND REFRACTION 133
The graphical representation of these results is exhibited
in Fig. 31, and from either the figure or the table it will be
seen that the agreement between theory and observation is
extremely satisfactory.
Another quantity that is capable of very accurate meas-
urement is the difference of phase between the two reflected
0.05
\
0.04
0.03
\
\
0.02
0.01
waves when one is polarized parallel and the other per-
pendicularly to the plane of incidence. The results for
diamond are shown in Fig. 32, the difference of phase being
expressed as a decimal fraction of a wave length, so that for
a difference marked 0.5 one wave is half a wave length be-
hind the other, and thus the crest of the first is in line with
the hollow of the second. It was pointed out earlier in this
lecture that, on the theory of an absolutely abrupt transi-
tion from one medium to another, the polarizing angle
would be given by the formula tan i = /*, and a table was
134
LIGHT
made out which showed that this is very nearly true for
most of the substances referred to. The examination of
the influence of a thin surface layer of transition on the
position of the polarizing angle shows that the layer should
affect this angle very slightly, and that it might either in-
crease or decrease it, according to the nature of the layer.
0.5
0.4
0.3
It
^ 60 62
.Angle of Incidence (i)
64 66 68
FIG. 32
70
72
74
In the case of a certain specimen of glass, for which the
theory of the transition layer predicted a polarizing angle of
56 23' 38", the mean of a most careful series of experiments
fixed this angle at 56 23' 30".
Theory also shows that if the first of the two media in
contact with one another have a higher refractive index
than the second, the whole of the light will be reflected
when the angle of incidence is greater than the critical angle.
This is the phenomenon of total reflection already referred
to, and here, as elsewhere, the agreement between theory
THE LAWS OF REFLECTION AND REFRACTION 135
and observation is as close as could be desired. The
following table and Fig. 33 set out a comparison between
theory and experiment for the difference of phase (A)
between two waves that are totally reflected, one being
Difference^/ Phase
0-* p
L.w k. o
\
S
X,
1 j
- .
~ -t
-
^
i i i
H 1
H
^ -
tft x 40 42 44 46 48 B0 52 64 6
Angle of Incidence (i)
FIG. 33
*> J
polarized parallel and the other perpendicular to the
plane of incidence. The differences of phase are expressed
as decimal fractions of the wave length, and, as before, i
denotes the angle of incidence. The substance dealt with
experimentally had a refractive index, ^ = 1.619, and a
critical angle of 38 9'.
i
38 13'
39 58'
41 59'
44 3'
46 4'
A (theory) .
.488
.457
.379
.364
.358
A (experiment) . . .
.489
.457
.377
.364
.359
i
47 54'
49 58'
51 57'
53 58'
55 57'
A (theory) ...
356
356
360
363
368
A (experiment) . . .
.356
.357
.360
.363
.365
All these tables and figures have reference to reflection
from transparent, non-crystalline substances. If the re-
flector be a crystal, or if it be more or less opaque, theory
136
LIGHT
and experiment agree in showing that the laws of reflec-
tion may be considerably modified. The phenomena with
crystals will be dealt with in a later lecture, but we shall
100
90
80
70
60
60
#>
*! n/\
J
H
2 II
/
/
/
/
S
/
R
S*
^
^
^
?
M
-
. ,
_
.
_
_^-
-~^.
ft
"*""*
^
^v^
T?~
*
****.
>^
\
/
\
n
Percentage Reflectet
m ^g 8 %
s
** j,
,/
=
) 10 20 30 40 60 60 70 80 90
Angle of Incidence (i)
FIG. 34
not have time for more than a passing reference to the laws
of reflection from opaque substances, such as metals. In
this case what corresponds to the refracted wave is absorbed
by the metal, but theory enables us to predict all the details
THE LAWS OF REFLECTION AND REFRACTION 137
of the reflected beam. The laws are more complex, but
the general character of the results has some resemblance
to that for transparent reflectors. This will be made evi-
dent by a comparison of Figs. 29 and 34, which represent
corresponding quantities for glass and steel. It will be
0.5
n 4
/
/
/
0.3
0.2
^0.1'
/
/
x
7
/
/
/
x
^^
^
f
.
J
-^
30 40 50 60 70 80 91
^ Angle of Incidence (i)
FIG. 35
observed that in both cases for light polarized parallel to
the plane of incidence the intensity of the reflected beam
increases steadily with the incidence. With light polarized
perpendicularly to the plane of incidence, the intensity
in both cases begins by diminishing, reaches a minimum,
and then increases rapidly. The main difference is that
the amount of light reflected at normal incidence is very
much greater for the metal than for the transparent sub-
stance, and that even at the angle where the reflection from
the metal is a minimum (called the quad-polarizing angle
from its resemblance to the polarizing angle of a transparent
138
LIGHT
medium), there is still a considerable quantity of light re-
flected from the metallic surface. The difference of phase
between the two reflected waves is represented graphically
in Fig. 35 for the case of reflection from gold. This figure
should be compared with Fig. 32, which is the corresponding
figure for the case of reflection from a transparent substance.
It will be seen that in all cases the crosses lie closely along
the curves, indicating on all points an excellent agreement
between theory and observation. The numbers corre-
sponding to these figures are set out in the following
table:
i
R
(THEORY)
R
(EXPERIMENT)
R'
(THEOBY)
R'
(EXPERIMENT)
A
(THEORY)
A
(EXPERIMENT)
30
50.5
50.1
60.4
60.7
.028
.032
40
46.5
46.2
64.0
64.2
.052
.056
50
41.0
41.0
68.9
69.4
.088
.088
60
33.9
34.1
74.8
74.5
.135
.130
70
26.7
26.5
82.1
82.3
.211
.210
75
25.4
25.5
86.1
86.1
.265
.265
80
29.5
27.5
90.4
90.3
.331
.324
I hope that by this time enough has been said to show you
that modern optical theory gives a completely satisfactory
account of reflection and refraction, telling us all that we
can want to know with the utmost precision, and agreeing
in its predictions on every point with the most accurate
measurements of the best experimenters. We may thus
feel that we have our feet on solid ground when we set out
to apply this theory to aid us in the solution of any problem
that may present itself. In the time that remains of this
lecture I wish to speak mainly of the application of the
THE LAWS OF REFLECTION AND REFRACTION 139
laws of reflection and refraction to the design and con-
struction of optical instruments. Clearly, if I am to do this
at all effectively, I must limit myself strictly. The number
and variety of optical instruments is enormous, and it
requires not a little thinking to suggest many instruments
of great precision that do not involve some optical principle.
Optics has been called the " directing science" of modern
times, because the principles that have been developed in
its study have formed the basis of many of the most far-
reaching speculations in modern science. It deserves the
name perhaps even more truly for another reason. The
advancement of science depends largely on the precision
with which its researches can be conducted. Optical prin-
ciples enter into nearly all instruments of precision, and thus
the whole army of science is interested in these principles,
and should realize that it is under a deep obligation to those
men who have established them so firmly.
The laws of reflection and refraction that are most fre-
quently made use of in the design of optical instruments
are those simpler ones that deal with the directions of the
rays. These laws have already been stated and discussed,
but perhaps you will bear with me if I call your attention to
a different mode in which they may be presented. We have
seen that if a ray of light proceeding from A (Fig. 36),
strike a surface BC so as to be reflected to E, the lines
AB and BE will be equally inclined to the reflecting surface.
Suppose, now, that we endow a ray of light with intelligence,
and set it this problem: to start from A, strike the re-
flecting surface somewhere, and be reflected to E, and to
choose its path so that it will reach E as quickly as possible.
If you have any skill in elementary geometry, you will
be able to prove that B, the point of striking the reflector,
140 LIGHT
must be chosen so that AB and BE make equal angles with
BC ; in other words, the law of reflection must be obeyed.
Similarly, if you take the corresponding problem in re-
fraction, and ask the ray to set out from A (Fig. 36), be
refracted into another medium, and reach a point E in the
shortest possible time, you will find that here, again, the law
of refraction will have to be obeyed. In both cases you
can prove the statements by showing that the time of pass-
BQ
Reflection
FIG. 36
age along ABE is less than that along any other route, such
as ACE, and in the second problem you must bear in mind
that the velocity in any medium is inversely proportional to
the absolute refractive index of that medium. It would thus
appear that rays of light always try to reach their destina-
tion as quickly as possible a curious principle. It would
be very interesting to trace its development, its limitations,
and its applications to a variety of problems. However,
there is no time for this now, nor can we do more than refer
to the fact that this principle has suggested to science a much
more far-reaching law, what is known as the Principle of
Least Action, the greatest generalization of modern science.
The principle was first enunciated a century and a half
ago by Maupertuis, then president of the Berlin Academy.
THE LAWS OF REFLECTION AND REFRACTION 141
He laid it down because, in his judgment, it was eminently
in accord with the wisdom of the Creator. More modern
men of science do not often feel so confident about sharing
in the secrets of Providence; but they find the principle
none the less useful in making for the great end they have in
view to comprehend all knowledge in a single law.
To return to the application of the laws of reflection and
refraction, I repeat that it is necessary to limit myself very
strictly. You will find large treatises on Geometrical Optics,
which are taken up wholly with applications of the simplest
of these laws, and whole books that treat of their bearing
on the construction of special instruments. In the short
time that remains in this lecture, it is obviously impossible
to cover so much ground. I must select a single illustrative
example, and deal with one optical instrument, and even
with that in a very cursory manner. What is this instru-
ment to be? The one most generally interesting would
be the human eye, for there we have an optical instrument
that we must all use. Apart from that, it is extremely
interesting merely as an illustration of optical principles.
It is truly a wonderful instrument or combination of instru-
ments. It is at the same time a microscope, a telescope,
a range-finder, a stereoscope, a photometer, a kinemato-
graph, and an autochrome camera. An instrument that
serves so many purposes can scarcely be expected to be
free from imperfections, and the eye is not without its
defects. At the same time, to the student of optics it is
as interesting in its defects as in its strength. How to
cure these defects or how to minimize their evil conse-
quences is a human problem that requires for its successful
solution an intimate knowledge of the scientific principles
here discussed. However, the eye is not an instrument
142 LIGHT
that we have completely under our control ; at the best we
can supplement it. So it will be better for our present pur-
pose to take another instrument, where there are no such
limitations on our actions, and endeavor to indicate how
our knowledge of the laws of light may be employed to
make it as effective as possible. To this end, let us select
the Astronomical Telescope, the purpose of which is simple
and well known, to enable us to see distant objects as
clearly as possible, and in some cases to photograph their
details or their relative positions.
I need not spend time in emphasizing the fundamental
idea, which is to get an image of the object near at hand,
and look at this image through a magnifier. You are all
doubtless quite familiar with the idea of the image of an
object. You can obtain this by reflection from a mirror
which is either plane or curved. The plane mirror is the
only perfect optical instrument, in the sense that it forms
an image that is absolutely faithful to the original, free
from all distortion or other defects. A curved reflector,
as you know, produces a certain amount of distortion,
which is very marked if the object be a large one, such as
the human figure. You can also get an image by refraction,
as with a pair of spectacles, a hand magnifier, or a photo-
graphic lens with one or other of which every one is
more or less familiar. However, although the fact of an
image being formed in some such way is well known, you
may not have thought of the mode in which this image is
produced, or of the bearing of optical principles upon its
formation. Here we have time only for the briefest out-
line. The fundamental principle, as usually stated, is that
the image of a point is a point. Each point of an object
has its image, and the whole collection of such points forms
THE LAWS OF REFLECTION AND REFRACTION 143
a picture more or less like the original. Is it true, however,
that the image of a point is a point ? Yes, absolutely so,
if the reflector be a plane mirror ; but not so for any other
case. In all such cases, if we take a series of points in the
object, the rays from any one of them will, in general, after
reflection or refraction, or both, at best pass only approxi-
mately through a corresponding point in the image. They
may all pass very near indeed to this point in the image,
but again, many of them may pass some distance away,
and the clearness of the image will depend on how close to
a point the rays from any point of the object converge.
If we follow out the consequences of the laws of reflection
and refraction, we find that the rays from a point converge
more nearly to some other point if they all strike the reflect-
ing or refracting surfaces very nearly at right angles than if
they strike it at oblique and widely varying angles. The
latter, at best, will give a blurred image; the former will
make for clearness. Hence, in our telescope we must ar-
range that all the reflecting and refracting surfaces are
"square on" to the impinging rays, and we must choose the
form of these surfaces so that a slight departure from the
perfect square will introduce as little indistinctness as
possible.
In the case of a reflecting telescope the form of the re-
flecting surface is easily determined. The telescope being
used for astronomical purposes, the incident rays come
from extremely distant points, so that we have practically
to deal with a series of parallel rays striking the reflector.
It is a simple problem of geometry to prove under such
circumstances that the form of reflector that will give the
clearest image is a paraboloid the surface formed by re-
volving a parabola about its axis. Figure 37 represents a
144
LIGHT
portion of a parabola of which AX is the axis, S the
focus, AS the focal length, and BE' the aperture. The
geometrical property of the parabola, which makes it
useful for this
B optical purpose,
is that if P be
any point on the
curve, and PR
be drawn paral-
lel to the axis,
then the lines
SP and PR
make equal
angles with PG,
which is at right
angles to the
curve at P.
Hence a ray of
light that comes
from a distant
point in the di-
rection PR will
be reflected to
the focus S,
wherever be the
point P.
So much for
the form of the
reflector; what next as to its material? We want to
have the image as bright as possible, so we must have a
surface with a high reflecting power. Theory and ob-
servation agree in indicating some of the metals as the
FIG. 37
THE LAWS OF REFLECTION AND REFRACTION 145
best reflectors. In the earlier reflectors speculum metal
was commonly employed as being a fairly good re-
flector and not too expensive. Silver, however, is a
much better reflector, and any objections to its use
have been overcome by the discovery in recent times of
thoroughly satisfactory methods of depositing it chemically
upon glass. The thin film of silver is not expensive, and
the glass supporting it, if carefully made, is fairly rigid, and
so not very easily distorted. Freedom from distortion is
extremely important where good results are required, for a
slight change from the paraboloidal form will give different
images in different parts of the reflector and a consequent
blur. In fact, in the best modern reflectors, the greatest
care is taken to preserve their form ; they are kept as free
as possible from changes of temperature, and the system
of support is planned with the utmost thoroughness. It
was mainly through lack of such precautions that the great
reflectors of the past proved, in many ways, so disappoint-
ing.
Consider next the problem of the size of the reflector.
What is to be its aperture BB', and its focal length AS ?
A considerable increase in aperture will make the instru-
ment more cumbrous and greatly add to its cost. Its
countera vailing advantages are mainly two. In the first
place, a larger aperture collects more light, and so gives
a brighter image. This may be a matter of great im-
portance, if we wish to see or to photograph very faint
objects. The brightness of the image depends upon the
area of the aperture, and is therefore proportional to the
square of the diameter BB'. Thus, if BB' be doubled,
the brightness of the image will be increased fourfold.
The second important advantage of a large aperture
146 LIGHT
will be more fully appreciated after we have dealt with
Diffraction. In the lecture on that subject it will be shown
that the image of a point is not a point, but a disk whose di-
ameter depends upon the size of the aperture, being smaller
for large ones than for small. If you are looking at two
distant objects (e.g. a double star) through a telescope,
each point will appear as a disk, and the smaller are the
disks the less will they tend to overlap and produce a
blurred effect. Hence, if great resolving power is required,
the disks must be as small as possible, and this demands a
large aperture. The first great reflector (that of Lord Rosse)
was made more than half a century ago, and was 6 feet in
diameter. After a time a reaction set in against reflectors,
but they have come into prominence again of late, and now
such an instrument, with the enormous aperture of 100
inches, is being made for the Mt. Wilson Solar Observatory.
As to focal length, the advantage of increasing this is that
the size of the image is magnified in proportion. If you
double AS, you double the image, but there is a correspond-
ing disadvantage in greater length of telescope, and so
greater inconvenience and expense. Lord Rosse's telescope
had a focal length of 54 feet and was exceedingly cumbrous.
Having considered such questions as the size, form, and
material of the reflector, you may look for a moment at
the problem of making the glass support for the reflecting
film of silver. The glass must be as free as possible from
flaws or strains, so as to minimize the danger of a change
of shape, and to obtain a suitable disk of glass proves, in
the case of a very large reflector, a very arduous process.
Once this has been secured, the front surface of the disk is
made concave by means of a tool of suitable curvature. It
is important to avoid differences of curvature in different
THE LAWS OF REFLECTION AND REFRACTION 147
parts of the surface, and any errors of this kind can be
detected with extraordinary nicety merely placing the
finger on the glass will cause a swelling of the surface that
can easily be detected. After a uniform curvature has
been obtained, the next step is to set to work in the process
of polishing to hollow out the surface in the center so as to
produce an exact paraboloidal form, any departure from this
form being readily discovered by a simple optical device.
FIG. 38
Then the surface is silvered by one of those exceedingly
ingenious devices of modern times designed for this end,
and, let us hope, an almost perfect reflector is the result.
Now, if such an instrument were turned toward a star or
other heavenly body, it would produce an image of the
object in the neighborhood of the focus S. With great
focal length this image might be fifty feet or more
away from A, and so would be inconveniently placed for
purposes of close inspection. This inconvenience may
be avoided by intercepting the rays as they converge
toward S, and reflecting them backward so as to converge
to a point C behind the large reflector (Fig. 38). It is a
simple problem of geometry to determine, by the aid of
the laws of reflection, the form of the reflecting surface
that will produce this result. The surface must be a hy-
148 LIGHT
perboloid formed by the revolution about its transverse
axis of a hyperbola whose foci are S and (7, and it is made
by the same general processes as are employed in forming
the paraboloid. In order that the rays should reach C.
a hole would have to be made in the center of the large
reflector in the neighborhood of A. This has been
done in some telescopes, but the plan has many disadvan-
tages, and these may be avoided by again intercepting
the rays as they converge toward C by a small plane mirror
at D, and reflecting them to one side so as to form an image
at F. A reflecting apparatus made in this way will give
very good definition near the optic axis, but if the rays are
oblique to this axis the images will be indistinct. It is
therefore important that the instrument should be kept in
almost perfect adjustment, and the greatest care must be
employed to secure this, if the best results are to be obtained.
Thus far, in considering the formation of an image of an
object* we have supposed that this is achieved by means of
reflection. You need scarcely be reminded that the same
end can be reached by means of refraction. You must
all be more or less familiar with the action of a lens in
bringing the rays of light from a point to a focus, and it is
not difficult to investigate the features of the image thus
formed, by aid of the laws of refraction. What has already
been said as to the size of the aperture and the focal length
of the lens applies to a refractor just as to a reflector.
The form of the refracting surfaces is determined mainly
from the consideration that two defects must be specially
guarded against, these being known technically as chro-
matic effects and spherical aberration. The latter defect
has already been referred to, without the name. It has been
remarked that if rays from a point strike a surface obliquely,
THE LAWS OF REFLECTION AND REFRACTION 149
they are not brought (either by reflection or refraction)
to the same focus as when they strike the surface almost
at right angles. If, then, we have a number of rays striking
such a surface, some of them nearly normally and others
much more obliquely, there will be no definite image of a
point, and the whole image will be blurred and indistinct.
FIG. 39
Investigation shows that it is possible to lessen this indis-
tinctness by increasing the number of refracting surfaces.
A common arrangement is to have a double objective, such
as is illustrated in Fig. 39 a. This is made of two lenses
of glass of different refractive powers, one (Lj) of flint and
the other (L 2 ) of crown glass. The curvatures of the various
surfaces are arranged so as to make the defect due to rays
striking one surface obliquely counterbalance that due to
the other surfaces, and in every objective of any value
this is done with great precision.
150 LIGHT
In constructing the lenses it is important to avoid hav-
ing different curvatures in different belts of the lenses, as
this will inevitably introduce aberration and cause a blur.
Also, as the curvature of each surface must be maintained
constant, care must be taken to avoid its change due to
fluctuations of temperature, to flexure from the weight,
or any other causes. The danger of flexure is of course
much less serious with small lenses than with the large ones
such as those of the great 40-inch refractor of the Yerkes
Observatory. To avoid flexure with such large lenses, we
must have considerable thickness in the center of the lens,
and this introduces a serious defect when the telescope is
to be used for photographic purposes. The amount of
light absorbed in passing through a considerable thickness,
even of the clearest glass, is far from negligible, and it in-
creases enormously for those light-waves of high frequency
which play the leading part in photographic work. Hence,
if we wish to take a photograph of a faint object, so that
we cannot afford to lose much light, a thick lens is objec-
tionable. This is one of the reasons why refractors are
being replaced by reflectors for some of the work in modern
astronomy. Perhaps a stronger reason, however, is that
the reflector avoids entirely the serious difficulties due to
chromatic or color effects. The law of reflection is the
same for all colors, so that the position of the image after
any number of reflections is quite independent of the
color of the light, and no chromatic effects can possibly be
introduced by the process of reflection. With refraction,
however, it is very different. The laws of refraction show
that the position of the image depends on the refractive
index of the refractor, and this again depends on the color
of the incident light. White light, as we have seen, is a
THE LAWS OF REFLECTION AND REFRACTION 151
composite of many colors, and the image formed by each
of its constituents will be in a different place, and of a
different size. Clearness and precision in the image thus
appear to be impossible, and the question must arise can
this be avoided ? The answer is that it can, at least in a
partial manner. If we have two lenses, one may be made
of such a form and material that it will throw the red image
farther away than the blue, while the other reverses things
by throwing the blue farther away than the red. In com-
bination it may be arranged that they throw the two images
together. This is one reason why the objective of an
astronomical telescope is always made up of at least two
lenses, such as the double objective depicted in Fig. 39 a.
It is an easy matter to calculate how to arrange two lenses
of given materials so as to combine any two given colors.
If the telescope is to be used for visual work, it is natural
to combine two colors to which the eye is most sensitive,
such as green and yellow. This combination, however,
will be of little use for photographic work, as the rays that
are most important in that field have been neglected. To
improve matters, we may do as Ritchey did with the Yerkes
refractor, and put in a yellow screen to cut out the blue
and violet; but of course we do this at the expense of the
light that is most effective photographically, and it is often
our great end to conserve what little light there is. In any
case, when two differently colored images have been com-
bined in this way, the other colored images are not, as a
rule, combined. Their presence in different positions gives
rise to what are called secondary spectra, which not only
produce indistinctness, but cause a considerable loss in the
light that contributes effectively to the brightness of the
image. Thus it has been calculated that the loss from
152 LIGHT
this cause with the Lick 36-inch refractor was about one-
quarter of the whole light, and with other refractors of
shorter focal length the loss was considerably greater.
Modern researches and experiments in the manufacture
of glass have made it possible to select two glasses that
in combination avoid these secondary spectra almost
entirely. Unfortunately, however, the objectives so made
have not been wholly free from defects, the most important
arising from a lack of permanence in the quality of the
glass. With a triple objective consisting of three lenses,
Z/ 1; L 2 , Z/g, such as is depicted in Fig. 39 b, the chro-
matic effects can be avoided almost perfectly, but as yet
no very large refractors have been equipped in this fashion.
The cost, of course, is greater, and the extra lens in-
volves more loss of light by absorption, a serious thing,
as we have seen, especially in the photography of faint
objects.
So far we have been occupied entirely with the design
and construction of the objective, which forms the image
of an object, whether by reflection or refraction. We have
still to inquire what means are employed to get a close view
of the image so formed. For this purpose an eye-piece is
used, and this is designed to magnify the image, just as
when you take up a hand magnifier to look closely at a
small object. Our time is too far exhausted to enable us
to go into details as to the arrangement of the parts of this
eye-piece. Suffice it to say that, as a rule, it consists
of two lenses so constructed and placed as to diminish as
much as possible the defects due to spherical aberration
and the chromatic effects. It is not completely achromatic,
but an effort is made to bring it about that the different
colored images that are formed should have the same
THE LAWS OF REFLECTION AND REFRACTION 153
apparent size, as this avoids the indistinctness due to a
series of colored images overlapping one another.
The point that I have hoped to make clear to you in the
latter part of this lecture is that the design and construction
of a modern optical instrument is no haphazard process,
guided by rule of thumb. On the contrary, every detail is
carefully planned and calculated with the aid of the funda-
mental laws of reflection and refraction. Calculation, on
the basis of these principles, determines the size and the
form of the various parts; calculation determines their
relative position, calculation determines even the ma-
terials of which they are made. Absolutely nothing is
left to chance or guesswork; everywhere law and intelli-
gence are supreme.
VII
THE PRINCIPLE OF INTERFERENCE
THUS far, in dealing with the theory of light, we have
emphasized the idea of a periodic disturbance propagated
through a medium, and we have emphasized this because
the idea of periodicity is the fundamental one. Any such
periodic disturbance may be called a wave, and the theory
a wave theory of light; but it will be well to guard your-
selves against being misled by following too closely the
analogy presented by the familiar phenomena of water
waves. Here, too, you have the fundamental idea of a
periodic disturbance propagated with a definite velocity,
and it is doubtless because of this that the phrase a wave
of light is so generally employed. The analogy, however,
is not complete, and must not be pressed too hard; for
one reason, water waves, as ordinarily observed, are sur-
face phenomena; if you could see what goes on below the
surface, the analogy would be much more instructive. At
the same time there is much that arises in discussing light
that can be most conveniently spoken of in language that
is suggested by the familiar phenomena of water waves.
A common term when dealing with such matters is the
wave-length. In the case of waves in water this is some-
thing that you can readily see and measure, the distance
from crest to crest of consecutive waves. Suppose that you
are watching a swarm of corks floating on the water, and ob-
serve how they rise and fall as waves pass over them. If
154
THE PRINCIPLE OF INTERFERENCE 155
you fixed your attention on two successive corks, each of
which was at the highest point of its path, they would, of
course, be each on the crest of successive waves. After a
definite interval of time (the period) they would each
once more be on the crest of a wave, having fallen and
risen in the interval as the wave-form advanced. The
wave-length is the distance from crest to crest, and you
can see that there must be a relation between the wave-
length (X), the velocity of the wave-form (v), and the period
(p = l// ; where /is the frequency). This relation is, in fact,
\ = vp = v/f. In the case of light the velocity is always the
same where there is no matter (that it changes with the
frequency in the presence of matter was explained at con-
siderable length in the lecture on Dispersion). Hence, as
the frequency (/) changes with the color of the light, so
must the wave-length (X). In other words, differently
colored waves have different lengths. Waves of high fre-
quency, such as violet waves, are short; waves of lower
frequency, such as red waves, are longer ; what the actual
lengths are and how they are measured will appear in a
later lecture.
So far we have spoken of a single train of waves ; but
what if more than one train moves across the same space ?
It is an interesting and instructive thing to observe, if a
sheet of water be at hand. Throw in two stones at A and B
respectively. You will see a wave-form running outward
from each of these centers, and in due time the two trains of
waves will cross one another's path. A curious pattern will
be the result, and you may learn much by trying to account
for its leading features. The clue to everything here is
the Principle of Superposition of Small Motions, or the
Principle of Interference as it is usually called when its
156 LIGHT
applications to optical phenomena are under considera-
tion. The principle lays down a rule for determining the
effect of combining two small displacements due to dif-
ferent causes. It states that each cause produces the
same effect as it would were the other cause absent, and
that in computing the displacement due to the combina-
tion of both causes we have merely to add together the
displacements due to each separately, of course taking
account of the direction of the displacements in the process
of addition. Thus, if the motion due to one cause would
raise a point an inch, and that due to another would raise
it half an inch, then the point would be raised 1 + J, or
an inch and a half, under the combined influence of both
causes. If, on the other hand, one cause would raise a
point an inch and the second depress it half an inch, the
combination would raise it 1 J, or half an inch. Sup-
pose that we accept this principle and apply it to two
trains of water waves of the same height and length, and
moving in the same direction. What would be the com-
bined effect of two such waves? The answer would de-
pend entirely on their relative phase. If crest corresponded
to crest so that the waves were "in phase," the two would
combine into a single wave of double the height of each.
If, however, crest corresponded to furrow, so that there
was a difference of phase of half a wave-length, then the com-
bination would produce no wave at all, but absolute rest.
The crest of one would just fill up the furrow of the other,
and the two waves might be said to interfere with one an-
other. It is on this account that the principle is com-
monly spoken of as Interference. It is a principle that
was well known to Newton, and was applied by him to
explain certain phenomena of the tides. However, it was
THE PRINCIPLE OF INTERFERENCE 157
reserved for another great Englishman, Thomas Young,
to realize that the same principle is applicable to light and
to use it as a means of overcoming most of the obstacles
that had retarded the progress of the science of optics.
Young's is one of the very greatest names in science,
although almost wholly unknown to the man in the street.
He was endowed, according to Helmholtz, with "one of
the most profound minds that the world has ever seen."
His application of the Principle of Interference to light
was only one of his strokes of genius ; but it was far-reach-
ing in its consequences, and made Young in a sense the
father of the wave theory of light. It was he, more than
any one else, who, in the early days, just a century ago,
turned men's speculations along the track that has led to
so much in more recent times. Perhaps you would like
to hear how he expressed himself, as it is always interest-
ing to listen to an original thinker when he is expounding
his own ideas. Here, then, is a brief extract from his
writings on the subject of Interference:
"It was in May, 1801, that I discovered, by reflecting
on the beautiful experiments of Newton, a law which ap-
pears to me to account for a greater variety of interesting
phenomena than any other optical principle that has yet
been made known. I shall endeavor to explain this law
by a comparison. Suppose a number of equal waves of
water .to move upon the surface of a stagnant lake with
a certain constant velocity, and to enter a narrow channel
leading out of the lake. Suppose, then, another similar
cause to have excited another equal series of waves, which
arrive at the same channel with the same velocity and at
the same time with the first. Neither series of waves
will destroy the other, but their effects will be combined;
158 LIGHT
if they enter the channel in such a manner that the eleva-
tions of one series coincide with those of the other, they
must together produce a series of greater joint elevations;
but if the elevations of one series are so situated as to
correspond to the depressions of the other, they must
exactly fill up those depressions, and the surface of the
water must remain smooth; at least I can discover no
alternative, either from theory or from experiment. Now
I maintain that similar effects take place whenever two
portions of light are thus mixed, and this I call the general
law of the Interference of Light. I have shown that this
law agrees most accurately with the measures recorded in
Newton's " Opticks, " relative to the color of transparent
substances, observed under circumstances which had never
before been subject to calculation, and with a great di-
versity of other experiments never before explained."
I shall direct your attention in a moment to some ex-
periments designed to test or illustrate the Principle of
Interference, but before doing this I should perhaps state
explicitly that in applying it to the explanation of optical
phenomena you are not restricting yourself to any special
form of the wave theory of light. It is a principle that is
applicable to displacements of any kind, and its most im-
portant consequence for our present purposes is that an
upward displacement in the ether due to one cause may
be exactly counteracted by an equal and opposite down-
ward movement due to some other cause, and that this
will inevitably be the case if there be a certain phase rela-
tion between the two periodic movements. It is in this
way that two lights may produce darkness in certain
places, although it may at first seem paradoxical that a
combination of lights should produce darkness. Further-
THE PRINCIPLE OF INTERFERENCE
159
more, if you are to understand the experiments that are
about to be referred to, you should call to mind that white
light is of a composite character, and that, by suppressing
some of its constituents, color effects are produced. At
one place blue may be suppressed by interference, at an-
other green, and at another red, so that interference phe-
nomena should be characterized by bands of color wher-
ever white light is employed in producing them.
E
FIG. 40
One of the most famous of Young's experiments to
test his theory of interference is, in principle, as fol-
lows. Light is allowed to stream through, say, a verti-
cal slit the position of which is indicated by S (Fig. 40),
and to fall on two other vertical slits, A and B, which
are very close to one another in a screen parallel to that
containing the first slit S. The light is intercepted on
a vertical screen indicated by the section ECPF in the
figure. Now if we consider a point such as P on this
screen, it will be observed that it is illuminated by light
that comes from two sources, A and B respectively. As
things are arranged, the light that sets out from A at any
moment will be in the same phase as that which has B
as its starting-point; but that which travels to P along
AP will reach P in a different phase than the light from B,
for the two started together and moved at the same rate
along roads of different lengths. If the point P be so
160 LIGHT
situated that the difference between AP and BP be half
a wave-length, or any odd multiple thereof, the two lights
reaching P will interfere and nullify one another. Hence
the screen EF will not be uniformly illuminated, but there
will be a series of dark vertical lines, or of colored bands,
according as the incident light is homogeneous or other-
wise. If one of the slits (A or B) be covered, the bands
should disappear. All these
phenomena may be observed,
and the position of the bands
and the arrangement of the
colors are found to conform
in the closest manner to the
predictions of the theory thus
sketched. Figure 41 gives an
indication of the alternations of light and shade on the
screen EF.
Unfortunately, I am not able to show you Young's
experiment, owing to the difficulty of exhibiting the
phenomena to a large audience, but you will find it easy
to make the experiment for yourselves. One method of
proceeding is to rule two narrow lines very close to one
another on a photographic plate that has been developed,
and then to look through the slits so formed at the light
that shines through a slit in front of a bright light, such as
the electric light. A still simpler procedure is to make
two pinholes close to one another in a card, and look
through them at the light streaming through another hole.
With a little care you will see the interference fringes
quite distinctly. Another simple experiment designed to
show interference is due to Fresnel, one of the great names
in the development of the theory of light. He made light
THE PRINCIPLE OF INTERFERENCE 161
from a slit S (Fig. 42) fall on two mirrors, A and B, that
had their edges parallel to the slit and their planes in-
clined at a very small angle. After reflection from these
two mirrors, the two streams of light were in a condition
to interfere with one another, and a series of bands similar
to those just described made their appearance on a screen
PE. With this experiment, as with Young's, it is difficult
to arrange things so as to exhibit the phenomena to many
FIG. 42
persons at once, but you can repeat FresnePs experiment for
yourselves. Take two pieces of the same glass, blacken
them on the back, and lay them on a board that is covered
with a black cloth. Raise the edge of one strip of glass
very slightly, and adjust the slit so as to be parallel to the
common edge of the pieces of glass. With proper care in
the adjustment, you will get interference fringes exhibited
to the eye properly placed to receive the light, and you
will find that these fringes disappear if one of the reflected
beams is suppressed by blackening one of the mirrors. A
modification of FresneFs experiment, due to Lloyd, should
perhaps be mentioned. Take a strip of plate-glass blackened
at the back, and allow light to fall upon it at nearly grazing
incidence, as in Fig. 43. Light from a slit S reaches a
screen at P by two paths, one directly along SP, and the
other along SBP after reflection at the mirror. These two
162
LIGHT
beams, the one direct and the other reflected, may inter-
fere and give rise to fringes, as before. In this, as in all
the experiments referred to recently, considerable care
must be exercised in the adjustments, otherwise no results
or spurious results will be obtained. FresneFs device, and
Lloyd's modification of it, consist in producing interference
between the two parts of a beam that have been separated
by reflection. Fresnel also arranged to split the beam by
means of refraction. To do this he employed a biprism,
consisting of a piece of glass made in the form of two
FIG. 44
prisms of very small angles placed back to back. In Fig. 44,
the shaded portion represents a biprism, S a source of light,
PE a screen. The light from S that falls upon the upper
portion of the prism is bent downwards and made to pro-
THE PRINCIPLE OF INTERFERENCE 163
ceed as if from S^ while that which falls upon the lower
portion is bent upwards and proceeds as if from S 2 . Thus
Si and $ 2 correspond to A and B in Fig. 40, representing
Young's experiment, and the explanation of the interfer-
ence fringes is the same as was there indicated.
All these experiments are specially designed to exhibit
interference fringes and to test the explanation by a
comparison between theory and observation as to the
exact position of the bands and the arrangement of their
colors. Kindred phenomena, however, are obtained in
almost countless other ways, many of them far more
striking and beautiful than those to which reference has
just been made. It has been explained that in order that
waves of light may interfere, they must set out simul-
taneously from the same source and meet with such dif-
ferent treatment that one wave becomes half a wave-
length in phase behind the other. Now think of a beam
of light falling on a thin film of any material. Some of
the light will be reflected at the first face, while some will
penetrate the film, be reflected at the second face, and,
after emerging from the film, be in a condition to interfere
with what was first reflected. If the film be of the proper
thickness, this interference will be inevitable, and as a
consequence some of the light will be suppressed in places,
so that we shall see alternations of light and darkness, or
variations of color, according as the incident light is
homogeneous or composite. You must all have observed
the brilliant colors produced in this way by a thin film of
oil on the surface of water. You may see the same thing
here by looking at the beautiful color on the wall, pro-
duced by reflecting light from the surface of the water in
this hand tray after a drop of turpentine has been allowed
164 LIGHT
to fall upon the water. Much more beautiful effects, due
to similar causes, are obtained with a soap-film, as every-
body knows who has seen a soap-bubble. Fortunately,
youth is not a question of age, and the blowing of such
bubbles has afforded interest and amusement to genera-
tions of young people between seven and seventy. Nor
have philosophers been ashamed to enter into the game
and to discuss the phenomena in their grave way. If it
be true that to the poet's mind
" the meanest flower that blows can give
thoughts that do often lie too deep for tears/'
then it need cause no surprise that so common a thing as
a soap-bubble has engaged the serious attention of the
greatest men of science, such as Boyle and Newton of
olden times, Stokes and Kelvin of our own day, to select
only a typical few. All the gorgeous phenomena of color
exhibited by soap-bubbles are explicable by means of the
principle of interference. The color that is suppressed by
interference varies with the thickness of the film, its re-
fractive index, and the angle of incidence of the light that
falls upon it. Theory enables us to calculate all the
details and to predict what will happen with a film of
given thickness when the wave-lengths corresponding to
the different colors have been determined. How these
wave-lengths may be measured will be indicated in a later
lecture on Diffraction. Meanwhile, as the phenomena of
the soap-bubble are somewhat complicated by the curva-
ture of the surface, it may be well to show you similar
color effects with a flat film. I dip this ring into a solu-
tion of soap, fix it in a vertical plane, and by means of a
lens bring the light reflected from the film to a focus on
THE PRINCIPLE OF INTERFERENCE 165
the screen. The exact interference effects depend on the
thickness of the film, and therefore change as the thick-
ness alters while the liquid streams down. The image on
the screen is inverted by the lens, so that everything
appears upside down. The upper part of the film is seen
at the bottom of the picture on the screen, and you will
observe that the liquid seems to be streaming upwards.
Notice the changing color as the liquid thins away from
the top of the film. First you see a bright green, then it
changes gradually until now you have a deep red. Now,
again, in this part it is blue, now violet, now quite black,
and now the film has broken, having become too thin to
bear the strain of its weight.
An interesting modification of this experiment is to
arrange things so that the light comes from a narrow slit,
and after reflection, as before, from the film, passes through
a prism before falling on the screen. If light were re-
flected from a single surface and treated in this way, the
prism would separate the different colors and produce the
familiar spectrum. With the film, however, there will be
places where the light is cut out by interference, so that,
as the film thins, dark bands will be seen to travel across
the spectrum. You can see them distinctly in the ex-
periment that Mr. Farwell is now conducting.
You observed in these experiments with films that just
before the film broke it looked quite black at the thinnest
part. This is a curious fact, and one that seemed para-
doxical for a time. Newton observed the same thing with
an ordinary soap-bubble, and you can easily repeat the
observation. Blow such a bubble, and cover it with a
glass to screen it from air currents, and so prevent its
breaking too soon. As the liquid drains downwards, the
166 LIGHT
film gets thinner at the top, and just before it breaks this
part looks quite black. At first sight this seems contrary to
what might be expected. As this portion of the film is
extremely thin, it takes practically no time for light to
travel across it and back to the upper surface, so that
you might expect the light that has made this short pass-
age to be in the same phase as the light that was reflected
at the first surface. If this were so, the two waves should
reinforce one another instead of interfering, so that we
should have brightness instead of darkness. However, on
examining the matter by the aid of theory, it appears that
at one of the reflections, but not at the other, there should
be a change of phase of half a wave-length in the very
act of reflection, and this completely accounts for what is
observed.
All the bands of color produced by interference that
you have seen to-night have been arranged in straight
lines, but it is easy to get them in other forms. Here,
for example, is a simple modification of our experiment
with the flat film. With these acoustical bellows I pro-
duce a slight blast and direct it almost tangentially on the
surface of the film. This sets the liquid in the film in
motion, and arranges it in regions of varying thickness,
producing, as you see, brilliant curves of color. In one
case you have a series of concentric circles, such an arrange-
ment of color as is found in the famous phenomena of
Newton's Rings. These Newton studied with great care,
the second book of his "Opticks" being almost wholly
devoted to a discussion of their features. Newton's ar-
rangement for producing these rings is extremely ingen-
ious, because extremely simple and extremely effective.
It consists in pressing together two pieces of glass, one or
THE PRINCIPLE OF INTERFERENCE 167
both of them being slightly curved (Fig. 45 a). When
light is allowed to fall on this and to be reflected, a beauti-
ful series of colored rings is seen arranged in concentric
circles round a central spot. At all points such as P
(Fig. 45 b) on a horizontal circle of which is the center,
the thickness of the air-space between the two pieces of
glass is the same, and equal to PN. Thus waves that
pass to and fro in this region have to traverse an air film
of this thickness (PN). If, then, PN be of the length
necessary to produce the requisite phase difference for
(a)
FIG. 45
waves of a given length, there will be interference, and
the corresponding color will be absent from this region.
Thus, we should expect to see a series of colored rings if
the incident light be composite like sunlight, and there is
no great difficulty in predicting the main features from
theory and verifying the correctness of this theory by
careful observation of what actually takes place. The
most important laws were discovered by Newton by in-
duction from his experimental results. Thus, he found the
law of the radii of the rings, viz. that at a given angle of
incidence the radii of the different rings are proportional
to the square roots of the numbers 1, 2, 3, 4... (These
different rings are spoken of as rings of different orders.)
He found also in what way the radii varied with the angle
of incidence, and verified his law with wonderful accuracy,
considering the rough instruments of measurement at his
168
LIGHT
disposal. The following table compares the radii of a
ring of a given order for different angles of incidence on
the glass, and shows how Newton's law and Newton's
experiments agreed with one another. Moreover, by
means of a prism Newton analyzed the light before it fell
INCIDENCE
o
10
20
30
Radius (law)
1
10077
1032
1075
Radius (experiment) . .
1
1.0077
1.033
1.075
INCIDENCE
40"
50
60
70
Radius (law) . ...
1.142
1.247
1.415
1.71
Radius (experiment) . .
1.140
1.250
1.4
1.69
upon his ring apparatus, and so was enabled to inves-
tigate the phenomena when employing light of a single
color, and to see in what way a change of color affected
the size of the rings and their distinctness. "I found/'
he says, "the circles which the red light made to be mani-
festly bigger than those which were made by blue and
violet. And it was very pleasant to see them gradually
swell or contract according as the color of the light was
changed." As the radii of the rings depend on the color,
the larger (red) rings of one order will tend to overlap
the smaller (blue) rings of the next higher order. This
overlapping will produce indistinctness, so that it will be
difficult to see the rings of high order when the incident
light is white. If, however, homogeneous light be em-
ployed, there is no possibility of overlapping, so that far-
more rings may be seen. "I have sometimes," says New-
ton, "seen more than twenty of them" (when working
THE PRINCIPLE OF INTERFERENCE 169
with a prism to produce homogeneous light), "whereas, in
the open air" (without the prism), "I could not discern
above eight or nine." Instead of using a prism, we may
get what is very nearly homogeneous light by interposing
colored screens in front of the powerful electric light in
the lantern. These screens cut off a good deal of the light,
so that the phenomena, as you see, are not so brilliant as
before; but if you look carefully, you will have no diffi-
culty in making out the main features. Now there is a
red screen and you see the red rings (of course no other
color is possible with this arrangement) ; now we have a
blue screen, and you notice the blue rings distinctly smaller
than the red ones that you have just been looking at.
Since Newton's day there have been many modifications
of his experiments and many new phenomena of a kindred
character discovered; but there is nothing that is not
completely accounted for, down to the minutest detail, by
means of the principle of interference coupled with the
known laws of reflection and refraction.
All these examples of interference have been produced
by apparatus that has been specially designed to exhibit
this effect. Not infrequently, however, we meet with
similar phenomena where no such pains has been taken
to produce the result. In such cases the design, if design
there be, is not of man's contrivance. Thus you have all
observed that polished steel becomes colored when it is
exposed to the air. A thin film of oxide is formed on the
surface, and produces interference effects by reflection like
any other film. Antique glass, especially when it has long
been buried, becomes coated with a thin layer that shows
beautiful interference colors. The wings of a butterfly
owe their color to their delicate ribbed structure and the
170 LIGHT
interference that this produces. The gorgeousness of a
peacock's tail is due to the same cause. You will observe
that the color of this feather is not intrinsic ; it changes
with the incidence of the light, as you see when I turn it
in the lime-light. The changing colors of opals are ex-
plained in the same way, and so are those of mother-of-
pearl. If you examine such an object closely with a
microscope, you will find that it is made up of layers, and
that the surface cuts across these layers, and so presents a
series of minute grooves. The lights that are reflected
from opposite edges of these grooves are in the condition
to interfere, and you can easily see that the color changes
with the incidence of the light that falls upon the surface.
None of this beautiful color is really in the shell. Brewster
showed this conclusively when he stamped the shell on
black wax, thereby reproduced the grooves, and obtained
the same colors from the wax as from the original shell.
Before bringing this lecture to a close, there is just time
to refer, all too briefly, to an ingenious application of the
principles of interference to the problem of color pho-
tography. This was first made in 1891 by Lippmann,
but since that date considerable improvements have been
effected in the practical application of Lippmann's ideas.
The theory of the process is not without its difficulties,
but the broad lines of the explanation, as suggested by its
author, are easily seen. The first matter that must be
firmly grasped is that there is an intimate relation between
the intensity of light reflected from a very thin film and
its thickness. If the thickness be altered, so will the
brightness of the reflected beam. We saw a short time
ago that for a film so thin that it can scarcely be said to
have any thickness, there is no light reflected at all. Start-
THE PRINCIPLE OF INTERFERENCE 171
ing with this, let us imagine the thickness to increase
gradually, and consider the effect on the intensity of the
reflected light. For simplicity we shall suppose that the
light is incident normally and not obliquely. The re-
flected light will grow in intensity until the thickness of
the film is exactly half a wave-length of the light that is
used. (That length will depend, as has been seen, upon
the color of the light and upon the refractive index of the
film.) After this thickness of half a wave-length has
been reached, less light will be reflected, and this diminu-
tion will continue until a thickness of a wave-length has
been attained, when once more there will be no reflected
light. This variation of intensity is all accounted for by
the principle of interference. We are thus led to the
important conclusion that when dealing with thin films
less than a wave-length in thickness, we immensely in-
crease their reflecting power if we make their thickness
half a wave-length of the light that we wish to reflect.
Let us suppose that X R is the wave-length of red light
for the material of which the film is composed, and that
we make a film of thickness X R , and observe the light
that it reflects from a landscape or a picture. It will be
much more effective in reflecting red than any other color,
and its power of selective reflection will be greatly im-
proved if we back it by several parallel films of the same
thickness. With such an arrangement we shall practi-
cally see nothing but the red parts of the picture. With
other films of thickness % X G , where X G is the wave-length
for green light, we shall similarly pick out the green por-
tions, and with films of thickness X v (where X v is the
wave-length of violet light) the violet portions of our
picture. If, now, we have any means of combining these
172 LIGHT
three colored reflections, we shall have a faithful repre-
sentation of the original, according to the explanation set
forth in the earlier lecture on color photography.
The practical difficulty in carrying out such a process
that will probably first present itself to your minds will
be that of obtaining films of the right thickness. The
actual lengths of some waves of light will be set forth in
the lecture on Diffraction, and if you have any conception
of their minuteness, measured by any ordinary standard,
you will realize that it is quite hopeless by any mechanical
process to produce a film whose thickness is exactly J X R ,
or any of the other quantities that have been specified.
And yet such films can be manufactured quite accurately
by optical means. The device for doing this is, of course,
an essential feature of the Lippmann process; but the
same principle was employed a little earlier by Wiener.
It is another simple application of the Principle of Inter-
ference. Suppose that we have two series of waves mov-
ing through a medium, and that they are similar in every
other respect except that they are moving in opposite direc-
tions. These waves will be in a condition to interfere
with one another, and there will be a series of points N 1}
N 2 , N B ... at each of which the upward displacement in
one wave is exactly counteracted by the downward dis-
placement in the other wave that is moving in the opposite
direction. At such points, which are called nodes, the
displacement due to the two waves will be zero. At inter-
mediate points, L v L 2 , Z/ 3 ..., the two displacements will be
in the same direction, and will reinforce one another, and
these points, where there is a maximum of displacement,
are called loops. Investigation shows that the positions
of these nodes and loops are stationary, that they do not
THE PRINCIPLE OF INTERFERENCE 173
change from moment to moment. The aspect of this
combination of two trains of waves is thus very different
from that of either taken separately. The nodes always
remain at rest, and halfway between these points (at the
loops) the crests of the waves rise and fall periodically.
There is no moving of the wave-form in one direction
or the other, but a mere gradual change of height. Such
a set of waves are consequently called stationary waves.
They have often been set up in air and water; but the
difficulties of producing them with light-waves in the
ether and of demonstrating their existence were not suc-
cessfully overcome till 1890. In that year Wiener set up
these stationary waves by reflecting light from the silver
coating of a plate of glass, and proved their existence by
their effect on a thin film of sensitized collodion super-
posed on the glass. We should expect the photographic
action to be different at the nodes, where there is no dis-
placement, than at the loops where the displacement is
greatest, and Wiener succeeded in showing that the pho-
tograph was crossed by bright and dark bands at regular
intervals, and thus in affording another ocular demon-
stration of the soundness of the Principle of Interference.
Now there is one feature of these stationary waves that
has not yet been mentioned and that is specially impor-
tant for the purpose that we have in hand. The distance
between successive loops, as well as that between successive
nodes, is exactly half a wave-length. You will realize the
significance of this at once. It gives us an optical means
of producing a film, or a series of parallel films, whose
thickness is half a wave-length of any color that we wish
to use. Set up these stationary waves with red light, and
they will so act on the sensitive emulsion as to arrange it
174 LIGHT
effectively in layers whose thickness is X B , and when this
is afterwards viewed by reflection it will send back practi-
cally nothing but red light. Do the same with the other
colors, and this part of your problem is solved. You will
probably see, too, that it is not really necessary to have
these different films and to devise a means of combining
the pictures that they present by reflection. All the work
can be done by the same material. Each color that
strikes it will build up a little film by means of stationary
waves acting on the sensitive emulsion with special force
at regular intervals of half a wave-length, and this film will
be of just the right thickness to reflect that particular
color most copiously. The form of the object will be
produced, just as in ordinary photography, by the grada-
tions of light and shade over different portions of the plate,
the color by the thickness of the different films beneath
the several portions.
VIII
CRYSTALS
TO-NIGHT we are to deal with some of the optical
properties of crystals. It has been remarked in an earlier
lecture that the distinguishing feature of a crystal is its
structure. Its parts are not thrown together at random,
but are built one upon another according to some definite
plan. The result is that a crystal does not seem the
same when looked at from different directions. If you
could imagine yourself moving through water or glass
(which are not crystals), it would make no difference to
your rate of progress whether you went north, south,
east, or west. In a crystal, however, it might well be
different; the structure might be so arranged as to make
progress easier in one direction than in another. In
optical problems we are interested especially in the propa-
gation of waves, the speed of which for a medium like
the ether depends on the rigidity of that medium. Here
we need not stop to inquire exactly how the presence of
matter modifies the effective rigidity of the ether contain-
ing it ; but owing to the structure of a crystal it is natural
to suppose that its presence in the ether will modify the
rigidity differently in different directions. If we apply
general dynamical principles to the discussion of the
propagation of waves in such a medium (that is, a medium
with different rigidities in different directions), the first
175
176
LIGHT
striking result that we reach is that, as a general rule, for
a wave traveling in any given direction there are two
speeds with which the wave can travel. We may express
this by saying that two waves can travel through a crystal
in any given direction, and that in general these will
travel with different speeds. As there is a ray of light
corresponding to each wave, we see that when a ray strikes
a crystal it will give rise not to one, but to two different
rays within the crystal. This prediction from theory cor-
(o)
FIG. 46
responds to the well-known fact of double refraction pro-
duced by a crystal. Here are two double prisms of the
same size and shape. They are represented in section in
Fig. 46 a and b. The first is made of two prisms, ABD
and BDC, of the same non-crystalline material, glass.
The second (Fig. 46 b) is made in exactly the same way,
but is of crystal, Iceland spar. Now observe the difference
of behavior when a ray of light falls perpendicularly on a
face of each double prism and is afterwards received on
a screen behind the prism. With the glass the ray goes
straight through as indicated in Fig. 46 a and forms a
single patch at P on the screen. With the crystal the
ray splits into two on crossing B'D', each of these rays is
further bent on passing out of the prism, and on the screen
we see two widely separated spots of light, one at P l and
CRYSTALS 177
the other at P 2 - You see, then, that this double refraction
is no dream of the theorists, but an actual fact.
Theory, however, does much more than predict that
we should find two waves traveling in a given direction
with different speeds. It indicates, further, and this is
very important, that these two waves will be differently
polarized. When each is plane polarized, the planes of
polarization for the two waves are at right angles to one
another. This deduction from theory is amply verified
by experiment, and the use of crystals to produce or to
test plane polarized light is one of the regular resources
of an optical laboratory. You may remember that in
introducing the subject of Polarization we employed a
Nicol's prism to produce plane polarized light. Its power
of doing this depends entirely on its crystalline structure,
and you should have no difficulty in understanding its
action if you bear in mind two facts. The first is the one
just referred to, that for a given ray in a crystal the vibra-
tions must be confined to one or other of two planes at
right angles, say a vertical and a horizontal plane. It
appears that the molecules of a crystal are so arranged
that the ether cannot continue to vibrate to and fro along
any arbitrary direction, but must confine its movements
to one or other of two directions at right angles to one
another. A mechanical analogue was suggested on p. 101
and illustrated in Fig. 24 ; but it may not be out of place
to repeat that this is merely an analogy, and that it is
not suggested that the figure depicts the actual arrange-
ment of the molecules. The second fact to remember in
dealing with Nicol's prism is the fact of total reflection
when the angle of incidence exceeds the critical angle.
NicoFs prism is made by cementing together two prisms
178 LIGHT
of Iceland spar, as indicated in Fig. 47. When a ray AB
strikes the prism, it is split into two by double refraction,
and the two rays in the crystal EG and BF are differently
polarized, BC horizontally (say) and BF vertically. The
angles of the prisms are so arranged that BF strikes the
thin layer of cement between the prisms at an angle greater
than the critical angle. Thus, the ray BF is totally re-
flected along FH, and so does not emerge from the face D.
FIG. 47
The other ray, BC, passes over into the second prism and
emerges at D, polarized in a horizontal plane.
It has been stated above that, in general, two different
waves may be propagated in any direction. Theory, how-
ever, indicates, and experiment verifies, that there must
always be one, and in some cases two, directions in which
only a single wave can pass. Those directions are called
the optic axes of the crystal, and crystals are classified
into uniaxal and biaxal, according as they have one or two
of such axes. In the first case the arrangement of the
molecules of the crystal must be perfectly symmetrical
round the axis ; in the second case there is no such perfect
symmetry about any line. Theory, moreover, does much
more than indicate these general features ; it enables us to
calculate all the details of the wave-motion. Thus we can
compute exactly the speeds with which waves will travel
in any given direction. It is convenient to express the
CRYSTALS
179
speed in terms of the refractive index, it having been ex-
plained before that the speed is obtained by dividing a
known constant by the refractive index. The results can
be exhibited in a geometrical form by drawing lines from
a point 0, the directions of the lines indicating the direc-
tion in which the wave is traveling and the length of
the line measuring its refractive index. If lines are drawn
in all directions in this way, their ends will all lie on a
surface, which is called the Index Surface. Theory pre-
dicts the precise form of this. In the case of uniaxal
FIG. 48
crystals, where there is perfect symmetry about an axis,
the index surface consists of a sphere and a spheroid,
with the optic axis as a common diameter. A spheroid is
an egg-shaped surface with perfect symmetry about an
axis, so that you may think of the index surface for a
uniaxal crystal as being made up of an egg and a sphere.
You will realize at once that the surface might have two dis-
tinct forms : the sphere might be inside the egg (Fig. 48 a),
or the egg might be inside the sphere (Fig. 48 b). The
crystals will have different optical properties in the two
cases, and those of the first type are called positive crystals,
those of the second negative crystals. You will see from
180 LIGHT
the figure that a line drawn in any other direction than
the optic axis OA will cut the index surface at two dif-
ferent distances from the center 0, when it crosses the
sphere and the spheroid respectively. These two distances
represent the refractive indices (and so measure the speeds)
of the two waves that, we have seen, can be propagated
in any direction. You will notice that the law which
connects the refractive index with the direction of propa-
gation is quite different for the two waves. With the
sphere the radius is everywhere the same, so that for the
corresponding wave the refractive index is the same in
all directions. This is the case with ordinary non-crystal-
line substances, so that the ray obeys the ordinary laws of
refraction already discussed, and is consequently called the
ordinary ray. This deduction from theory, according to
which one of the rays in a uniaxal crystal should obey the
ordinary laws of refraction, has been completely verified
by experiment. Very careful estimates of the refractive
indices have been made for waves in all directions, and it
is found that the refractive index is absolutely constant,
or more strictly, the variations in its measurement never
exceeded 0.00002, a variation well within the limits of the
probable errors of the experiments that were made.
So much for one of the waves within a uniaxal crystal.
With the other wave and its corresponding ray the law
of refraction is less simple, and as the ordinary law is not
obeyed, the ray is called the extraordinary ray. As you
see from Fig. 48, the length of the line drawn from the
centre to the surface of the spheroid varies with the
direction of the line, so that the refractive index varies
with the direction of propagation of the wave. It is a
simple problem of geometry to compute its value for any
CRYSTALS
181
direction, making a known angle 6 with the optic axis.
The following table shows a comparison between theory
and observation for the refractive index (n) correspond-
ing to different directions (6}. It will be seen that the
agreement is excellent, the differences being of the order
of the probable errors of experiment :
n
(THEORY)
n
(EXPERIMENT)
9
n
(THEORY)
n
(EXPERIMENT)
2' 40"
1.66779
1.66780
46 46' 2"
1.56645
1.56653
4 19' 58"
1.66660
1.66663
49 23' 10"
1.55861
1.55876
7 51' 58"
1.66387
1.66385
52 42' 6"
1.54902
1.54914
11 23' 12"
1.65967
1.65978
58 39' 10"
1.53303
1.53312
17 8' 26"
1.64987
1.64996
61 39' 33"
1.52570
1.52573
20 26' 1"
1.64279
1.64287
63 9' 6"
1.52228
1.52241
23 50' 45"
1.63451
1.63455
66 14' 27"
1.51579
1.51571
25 49' 35"
1.62934
1.62930
72 18' 55"
1.50476
1.50475
29 18' 42"
1.61965
1.61974
75 36' 18"
1.50009
1.50005
34 48' 0"
1.60336
1.60336
79 6' 26"
1.49612
1.49610
35 58' 47"
1.59048
1.59058
80 14' 4"
1.49507
1.49507
40 49' 21"
1.58478
1.58487
87 6' 40"
1.49112
1.49114
45 45' 57"
1.57000
1.57014
89 49' 6"
1.49074
1.49074
These results have reference to uniaxal crystals which
are perfectly symmetrical about a line. With biaxal
crystals there is no such symmetry, and the optical proper-
ties are consequently more difficult to deal with. How-
ever, the same general principles lead to a complete solu-
tion of the problem, although the results are much less
simple. The index surface no longer consists of a sphere
and a spheroid, but of two sheets that are less familiar in
form. Its geometrical properties can be investigated
mathematically and the values of the refractive indices
for waves in any given direction easily computed. The
182
LIGHT
following table, corresponding to that just given for a
uniaxal crystal, compares theory and experiment for a
number of different directions in a biaxal crystal. In this
table r&! is the refractive index corresponding to the inner
sheet of the index surface, while n 2 represents the same
quantity for the outer sheet:
f
"i
(THEOEY)
i
(EXPERIMENT)
1
,
(THEOEY)
2
(EXPERIMFNT)
1.68103
1.68099
1.68533
1.68526
3 12' 50"
1.67714
1.67721
7 9' 10"
1.68465
1.68454
13 6' 20"
1.66298
.66300
17 2' 40"
1.68445
1.68448
21 4' 30"
1.64607
.64603
25 0' 50"
1.68443
1.68452
28 14' 10"
1.62824
1.62807
32 10' 30"
1.68443
1.68447
35 29' 20"
1.60900
.60897
38 27' 30"
1.68444
1.68453
45 14' 50"
1.58363
1.58365
49 13' 0"
1.68445
1.68457
60 1' 30"
1.55154
.55157
63 59' 30"
1.68447
1.68452
69 37' 40"
1.53784
1.53774
73 35' 50"
1.68448
1.68444
When we wish to estimate the velocities of the waves
that can travel through a crystal in any direction, it is
convenient, as has been seen, to know something of the
form of the Index Surface for the crystal in question.
There is, however, another surface which is referred to
perhaps even more frequently in discussions of the optical
properties of crystals. This surface is known as the Wave
Surface, and we must try to realize what is its significance.
If you throw a stone into a pool and watch the waves
spreading outward, you will have no difficulty in observ-
ing the position of the crest of the moving wave at the
end of any time, such as a second. As the wave moves
out with the same speed in all directions, the crest will
form a circle round the original point of disturbance as
CRYSTALS 183
center. If, instead of dealing with surface waves, you had
waves that spread out in all directions with equal veloci-
ties, then it is clear that after a second the crests would
all lie on a sphere. This, then, is the wave surface for a
uniform medium, the surface that contains the crests of
all the waves that have been moving outwards for a given
time, such as a second. In a crystal the waves move
with different speeds in different directions, so that the
wave surface is no longer spherical. Its form can be de-
termined from theory, and its geometrical properties dis-
cussed as fully as may be desired. As there are two
waves in any given direction, the wave surface consists of
two sheets, as does the index surface, and, just as with
that surface, its form is specially simple for a uniaxal
crystal. In that case the wave surface is made up, like
the index surface, of a sphere and a spheroid, as shown in
Fig. 48, with the difference, however, that (a) is the wave
surface for a negative, and (6) for a positive crystal.
A knowledge of the form of the wave surface is very
helpful when dealing with the optical behavior of a crystal.
It enables you, for example, to determine the directions
of the rays corresponding to waves in a given direction
and to exhibit by a simple geometrical construction the
directions of polarization in the two waves. The theory
shows that a ray is represented by the line drawn from
the center of the wave surface to the point of contact with
this surface of a plane which touches it, and is parallel to
the front of the advancing wave. I hold in my hand an
apple, and will suppose for the sake of illustration that it
represents a wave surface. In my other hand I have a
sheet of paper, and I shall take this to represent the front
of a wave of light moving through the crystal. The direc-
184 LIGHT
tion of this wave-front being known, the problem before
me is to determine the direction of the corresponding ray
of light. Move the sheet of paper parallel to itself until
it touches the apple at P; then, according to the theory,
if be the center of the apple, corresponding to the center
of the wave surface, OP is the direction of the ray. In
reality, of course, the
wave surface differs very
+ / g ~~ obviously from the sur-
face of an apple. It has
pj symmetry about a point
0, its center, and it con-
sists of two sheets, so that
planes in a given direc-
tion (both perpendicular
to a given line ON) will
touch it at two points,
P 1 and P 2 (one on each
F IG< 49 sheet), on the same side
of the center (Fig. 49).
In this figure the curves A 1 P 1 B 1 and ^L 2 P 2 J5 2 represent
portions of plane sections of the two "sheets," as they
are called, of the wave surface. OP 1 and OP 2 represent
the two rays for waves propagated in the direction ON,
and it should be understood that the three lines ON, OP 1}
and OP 2 are not, in general, in the same plane.
If you will return for a moment to the case of this apple,
you will see that as I move the sheet of paper in different
directions it touches the apple, as a rule, just in one point.
However, there is one striking exception to this general
rule. Now I hold the paper at right angles to the stem
of the apple, and you observe that it touches the apple
CRYSTALS 185
not in a single point, but in an infinite number of points
encircling the stem. The apple, as has already been re-
marked, is very different in form from the wave surface,
but the two surfaces have some points of similarity. If
you were to make a model of the wave surface, you would
find that it has four points that closely resemble that on
an apple near the stem (singular points is their technical
name), and that a plane that touches the surface in the
neighborhood of one of these points touches it not at an
isolated point, as is the general rule, but at an infinite
number of points forming a circle round the singular
point. It should still be true that a line drawn from the
center of the wave surface to any one of these points
where the plane touches the surface should represent a
ray of light corresponding to a wave-front parallel to the
plane in question. All the lines drawn thus from the
center to the various points of contact will form a cone,
so that we should expect that if we could get a wave of
light to travel in the right direction in a crystal, we should
see not two rays only, as in the ordinary case of double
refraction, but a whole cone of rays. That this phenome-
non was to be expected was first suggested from theo-
retical considerations such as have just been indicated.
The theory was developed by Sir W. Hamilton, and, at his
instigation, was put to the test of experiment by Lloyd.
Knowing what to look for, Lloyd had not much difficulty
in observing this phenomenon, and it is now well known
under the name of Conical Refraction. With the crystal
used by Lloyd, Hamilton's theory indicated that the
angle of the cone of rays formed in this way should be
1 55', and Lloyd's measurements made it 1 50', the agree-
ment being as close as could be expected in the determina-
186 LIGHT
tion of such a quantity. Here, then, we have an example
of something whose existence had never been suspected
until the theory of light suggested the search for it. Much
has been made of this prediction from theory, perhaps too
much. We have already seen far more wonderful agreement
between theory and observation in other fields of optics,
the only peculiarity of this case being that the theory
came before the observation and not vice versa. How-
ever, it should be remembered that the one aim of the
theory is to fit the facts, and it makes little difference
to the value of the theory whether the facts happen to
have been previously observed or not. This may be
largely a matter of accident, and the only advantage that
can be claimed for a theory that predicts the unknown is
that its power to do so should inspire extra confidence,
seeing that the theory cannot have been suggested by
this fact that is being explained, as is often the case with
"explanations."
In a previous lecture we saw how successfully the theory
of light can deal with the problem of reflection and refrac-
tion at the surface of a non-crystalline medium such as
glass or water. It is equally successful in its treatment
of crystals. Once the general laws of wave propagation
in such media are understood, there is no special diffi-
culty in proceeding by means of dynamical principles to
calculate the amplitudes and phases, as well as the direc-
tions and velocities, of the various waves that may arise.
Of course, the mathematical processes are more complex
than when we are dealing with non-crystalline substances,
but all the difficulties that present themselves have been
overcome. Just a few of the results may be referred to
here, in so far as they can be tested by experiment.
CRYSTALS
187
We have seen that, with a non-crystalline substance, if
light be incident at a certain angle, an angle that goes by
the name of the polarizing angle, the reflected light has the
peculiarity of being plane polarized. The position of this
angle for any substance is easily determined from the
simple law, due to Brewster, that the tangent of the angle
is equal to the refractive index of the substance. In the
case of crystals, theory indicates that there will also be a
polarizing angle, but that the law from which it may be
computed is less simple. With crystals the refractive
index is not a constant, but depends on the direction in
which the wave is being propagated and the nature of
its polarization. We should expect, therefore, that the
polarizing angle would depend on these things, and in this
theory and observation agree. The following table gives
a comparison between theory and observation as to the
values of the polarizing angle under different circum-
stances of reflection from a uniaxal crystal. The angle is
different according as the plane of incidence is parallel or
perpendicular to the plane containing the optic axis of
the crystal. These two cases are distinguished by sub-
scripts; thus, P 1 and P 2 . The angle is the angle that
the optic axis makes with the reflecting face of the crystal.
The results are shown graphically in Fig. 50 :
e
.0 25'
27 2'
45 29'
64 1' 30"
89 47'
Pi (theory) . . .
54 3'
55 25'
57 25'
59 25'
60 41'
PI (experiment) .
54 12'
55 26'
57 22'
59 19'
60 33'
P 2 (theory) . . .
58 55'
59 17'
59 48'
60 23'
60 41'
P 2 (experiment) .
58 56'
59 4'
59 48'
60 75'
60 33'
188
LIGHT
In the case of reflection from a non-crystalline substance
we have seen that at the polarizing angle the reflected
light is polarized in a plane parallel to the plane of inci-
56
^Q 10 20 30 40 50 60 70 80 90
FIG. 50
dence. With a crystal, however, this is not the case.
The plane of polarization deviates from that of incidence,
being inclined to it at a small angle, A, which can be cal-
culated from theory. The values of A obtained from
theory and experiment were as follows, for the case of
reflection from a uniaxal crystal whose optic axis was
parallel to the reflecting surface. The angle a denotes
the angle between the optic axis and the plane of incidence.
a
23 30'
45
67 30'
90
A (theory) ....
2 46'
3 54'
2 46'
A (experiment) . .
2 46'
3 57'
2 43'
When dealing with ordinary reflection, we made a com-
parison between theory and observation as to the differ-
ence of phase between two reflected waves which are
CRYSTALS
189
polarized respectively parallel and perpendicular to the
plane of incidence. The corresponding problem for crystal-
line reflection is more complex, but the general character
of the results is the same. This will be seen at once by
comparing Fig. 51, which shows how the difference of
0.5
0.4
0.3
0.2
I
55
57 c
58 c
59
FIG. 51
62
phase depends upon the angle of incidence in reflection
from a crystal, with Fig. 32 of the earlier lecture.
In this, as in some other lectures, I have brought before
your notice a number of tables and figures that will prob-
ably prove attractive or repellent according to the degree
in which you realize their significance. Their object in all
cases is to show how well, or how ill, the theory fits the
facts, and I hope that by this time their cumulative effect
will have convinced you that the modern theory of light
keeps always very close to the solid ground of fact. Such
things are full of interest to a serious scientist, as they
190 LIGHT
give him what, above all, he is anxious to have, a search-
ing test of his theories; but the optical effects with which
they deal do not make a very wide appeal. They would
not usually be described as beautiful, and few men, out-
side the narrow circle of the physicists, would display
much enthusiasm over tables of refractive indices, polariz-
ing angles, and the like. It happens, however, that with
crystals we can produce effects that are generally recog-
nized as extremely beautiful, and that the careful observa-
tion of some of these also serves, in a measure, as a test
of the accuracy of our theory of the propagation of light
in a crystal. You are aware, 'perhaps, that if you make a
solution of tartaric acid, pour it over glass, and evaporate
the water by means of a steady heat, you may, with proper
precautions, get a film of minute crystals of the acid de-
posited on the glass. Here is a glass disk upon which is
such a deposit. I place it between these two NicoFs
prisms, and allow the bright light from the lantern to
shine through the apparatus. If you direct your attention
to the screen, you will admit, at any rate, that the colors are
very gorgeous, and probably that the picture is a beautiful
one. Its beauty is enhanced by its irregularity, and this
is due to the fact that the little crystals on the glass pre-
sent their facets to the light at angles of all sorts. There
is thus a total absence of that mathematical precision
which is the only objection that can be brought against
the claim of beauty made on behalf of the phenomena
with which we are to be occupied during the remainder
of this lecture.
These phenomena are all produced by interposing a
thin crystalline plate between two Nicols. The effect of
each Nicol is to confine the vibrations to a definite plane,
CRYSTALS
191
so that the light that gets through a Nicol must be plane
polarized in a direction that depends on the way in which
the Nicol is turned. The effect of the plate of crystal is
to split up the incident wave of light into two waves,
moving forward with different speeds. By the time that
these two waves have traversed the crystal, they will have
FIG. 52
got out of phase, and if their difference of phase be of the
right amount, then, as we saw in the last lecture, they
will interfere and in combination produce darkness. If we
arrange things so that at different points of the plate the
difference of phase between the emerging waves is dif-
ferent, then there will be interference at some points and
not at others, so that we shall get alternations of light and
darkness. It is easy to see that if the incident beam be
parallel, we shall have no such alternations, but uniform
brightness (or darkness) over the plate. If AB (Fig. 52)
represent the front of a wave falling on the plate, this
will set up two waves moving with different velocities,
and these will emerge from the plate with a difference of
phase represented by ef in the figure. If A'B' and A"B"
192
LIGHT
be other wave-fronts, the phase differences on emergence
will be e'f and e"f f respectively. Now it is obvious that
if A'E' be parallel to AB, as will be the case if the incident
beam be parallel, then e'f will be equal to ef. Thus the
phase difference in the neighborhood of C r will be the same
as that at C, and it will be equally bright at these two
FIG. 53
points. If, then, we want alternations of light and dark-
ness, we must abandon a parallel incident beam. , If we
arranged that the incident beam should diverge from or
converge to a point, as indicated in Fig. 53, then any two
wave-fronts would not be parallel, but would be inclined
to one another, as represented by AB and A"B" in Fig. 52.
The differences of phase on emergence would be ef and
e"f" , and as these are different it might be bright at C
and dark at C".
We shall suppose that things are arranged to avoid a
parallel beam, and that the incident pencil of light is of
a diverging or converging character, with OQ for its axis.
We shall then examine the simplest case that can be pre-
sented, that of perfect symmetry, where we have a uni-
CRYSTALS
193
axal crystal, the plate of which is cut at right angles to
the optic axis, the direction of this axis coinciding with
that of the incident pencil. If we were to look down upon
the plate in the direction of the axis, and observe a plan
of the mechanical analogue referred to on pp. 101 and 177,
then, as there must be perfect symmetry about the axis,
the arrangement of the obstacles would be that repre-
sented in Fig. 54 a. At any point, P ly the vibrations
(a)
FIG. 54
must be confined to one or other of two directions, PR
and P!$, at right angles to one another. Of these the
first, PiR, is along the direction QPi, and the second is at
right angles to this. Now suppose that the first Nicol is
so placed that it stops all vibrations except those parallel
to QN l (Fig. 54 6). Then PjT 7 , which is parallel to QN 1}
may represent a displacement in the incident wave as it
strikes the crystal plate. Before considering what happens
to the 'wave within the crystal, it is convenient to " re-
solve" the displacement P 1 7 7 into its equivalent, P^R com-
bined with P!$, or what is the same thing, PR combined
with RT. It will be seen that RT is equal and parallel
to P!$, so that these two lines represent displacements of
the same magnitude and in the same direction. [This
194 LIGHT
" resolution" of a displacement P^T into two displace-
ments, P^R and RT, according to the " triangle law/' is
really a very simple matter, it being obvious that the final
displacement is the same, whether you go direct from P l to
T, or by two stages from P l to R, and then from R to T.]
Instead, then, of saying that in the incident wave there is
a displacement P{F parallel to QN lf we may say that
there are two displacements, one, P-JI, being in the direc-
tion QP V and the other, RT, at right angles to this. Dis-
placements in the first of these directions are characteristic
of one of the waves that the crystal can transmit, while
displacements in the other characterize the second wave.
These two waves, as we have seen, traverse the crystal
with different speeds, and emerge with a difference of
phase. What this phase difference is will depend, as ap-
pears from Fig. 52, on the angle at which the incident
wave strikes the face of the crystal. This will be the
same for all points P l that are at the same distance from
the axis Q, but will be different at different points along
the line QP. Let us suppose that the point PI is so placed
that the phase difference is one wave-length for the color
under consideration. How will the two waves of light of
this color combine after they pass through the second
Nicol? That, of course, will depend upon the position
of this Nicol. Let us suppose that the two Nicols are
" crossed," so that the second Nicol stops all vibrations
except those in the direction QN 2 (Fig. 54 b), where* A^QA^
is a right angle. Draw R U (Fig. 55) parallel to QN 2 and
therefore perpendicular to P^T or QNi. The displacement
represented by P-JH is equivalent to a combination of
two displacements, represented in magnitude and direction
by P a 7 and UR respectively. The displacement Pj7 is,
CRYSTALS
195
however, annulled by the second Nicol, which will not
permit a wave to pass unless the displacements therein
are parallel to QN 2 . We see then that, while PiR repre-
sents the displacement in one of the waves that emerges
from the plate of crystal, after this wave has traversed
the second Nicol the displacement is changed to UR.
The displacement in the other wave, represented byRT,
may be dealt with similarly. It is equivalent to two
displacements,
RU and UT,
and of these
the second is
annulled by the
Nicol, so that
the displace-
ment in this
wave as it comes
through the
Nicol is RU. Now we have supposed that P 1 is so
situated that the difference of phase between the two
waves is exactly a wave-length, and this/ as far as optical
effects are concerned, is the same as if the waves were
in the same phase. We have thus to combine two waves
that arc in the same phase, the displacements in which are
so related that one is represented by UR and the other by
the exactly equal and opposite RU. Clearly these two
displacements annul one another, so that the color cor-
responding to this particular wave-length is totally absent
from Pj. As everything is symmetrical round the axis,
this absence of color will apply to all points on a circle
whose radius is QP l and center is Q, so that there will
be a dark circle round the axis. The argument will apply
FIG. 55
196
LIGHT
FIG. 56
equally well to a point P 2 so chosen that the phase differ-
ence is two wave-lengths, or to P 3 , where it is three wave-
lengths, and so on. Thus
there will be a whole series
of circles round the axis,
which will be dark as far
as the color corresponding
to this wave-length is con-
cerned.
These concentric circles
will not, however, be the
only dark regions of the
field of view. Consider
any point P (Fig. 54) on
the line QN V The only
displacement at such a point that the first Nicol will per-
mit to pass must be in the direction QN^ and as this is
at right angles to QN 2 , the
corresponding wave will
not be able to get through
the second Nicol. There
must, therefore, be com-
plete darkness at P, and so
for any other point on lines
in the directions QN l and
QN 2 . Hence, we should
expect to see a series of
dark circles round the axis,
with a black cross whose
arms are parallel to the di-
rections QN 1 and QN 2 such as is represented in Fig. 56.
The difference of phase for the two waves that traverse
FIG. 57
CRYSTALS 197
the crystal depends on the velocities of these waves, and so is
different for waves of different length and color. Thus, the
points P-f^.. will have slightly different positions for
the different colors that go to make up white light,
and if the incident light be of this character, the rings
will be colored, giving the beautiful effect that you
now see on the screen. Figure 57 is from a photograph
of what actually appears, unfortunately, however, robbed
of all the beauty of color. You will observe that the
darkest part of the field corresponds exactly with the
cross and rings predicted from theory and indicated in
Fig. 56.
We have been dealing with the case in which the two
Nicols are " crossed." Suppose, now, that we turn the
second Nicol through a right angle, so that QN 2 of Fig. 54
coincides with QN l} and consider in what way this should
modify the results. As before, the displacement repre-
sented by P!# is equivalent to a combination of P-JJ and
UR (Fig. 55), but of these it is the second that is now
annulled by the second Nicol, so that when this wave
gets through the apparatus the displacement in it is repre-
sented in magnitude and direction by Pfl. In the other
wave the displacement RT is again equivalent to RU
combined with UT, and the first of these is annulled by
the second Nicol, so that UT represents the displacements
in the emergent wave. Thus the displacements in the
two waves are in the same direction, and being effectively
in the same phase, their combined effect is additive, and
instead of darkness we have brightness. Thus, where
formerly we had a series of dark rings we should now
expect a complementary series of bright ones. The cross,
too, instead of being black, will be bright. For if we take
198
LIGHT
a point such as P on QN^ the first Nicol confines its
displacements to the direction QN^ and these pass freely
through the second Nicol, and this is true also for a point
on a line at right angles to QN r Thus we have brightness
all along two lines at right angles, as you see from Fig. 58,
which represents the actual state of affairs, except, as
before, for the color.
In dealing with these
phenomena of rings and
crosses, I have attempted
merely to indicate the
general character of the
results that are to be ex-
pected and that are ac-
tually found to occur.
With the aid, however, of
the theory of wave prop-
agation in a crystal, it is
not difficult to predict
more of the details of the phenomena, such as the size
and relative intensity of the rings as well as their form.
A very great number of arrangements of the crystalline
plate and the Nicols have been examined, both from the
theoretical and the experimental point of view, and the
agreement between the two is thoroughly satisfactory at
all points. We have dealt only with the simplest case
that can present itself, that of a uniaxal crystal cut at
right angles to its optic axis, with the axis of the incident
light in the same direction as the optic axis. The re-
sults, of course, are more complex with crystals of a less
simple form, and it may suffice to refer very briefly to a
few other cases.
FIG. 58
CRYSTALS
199
Let us take first the case of two thin plates of the same
material and thickness, both cut with their faces parallel
to their optic axes, and held together with their axes at
right angles to one another. Theory shows that in this
case we should again see a dark cross, and that the other
dark lines in the field should be a series of rectangular
hyperbolas such as are represented in Fig. 59 a. This
figure shows the darkest portion of the field according to the
theory, while Fig. 59 b is from a photograph of what is
really seen.
Consider next a thin plate cut from a biaxal crystal,
with its faces at right angles to the bisector of the angle
between the optic axes. Put this plate between a pair of
crossed Nicols, and turn it so that the line joining the
ends of the optic axes is parallel or perpendicular to the
" principal planes " of the Nicols, i.e. is parallel to lines
such as QN 1 or to QN 2 of Fig. 54 6. If a beam of light
like that used before now fall upon the plate, we should
expect alternations of light and darkness. Investigation
shows that a black cross is to be looked for in this case
200
LIGHT
as before; but the other dark lines in the field will no
longer be circles or hyperbolas. Their form is easily deter-
mined from theory, and it appears that they belong to a
class of curves known as lemniscates, whose foci are at the
ends of the two optic axes. Figure 60 a shows the lines
drawn through the darkest part of the field, according to
the predictions of theory. Figure 60 b is from a photo-
graph of what is actually seen (except, once more, for the
CRYSTALS 201
color), and by comparing these two figures you will see
that there is an excellent agreement.
Lastly, let us turn the crystalline plate through an
angle of 45 from its last position and see the change that
takes place. The lemniscates should appear, as before,
but turned through half a right angle; and there should
be no black cross, its place being taken by a dark hyper-
bola going through the ends of the optic axes. The
darkest part of the field, according to theory, should appear
as in Fig. 61 a, and this should be compared with the
neighboring figure (61 b) from a photograph of the actual
appearance. These various figures give no idea of the
beauty due to the scheme of color; but they may serve
their purpose of bringing home to you with what accuracy
theory enables us to foretell what is to be expected under
any given circumstances, and to account for all the de-
tails of the phenomena that have been observed.
IX
DIFFRACTION
SUPPOSE you throw a stone into water at S (Fig. 62),
and watch what happens. A circular wave will travel out
over the surface of the water in all directions. At one
time the crest of the advancing wave will be at OP; a
little later it will have
moved on to EQ. How
\E is this effect produced?
The impact of the stone
causes a disturbance at
S, an up-and-down
motion of the water
there, and this is com-
municated to the neigh-
boring particles. Each
particle hands on the
disturbance to its neighbor; but in what way does it
hand it on? It looks somewhat as if the disturbance
could be passed along only in one direction. P seems
to pass on its motion only in the direction Pa, forwards
towards Q, and not backwards toward S, or laterally
along Pb or PC or Pd. If this were so, it would appear
to explain some of the phenomena. Thus, it would
explain why there is no disturbance behind OP (in the
direction toward 'S), and in the case of waves of light
and it is, of course, with the analogous problem in light
202
FIG. 62
DIFFRACTION 203
that we are interested why, if we put a screen in the
position OF, we appear to get a sharply defined shadow
extending to E, where SOE is a straight line. This familiar
phenomenon of shadows gave rise to the idea that light
moves in straight lines, and, as we have seen, the law of
the rectilineal propagation of light was one of the few
general laws of optics that were known to the world in OCA
pre-Newtonian days. The only objection to the law is ^
that it is not true. Light does not move in straight lines,
and the shadow of an obstacle is not sharply defined by
drawing straight lines from the source of light to the edge
of the obstacle. Closer examination reveals the fact that
light bends round a corner. This phenomenon was some-
times spoken of as the inflection of light, but is now always
referred to as diffraction.
When we look into the question of the amount of bend-
ing round a corner, and discuss it by means of the prin-
ciples to be referred to later, we find that the bending
depends very largely on the length of the wave, short waves
being much less bent than long ones. This dependence
of the bending on the wave-length is so important that it
may be well to make an experiment to bring it home to
you. In ordinary speaking you set up waves in the air,
and you know that these must bend freely, as you can
easily hear a person who is speaking round a corner. The
length of the waves that are thus set up by speech de-
pends on the pitch of the voice, but we may say that
normally they are four or five feet long. In my hand I
have a whistle that will produce very much shorter waves
than that. As it is now arranged it sends out waves
about four inches long, and by altering its mechanism I
can make the waves shorter and shorter. If one of you
204 LIGHT
were to go behind that large screen, and listen carefully
while I sound the whistle, you might be able to determine
whether there is anything resembling a sound shadow or
not. It will be better, however, to arrange things so that
all can observe the phenomena together. We can do this
easily by aid of this sensitive flame that you can all see,
and that will serve just as well as an ear (indeed, better
than that in some respects) to detect the presence of a
wave in the air. The manner of producing this sensitive
flame need not concern us at present, all that need be
known being that it is sensitive you observe that the
flame ducks when I blow this whistle and the disturbance in
the air strikes it. For our purposes this flame has the im-
portant advantage over the ear that it can be made sensi-
tive to waves that are too short to produce the sensation
of sound. It has already been pointed out that the eye
is sensitive only to waves whose lengths lie within a cer-
tain range, and the same is true of the ear. Very high
notes and very low notes cannot be heard, as they do not
affect the ear in the right way, and it should be remem-
bered when watching this experiment with the whistle and
the flame that very high notes are very short in wave length.
As I alter the effective length of this whistle, you can hear
that the note it emits gets shriller, and now that the wave
is so short that you hear no note at all, there is, as you see,
a somewhat sharply defined shadow of the screen. You
observe that when I move the whistle very slightly to
the right or to the left of a line joining the sensitive flame
to the edge of the screen, there is a perceptible difference
in the effect. In one case the flame is inside the shadow,
and is unaffected of the waves in the air; in the other it
responds to the action of these waves. You see, then,
DIFFRACTION 205
that although an ordinary sound-wave bends readily round
a corner, there is scarcely any bending perceptible when
the length of the wave is sufficiently short.
This problem of the bending of light round a corner has
presented difficulties almost from the beginning of modern
science. Newton knew some of the phenomena quite
well, but he did not observe them closely enough to grasp
all that was significant, and his failure to do so led him
seriously astray. He knew that the shadows of bodies
are bordered with colored fringes. He knew also that if
the light from a small source falls upon a body, the shadow
is not exactly coincident with the geometrical shadow, as it
is sometimes called, i.e. the figure formed by drawing straight
lines from the source of light past the edge of the opaque
body and observing where these lines are interrupted by
the plane on which the shadow is cast. Thus, in his first
observation on "The Inflexions of the Rays of Light," in
the third book of his " Opticks," he tells us that he let light
stream through a pinhole in a piece of lead and fall upon
various objects, and he then observed that "the shadows
were considerably broader than they ought to be, if the
rays of light passed on by these bodies in right (i.e. straight)
lines. And particularly a hair of a man's head, whose
breadth was but the 280th part of an inch, being held in
this light, at the distance of about 12 feet from the hole,
did cast a shadow which at the distance of 4 inches from
the hair was the 60th part of an inch broad, that is, about
four times broader than the hair." In this case there
seems to be a bending away from the shadow and not
into it. This puzzled Newton, and seemed to him so in-
compatible with a wave theory of light that he rejected
that theory. Listen to what he says in one of his famous
206 LIGHT
queries at the end of his book on optics. "Are not all
hypotheses erroneous in which light is supposed to con-
sist in motion propagated through a fluid medium ? If it
consisted in such motion, it would bend into the shadow.
For motion cannot be propagated in a fluid in right lines
beyond an obstacle which stops part of the motion, but
will bend and spread every way into the quiescent medium
which lies beyond the obstacle. The waves on the surface
of stagnating water passing by the sides of a broad obstacle
which stops part of them, bend afterwards, and dilate
themselves gradually into the quiet water behind the
obstacle. The waves of the air, wherein sounds consist,
bend manifestly, though not so much as the waves of
water. But light is never known to follow crooked pas-
sages nor to bend into the shadow. For the fixed stars, by
the interposition of any of the planets, cease to be seen.
And so do the parts of the Sun by the interposition of the
Moon, Mercury, or Venus. The rays which pass very near
to the edges of any body are bent by the action of the
body ; but this bending is not towards but from the shadow,
and is performed only in the passage of the ray by the
body, and at a very small distance from it. So soon as
the ray is past the body it goes right on/ 7 Had Newton
varied his experiments, and observed carefully enough, he
could have found a bending towards the shadow, as we
shall see later. Here, then, we have a striking case of a
very great scientist being led astray, and, as we now see it,
very seriously astray, by experimental evidence. Snares
seem to be laid along every path, and we may be en-
trapped by experiment just as well as by theory. There
are so many warnings up along the latter road that there
is not the same excuse for falling. And yet men fall, as
DIFFRACTION 207
Brewster did not so very long ago, if Tyndall reports him
fairly. " In one of my latest conversations with Sir David
Brewster, he said that his chief objection to the wave
theory of light was that he could not think the Creator
guilty of so clumsy a contrivance as the filling of space
with ether in order to produce light." Such a high a priori
road is probably the most dangerous of all.
To return to the problem of diffraction, there is by this
time not the slightest doubt that light does bend round a
corner. As we shall see presently, we have many care-
ful determinations of the amount of bending and of vari-
ous details of the phenomena. With the refinements of
modern instruments at our disposal, it is comparatively
easy to deal with these matters experimentally ; but when
we come to examine them from the standpoint of theory,
a number of difficulties arise. The form that the problem
takes in the mind of a mathematical physicist is something
as follows. A given disturbance is set up in the ether by
the presence of a source of light. This spreads out in a
known manner, and there is no special difficulty in calcu-
lating and predicting all the details of the phenomena to
be observed, provided that no opaque obstacle is present.
Suppose, however, an opaque body is put in the way of
the waves in the ether. How does this affect the motion
of the waves in the region beyond the body ? The physical
and mathematical conditions to be satisfied are easily
stated. We know the disturbance in the neighborhood of
the source, and we know the conditions to be satisfied at
all points of the boundary of the opaque obstacle. It
looks as if everything that we want should be within our
powers of computation, and in other fields many similar
problems have been successfully attacked. In the case of
208 LIGHT
optics, however, peculiar difficulties present themselves
owing to the extreme shortness of the waves of light, and
these difficulties have not as yet been successfully over-
come, except in a few very special cases. In general, the
complete solution of the optical problem of diffraction still
awaits us. I trust that you do not misunderstand me
here. It is not the case that there is any special difficulty
with the general theory, nor any apparent discrepancy be-
tween theory and observation. The difficulty that I speak
of is purely one of mathematical analysis, and arises en-
tirely from the limitations of our skill in that branch of
art. Doubtless it will be overcome in time.
Meanwhile we are constantly reminded that " Nature is
not embarrassed by difficulties of analysis/' and that, in
our interpretation of Nature, we must not allow such
difficulties to embarrass us unduly. Thus, in the present
case, although a rigorous mathematical solution is as yet
unattainable in general, it may be possible to get an
approximately accurate solution which is good enough for
practical purposes. As a matter of fact, this has already
been done, and the results are found to be as accurate as
we need in the present state of our experimental skill.
Thus the difficulties of mathematical analysis to which
reference has been made may very properly be handed
over to our successors, whose finer instruments and more
accurate observations may demand a correspondingly re-
fined analysis. The method that is generally adopted in
dealing with such problems to-day is to make use of what
is known as the Principle of Huyghens. Let us look once
more at Fig. 62, with which we dealt at the outset of this
lecture. A disturbance was set up at the point S, and
from this point waves traveled out in all directions. If this
DIFFRACTION 209
be true of the point S, we should expect it to be true for
any other point that is disturbed; whether the initial dis-
turbance be set up by a stone or some other agent can
make no difference, and there is nothing peculiar to S,
except that it happened to be the point that was disturbed
first. Hence, any other point, such as P, must be re-
garded as a center of disturbance from which waves pro-
ceed in all directions. The Principle of Huyghens merely
states that each point of the front of an advancing wave
may be regarded as a center from which secondary waves
spread out, not in one direction, such as Pa, but in all
directions. What will be the effect of the combination of
all the secondary waves thus set out is a question to be
answered by the help of the Principle of Interference,
which makes it clear that the effect will depend on the
amplitudes and phases of the various secondary waves
that have to be considered. To determine exactly what
is the law governing these features of the secondary waves
is a difficult problem. It was attacked by Stokes in a
famous memoir "On the Dynamical Theory of Diffraction."
In this the problem was to determine what must be the
amplitudes and phases of the secondary waves, so that in
combination these waves would give the actual disturb-
ance in front of the advancing wave and no disturbance at
all behind it. Interesting and instructive as was Stokes' s
discussion of this problem, his solution has not escaped
criticism. Amongst other things it has been pointed out
that the problem is really an indeterminate one. The
question asked is one that can have several answers, like
the question, What two integers, when added together,
make 6 ? and there is nothing to determine which of the
answers is to be preferred. Various laws have been sug-
210 LIGHT
gested other than the one that Stokes arrived at, and it
should be noted that, while differing in other respects,
they agree as to the disturbance produced by the secondary
waves in the only region where these waves are really
effective, i.e. in the neighborhood of the direction PQ.
The waves that travel in all other directions have their
influence neutralized through interference with other
waves. If, then, we wish to estimate the effect of all the
secondary waves that pass over Q, it appears that we
need consider those only that set out from the wave-front
OP in the neighborhood of P. It is for this reason that PQ
is sometimes spoken of as the path of the effective disturb-
ance that passes from P to Q, and this effective disturbance
constitutes the ray of light.
Let us suppose, now, that a screen OF is interposed so as
to interfere with the advance of the waves in the ether.
How will this affect the propagation of the waves and
the optical phenomena in the region beyond the screen?
This is a hard question to answer, owing, as has been ex-
plained, to the mathematical difficulties that arise in its
discussion. These difficulties have been completely over-
come only in one or two special cases, but an approxi-
mate solution has been reached in many others. To ob-
tain this, an assumption is made that is certainly not
justified if we insist on absolute rigor and exactness
throughout. Such a lofty attitude, however, makes prog-
ress impossible, and as practical men we prefer to make
some advance, even by means of an unjustifiable assump-
tion, provided we have reason to suppose that this assump-
tion will not lead us too far astray. The assumption
made is that the effect of the screen is merely to destroy
the secondary waves that, but for its presence, would be
DIFFRACTION 211
propagated from the various points of its surface, while
all the other secondary waves from points not on the
screen go forward just as if the screen were away. It is
easy to see that this cannot be quite strictly true. Con-
sider the simple case of a stream of water flowing in a
closed space between two horizontal boards represented in
section by AB and CD in Fig. 63 a. Each particle would
move horizontally, along lines such as the dotted ones
D
(a) (6)
FIG. 63
of the figure. Now put in an obstacle, such as OF in
Fig. 63 b. This would do more than merely stop the
onward rush of the drops of water that struck the obstacle.
It would affect the motion in the neighborhood of F, and
the motion below and to the right of that point in Fig.
63 b would not be just the same as at the corresponding
point of Fig. 63 a. In the case of waves it appears,
however, on investigation, that the error introduced by
this assumption is inappreciable except within a few wave-
lengths of the edge of the obstacle. We shall see before
the close of this lecture that there are something like
50,000 wave-lengths of light to the inch, and owing to this
extreme shortness, the region of error due to the false
assumption is so small as to be practically negligible.
Proceeding, then, with this assumption, we are able to com-
pute all the essential details of the optical phenomena in
a large number of interesting cases, and in many of these
to test our (admittedly imperfect) theory by comparison
212 LIGHT
with the most careful measurements that are available.
This was first done by Fresnel in a classical memoir on
Diffraction that was crowned by the French Academy in
1819. Fresnel considered the case of light falling on an
opaque screen with a straight edge. If the light were
propagated strictly in straight lines, there would be a
sharply defined shadow, coinciding with the geometrical
shadow, the contour of which is determined by drawing
FIG. 64
straight lines from the source of light to the edge of the
screen. Inside this shadow there would be absolute dark-
ness, and outside it uniform brightness. The curve of in-
tensity would then be the dotted curve of Fig. 64. In
this represents the position of the edge of the geometrical
shadow, the shadow being to the left of 0. OP represents
the intensity of the incident light, as well as that in the
bright part of the field at some distance from the edge of
the shadow. Fresnel showed that the theory that has
just been sketched would lead us to expect a distribution
of light that is indicated by the continuous line of the
figure (abode...). It will be observed that there is no
longer complete darkness to the left of 0, but that the light
fades away rapidly as we go into the shadow. Perhaps
the most striking result of the investigation is that outside
the shadow (to the right of in the figure) the intensity of
DIFFRACTION
213
the light is not uniform, but that there are a series of
bright bands where the intensity is much greater than the
average (c, e, #...), alternating with bands where it is
much less (d, /, h...). The theory indicates, and this
is fully confirmed by experience, that the exact distribution
of light depends on the wave-length of the incident beam.
Fresnel calculated the details for red light of wave-length
0.000638 millimeters or 0.000025 inches. The intensity of
the light at the brightest bands, corresponding to c, e, g...
of Fig. 64, when expressed in percentage of the intensity of
the incident light, was found to be 137, 120, 115, 113, 111,
110, 109..., and that at the intermediate darks bands
(d, f, h...) to be 78, 84, 87, 89, 90, 91, 92... Owing
to the difficulty of making very accurate measure-
ments of intensity, it was not easy to make a searching
test of the theory by comparing these results with those
derived from experiment. There is, however, another fea-
ture that is more easily measured with accuracy, and that
is the distances of the different fringes from the edge of the
geometrical shadow. The following table gives the posi-
tions, obtained from theory and also from observation, of
the first five dark bands for the red light used by Fresnel.
The results are set out for three different distances (d) of
ct=100
d = 1011
d=6007
Theory
Observation
Theory
Observation
Theory
Observation
First Fringe . .
2.83
2.84
2.59
2.59
1.14
1.13
Second Fringe .
4.14
4.14
3.79
3.79
1.67
1.67
Third Fringe. .
5.13
5.14
4.69
4.68
2.07
2.06
Fourth Fringe .
5.96
5.96
5.45
5.45
2.40
2.40
Fifth Fringe . .
6.68
6.68
6.11
6.10
2.69
2.69
214 LIGHT
the screen from the source of light. All the distances are
given in millimeters, and you will remember that one milli-
meter is equal to 0.03937 inches. It will be seen that the
agreement between theory and observation is excellent.
The position of the bright bands depends upon the wave-
length, and so on the color of the light. If, then, we em-
ploy a mixture of colors such as constitute white light, we
shall get a series of colored fringes in slightly different posi-
tions. These will tend to overlap one another, and the
overlapping will make it difficult to distinguish the outer
bands of color. Hence, for accurate measurements designed
to test any theory, it is expedient to use homogeneous light,
and so have only a single wave-length to deal with.
The same general method will enable us to discuss the
phenomena to be looked for in various other circum-
stances. Thus, instead of dealing with a single straight
edge, we may wish to examine the effect of two parallel
edges close together constituting a narrow slit. The simplest
apparatus to use for such experimental purposes is your
own hand. Hold two fingers together so that they are
very nearly closed, and look through the narrow opening
at a distant bright object. You will see a number of
colored fringes, but if you wish to investigate the phe-
nomena carefully, it will be better to take a little more
trouble and proceed as follows. Cut a slit about an
eighth of an inch wide in a black card and fix this in front
of a bright light. Look at this slit through the narrower
slit made by drawing with the point of a needle a straight
line on a piece of blackened glass, and hold the two slits
parallel to one another. You will at once observe a series
of colored spectra. If you make the light homogeneous by
interposing, say, a red glass between the light and the
DIFFRACTION
215
first slit, you will see a series of bright red bands, R 1 R%...
(Fig. 65), on each side of the central image R, and you
will notice that their intensity diminishes as you get
further away from the central band. On replacing the
red by blue, you will observe a similar effect, but the bright
blue bands will be narrower and closer together than were
the red, as is indicated roughly in the figure by the posi-
tions of the rectangles B, B v .. You see from this that
if both colors are present together, the different bands will
overlap, and you will understand the various spectra that
R
^ PI p
R
R 3
*i
R
*,
R 2
FIG. 65
are seen when white light is employed. By fixing a nar-
row slit on the end of your opera glasses, you can readily
see these spectra and examine their details at your leisure.
Closely allied to the case of a narrow slit is that of a
narrow obstacle placed in the path of a beam of light.
Reference has already been made to Newton's experiment
with a human hair, which exhibits the phenomena. You
can easily see this for yourselves by partially closing your
eyes and looking at a bright light through your eyelashes.
A fine wire is now placed in front of the lantern, and you
observe that the dark shadow on the screen is bordered
with colored fringes, and now that a mesh of wires is sub-
stituted for the single wire, you see that the color effects
are quite gorgeous. The effects to be expected from
apertures and obstacles of various forms have been care-
fully examined both theoretically and experimentally, and
216 LIGHT
the agreement between theory and observation is, on all
points, most satisfactory. We have time only to select a
single example, that of a circular aperture (and the cor-
responding case of a circular obstacle). This is especially
important, owing to the fact that most optical instruments
(telescopes, microscopes, and the like) are arranged so that
the light passes into them through a circular aperture.
The mathematical analysis of the case is long and some-
what complex, but the fundamental principles employed
are the same as those that have already been explained.
The investigation shows that where light shines through a
circular aperture upon a screen, the screen is not uni-
formly illuminated, but that there are marked variations
in the intensity at different portions of the circular patch
of light. The points where the brightness is least con-
stitute a series of concentric dark rings whose radii can
be determined from theory, and, of course, observed ex-
perimentally. The sizes of these rings depend on the
color of the light, so that when white light is employed,
the screen exhibits a series of colored rings. Lommel
made careful determinations of the radii of these rings
for various colors, and compared his observations with the
deductions from theory. The results for the first four
dark rings are set out in the table below for a few cases,
but Lommel dealt with over 180 such cases, and in all of
these the agreement between theory and observation was
as good as in those here selected. The different colors
used were red, orange, green, and blue, corresponding to
the spectral lines known as C, D, E, and F and to wave-
lengths of 0.0006562, 0.0005889, 0.0005269, and 0.0004861
millimeters. The radius of the aperture was 0.28, the
distance of the edge of the aperture from the source of
DIFFRACTION
217
light was 2120, and of the source of light from the screen,
2210.4. These numbers and those in the table all repre-
sent millimeters.
BLUB
GREEN
ORANGE
RED
Theory
Observation
Theory
Observation
Theory
Observation
Theory
Observation
0.015
0.032
0.034
0.057
0.056
0.082
0.082
0.156
0.158
0.179
0.175
0.308
0.305
0.237
0.231
0.254
0.254
0.275
0.276
0.403
0.406
0.343
0.338
0.333
0.333
0.361
0.361
0.449
0.451
Theory also enables us to calculate the intensity of the
light at different positions on the screen. It thus appears
that about 84 per cent of the whole light is inside the first
dark ring. The central spot is not, however, of uniform
brightness, but shades off as we proceed outwards from
the center, the intensity halfway between the center and
the first dark ring being about 37 per cent of that at the
center. Perhaps the most important result to bear in
FIG. 66
mind is that the image of a point is not a point, but a
complicated system of rings of the kind indicated roughly
in Fig. 66 a. Figure 66 b represents the image of two
points close together, and shows how the two images tend
218
LIGHT
to overlap and produce a blurred effect. Fortunately, most
of the light is confined within the first ring, so that we do
not go far wrong in supposing that the image of a point
as seen through a telescope is a small disk. Do what we
will, however, we cannot make this disk shrink to a point,
and when we take a photograph we set the light the diffi-
cult problem of drawing a clear picture with a blunt
pencil. The bluntness of the pencil depends upon the
diameter of the little disk of light, and to sharpen it as
much as possible we must increase the size of the aper-
ture and use light of the shortest wave-length that can
be employed. Fortunately, for photography, the short
waves have great actinic power; but the other require-
ment, that of a large aperture, is not so easily satisfied
and, as it involves great size, adds seriously to the cost of
the best telescopes used for astronomical purposes.
The corresponding problem presented by the shadow of
an opaque disk was also solved by Lommel. Here, too,
we have a series of alternations of light and darkness, giving
the appearance of a number of concentric rings with their
center at the center of the shadow. The table below gives
the radii of the first four dark rings in a few cases; but
Lommel dealt with over sixty cases in all, and found the
same good agreement between theory and observation.
BLUE
GREEN
ORANGE
BED
Theory
Observation
Theory
Observation
Theory
Observation
Theory
Observation
0.088
0.090
0.096
0.096
0.109
0.113
0.119
0.124
0.200
0.197
0.219
0.220
0.242
0.237
0.268
0.265
0.307
0.310
0.335
0.333
0.369
0.367
0.403
0.400
0.406
0.406
0.438
0.440
0.478
0.479
0.525
0.525
* OF THE
UNIV
DIFFRACTION 219
i^C>
Here the radius of the disk was 0.32, and the distance of
its edge from the source of light was 1485. Observations
were made with the four colors previously mentioned,
blue, green, orange, and red, the distance of the screen
from the source of light being 1639.9, 1642.6, 1643.3, and
1643.2 for the different colors. All the numbers represent
millimeters. The different radii for the different colors
give an idea of the amount of overlapping when white
light is employed, and of the arrangement of the colors in
the fringes. In this case also theory enables us to calcu-
late the intensity of the light at different points in the
shadow. In this connection one feature may be pointed
out, as it is probably unexpected. It appears from the
investigation that at the very center of the shadow there
should be a bright spot, and that this should be just as
bright as if there were no disk present to cut off the light.
This deduction seemed so absurd when it was first an-
nounced that it was regarded as a serious objection to the
wave theory. A little care, however, in experiment showed
nevertheless that, however unexpected or seemingly im-
possible, it was none the less perfectly true. If you have
the resources of a physical laboratory at your disposal,
you will find no great difficulty in trying this for yourself.
You will need a carefully made circular disk that is not
too large, and you will need to make the necessary adjust-
ments with some precision. I will modify the experiment
so as to exhibit the result to the whole audience and deal
with sound-waves rather than with light, so as to work
on a larger scale. The mathematical analysis is very
similar in the two cases, but the sound-waves have the
advantage of being much longer, so that we do not need
the same refinement. Introducing you once more to this
220 LIGHT
whistle and sensitive flame, I fix a circular disk of glass,
about a foot in diameter, between the two. By moving
the whistle into different places, you observe that there is
a marked sound shadow behind the disk; but now that,
after some adjustment, I have got the whistle so that it
is exactly opposite the center of the disk, you see that
the flame ducks, and by doing so indicates the presence of
a considerable disturbance in the air.
The applications of the theory of diffraction to the
construction of optical instruments and to the explanation
of various optical phenomena are so numerous that it
would be impossible in the time at our disposal to deal
with them at all adequately. In the short time that re-
mains to me for this lecture I shall endeavor to explain
very briefly how it is that the principles of diffraction
enable us to measure the lengths of different waves of
light and to measure them with wonderful accuracy.
Several methods may be employed for this end, but I
shall confine myself to what is the simplest for purposes
of exposition. This measures the wave-lengths by the
aid of a diffraction grating, an extremely simple instrument
as far as its appearance is concerned. It is made by rul-
ing a great number of very fine parallel lines on speculum
metal or glass. The former is viewed by reflection, as the
metal reflects a large proportion of the incident light, and
is called a reflection grating. The glass reflects some light,
and usually transmits more. If viewed by transmission,
i.e. if the incident light be allowed to stream through the
grating and the transmitted beam be then examined, the
arrangement is described as a transmission grating. In
either of these cases the effect of the grooves made by
ruling is to scatter irregularly the light that falls on them,
DIFFRACTION
221
so that the grooves behave as if they were opaque and
destroyed the light that strikes them. Let us consider
light falling normally on a transmission grating, a cross-
section of the surface of which is represented in Fig. 67.
The thick lines in this figure, such as x^, z 2 a 3 ..., show
the positions of the grooves, which, as we have just seen,
FIG. 67
practically stop all the light that falls on them. Waves
enter the instrument through the portions a-^x^ a%x 2 ..., and
if we consider a^ as the front of an entering wave, then
every point on this front is to be regarded (as was stated
earlier) as a center of disturbance from which waves, and
therefore rays, spread out in all directions. If the front
of the incident wave were complete, that is, if there were
no obstructing grooves, the waves that spread out laterally
in any such direction as a^ would be nullified by inter-
ference with the waves that proceed from other portions
of the wave-front, and it would only be directly in front
of ! that the effective disturbance would be appreciable.
The grooves, however, cut out some of the waves that
222 LIGHT
would contribute to this interference. This must modify
the results, so that it may well be that there is an ap-
preciable disturbance in some such direction as a^.
To investigate this matter more fully, we must bear in
mind the fundamental idea that lies at the root of the
Principle of Interference; namely, that two waves that
are similar in all other respects, but that differ in phase
by half a wave-length, or any odd multiple thereof, will
interfere and produce darkness, while if they differ in
phase by a whole wave-length, or any multiple thereof,
they reinforce one another and give greater intensity of
light. Let us consider all the secondary waves that travel
outward from the various points of the incident wave-
front in a given direction, such as a^ (to which a z n 2 and
a 3 n 3 in the figure are parallel). The difference of phase
between the waves from a l and a 2 is represented by a^',
where a^ is perpendicular to a^n^ This will also be
equal to the difference of phase between the waves from
&! and & 2 , provided a 2 6 2 be equal to ajb^ Now if the grooves
be of exactly the same width, and the spaces between them be
equal, it will be possible to divide all the spaces into the
same number of equal parts, so that a 1 & 1 = 6 1 c 1 = ... = a 2 6 2 =
& 2 c 2 = ...=a 3 & 3 = & 3 c 3 = .... We shall also have a 1 n 1 = a 2 n 2 =
a 3 n 3 = ..., and the difference of phase between the secondary
waves from a l and a 2 will be the same as between those from
&! and 6 2 or from c l and c 2 , or from a 2 and a 3 or from 6 2 and b 3 ,
and so on. Let us suppose, further, that the incident light
is homogeneous, i.e. all of the same wave-length, and that
a^i is half this length. Then if all the secondary waves
could be brought together without relative change of
phase, the wave from a 1 would interfere with that from a 2 ,
the wave from 6j would interfere with that from 6 2; and
DIFFRACTION 223
so on, thus producing darkness in the direction
The combination of the different secondary waves
is simply effected by means of a lens, which bends
the rays so as to bring them to a focus, and alters the
direction of the wave-motion without changing the rela-
tive phase of the different waves. Let, then, OA in Fig. 68
represent one of the lines in the grating, and OB a line
drawn at right angles to
the plane of the grating
to meet a screen, on which
the light falls, at B. If
OD 1 be drawn in the di-
rection represented by
a^ in Fig. 67, and DjZy
be drawn on the screen
parallel to OA, then from
what has been said it will
be seen that Di/Y will coincide with a dark line on the
screen. This, however, will not be the only dark line,
for the same interference will take place when a-pii is
equal to any odd multiple of half a wave-length as when
it is simply half a wave-length. If OZ) 2 , OZ) 8 ,... be
the directions corresponding to phase difference of three
half wave-lengths, five half wave-lengths, and so on, then
there will be dark lines D 2 D 2 ', D 3 D 3 ',..., all parallel
to OA. We have dealt with the case where a^ is half
a wave-length or any odd multiple thereof. Let us sup-
pose next that a^ is a wave-length, or any exact number
of wave-lengths. Then the various secondary waves, in-
stead of interfering, will reinforce one another, and the
corresponding portions of the field will be unusually
bright. We shall thus have a series of bright lines, such
224 LIGHT
as #!#/, # 2 ZY>--> m Fig. 68. On comparing the triangle
a^aj of Fig. 67 with OBB l of Fig. 68, it is seen that these
triangles have equal angles. The angle a^n^ is equal to
the angle OBB l} as each is a right angle, and the angle
n^aj is equal to the angle BOB V since OB is perpendicular
to tt^, and OB l is parallel to a^n^ and therefore perpendicu-
lar to n^. As the two triangles have equal angles, it
follows geometrically that they must be similar triangles
differing only in scale. Hence the ratio of a^ to a x a 2
must be equal to the ratio of BB l to OB lt or, in algebraic
symbols, ^1 = - 1. Thus we have a^ = a^ x 1. Now
.
On 1
can be measured accurately by counting the number
of grooves in a given distance. Thus, if on the grating
there are twenty thousand lines to the inch (there are
more than this on many good gratings), then a^ is one
twenty-thousandth of an inch. The distances BB 1 and
OB 1 might be measured directly, but it is only their ratio
that is wanted, and this can be determined most simply
and accurately by the aid of trigonometry, once the angle
BOB l has been measured. The measurement of this
angle can be made with great precision and then, from
T>T>
the equation ohtti = a^ x J = a^ sin BOB l} the quantity
is readily calculated. It has been indicated, however,
that this quantity a^ is the wave-length of the light
with which we are dealing, so that the problem of deter-
mining the wave-length has been solved.
If the process thus sketched be carried out carefully
with a good grating, the wave-lengths may be determined
with marvellous accuracy. There are several ways of
testing the results. Thus, if we deal with the bright line
DIFFRACTION 225
B^BI, the calculated value of a^ should be the wave-
length. If we make similar measurements with B^B^,
then the corresponding value of a^ should be twice the
wave-length; with B B B B ' it should be thrice this length,
and so on. The consistency of the various estimates of
the wave-length thus obtained will enable us to form an
estimate of the accuracy of our results. Then, too, we
need not confine our attention to the case of light that
strikes the grating at right angles to its surface. This case
has been dealt with and illustrated in order to simplify
the mathematical discussion as much as possible; but it
requires a very slight effort to extend the argument to the
more general case of oblique incidence and to obtain a
corresponding formula for the wave-length. By making
observations at various angles of incidence and computing
the wave-length, we have other means of testing the con-
sistency and accuracy of our results, and when all pre-
cautions are taken, it is found that these results are
marvellously concordant. For this end, of course, a good
grating is indispensable, and a good grating is an instru-
ment that requires great care and skill in the making.
The rulings must be made with almost perfect accuracy,
for the argument supposes that the distance between the
various grooves and their width is uniform throughout,
and if this be not the case errors will inevitably creep in.
There are other methods of measuring wave-lengths
than the one here described, but time will not permit us
to discuss them. Suffice it to say that few things can
now be measured with such wonderful precision as the
length of a wave of light. Such is the accuracy that has
been attained, that it has been seriously proposed that
the length of a wave of light emitted under certain condi-
Q
226 LIGHT
tions from a specified substance should be adopted as the
standard of length. This standard would have some ad-
vantages over any that are now in use, for all these are
subject to slow and uncertain changes, and the one thing
to be required of a standard above all else is that it should
not change. The length of a wave of light emitted by a
substance depends on properties of the ether and of the
atom that, there is reason to believe, are invariable, so that
this length seems capable of serving as a true standard.
With this end in view Michelson devoted himself for some
time to the problem of determining the length of the
standard meter in wave-lengths. For this purpose he em-
ployed certain radiations from cadmium, which were
chosen on account of their simple character. He found
that the number of light-waves in the standard meter in
air at 15 C and normal pressure was 1,553,163.5 for the
red waves from cadmium, 1,966,249.7 for the green, and
2,083,372.1 for the blue, and that the measurements could
be made so accurately that he could safely say that the
errors were less than one part in two millions.
The following table gives some details with reference to
wave-lengths and frequencies of the waves corresponding
to different parts of the spectrum. The letters ABC...
are the names by which these lines in the solar spec-
trum are known, and an indication of their color is given.
The wave-lengths are expressed in millionths of a meter,
and the frequencies in million millions per second.
DIFFRACTION
227
LINE OF SPECTRUM
WAVE-LENGTH IN
MlLLIONTHS OF A
METER
NUMBER OF WAVES
TO THE INCH
FREQUENCY IN
MILLION MILLIONS
PER SECOND
A
0.75941
33,447
395
B
0.68G75
36,986
437
C (red)
0.65630
38,702
457
D (orange)
0.58930
43,102
509
E (green)
0.52697
48,200
569
F (blue)
0.48615
52,247
617
G (violet)
0.43080
58,960
696
H
0.39715
63,956
755
Before closing this lecture there is one feature of the
phenomena observed when using a grating that must
not be overlooked. We have seen that the position of
the bright lines, such as B-JZi, depends upon the length of
the wave employed. It follows that, if the incident light
be white, the bright lines corresponding to its various
colored constituents will have different positions, so that
instead of a single bright white line at BiBi, there will be
a whole series of such lines forming a continuous spectrum,
with all the colors of the rainbow, in the neighborhood of
#!#/. There will be a similar spectrum near J2 2 -B 2 ', an d
so for the other lines, and to distinguish these various
spectra from one another they are spoken of as spectra of
the first order, second order, or third order, and so on, as
the case may be. It was mentioned in the lecture on
Spectroscopy that a prism was not the only means of
producing dispersion and obtaining a spectrum, and we
see now how this can be done by means of a diffraction
grating. The spectrum produced by a grating has one
great advantage over that formed by a prism in that the
distances of the various colored lines from a certain fixed
228 LIGHT
line are proportional to the wave-lengths, as the above
investigation shows. There are other advantages that
cannot now be discussed, but we may say that for many
purposes of accurate measurement, where a spectrum is
involved, it is better to produce this spectrum by diffrac-
tion rather than by means of a prism.
X
I
LIGHT AND ELECTRICITY
SCIENCE has a vaulting ambition. It views the whole
field of human knowledge and strives to possess it all.
It sets about this tremendous task, however, in a business-
like way and recognizes clearly that, for practical effec-
tiveness, the beginning of wisdom is limitation. To at-
tempt too much is to court failure, and, to avoid this,
barriers have been placed across the field of knowledge,
and individuals are advised to work strenuously within a
little fenced-in portion of the whole field. It is well, how-
ever, occasionally to reflect that all the fences are artificial,
and that they have been put up for practical purposes and
for reasons that may not appeal to the more mature judg-
ment of later generations. It is natural and convenient
to fence off from one another things that seem to have
little or nothing in common, but a deeper insight may
reveal the fact that there is the closest relationship be-
tween what are apparently quite different things. The great
divisions of natural science into Physics, Chemistry, and
Biology are proving, after all, to be entirely artificial, and
barriers between them are being broken down almost
daily. And if this be true of the great divisions, it is true
even more obviously of the subdivisions. In some cases
it is difficult to find any traces to-day of barriers that in
earlier ages seemed natural and inevitable. Thus, in one
field you had to deal with what affects the ear and goes
by the name of sound; in another your problem was to
229
230 LIGHT
discuss the mechanical properties of gases and the laws of
motion within them. In the field of sound you learned
to distinguish one sound from another by its intensity,
by its pitch, and by its quality, and in process of time you
established various laws of sound that enabled you to
foretell the intensity, pitch, and quality of sounds emitted
under various conditions. In the other field you found
that waves could be set up in gases, and that these could
be distinguished by their amplitude, by their frequency,
and by their form, and you learned, by the aid of me*-
chanical principles, to calculate the amplitude, frequency,
and form of the waves set up in given circumstances. In
time it seemed expedient to knock down the fence be-
tween the fields, for by postulating a relation between the
intensity and the amplitude, the pitch and the frequency,
the quality and the form, it was possible to explain all the
peculiarities of sound on mechanical principles, and to
test the theory by experiment in the most rigorous fashion
that could be demanded. Thus to-day the problem of
sound is regarded as a small part of the wider subject of
vibrations (in air and other media), the vibrations being
confined to narrow limits determined by the structure of
the ear.
No two physical sciences seem, at first sight, more
widely separated than light and electricity. My aim in
this lecture is to show that they are in reality most in-
timately related. To this end let me begin by reminding
you of the broadest outlines of the theory of light. We
have seen that in order to coordinate the great mass of
phenomena that have been observed in the field of optics,
it is necessary to postulate the existence of a medium
that we call the ether, and that we endow with definite
LIGHT AND ELECTRICITY 231
and peculiar properties. This ether is capable of trans-
mitting disturbances by means of waves that travel through
it with a speed that is determined by the properties of the
ether, but that have frequencies depending entirely on the
source of the disturbance. If the frequency be within cer-
tain limits that are determined not by the source of the dis-
turbance but by the structure of the eye, the waves will
produce the sensation of light. If, however, the frequency
be higher than the limit set by the eye, then no light is
seen; but the waves may show their presence in other
ways, e.g. by their influence on a sensitive photographic
plate. On the other hand, if the frequency be somewhat
lower than this limit, the waves will produce the sensation
of radiant heat, and if it be very much lower, they will give
rise to electrical phenomena. Thus, from this point of view,
the distinction between photographic action, light, radiant
heat, and electricity is mainly a question of frequency, and
light is seen to be only a small portion of the problem
presented by the propagation of waves in the ether.
As a matter of history the science of electricity was
built up quite independently of that of light. It soon
appeared that to account satisfactorily for electrical phe-
nomena it was necessary to postulate the existence of an
ethereal medium, and in the process of time it became
evident that exactly the same ether, with just the same
peculiar properties, was required for electricity as for light.
The idea of some such medium is a very old one in scientific
speculation, but it was not until about seventy years ago
that the great electrical researches of Faraday placed it
as a leading article of faith in the creed of the scientist.
About thirty years later came the epoch-making work of
Clerk Maxwell. He was deeply imbued with Faraday 's
232
LIGHT
ideas, but had the great advantage of being a skilled
mathematician as well as a physicist. He set himself the
problem of considering minutely the manner in which a
disturbance would be propagated in the ether. Waves
would be set up and would travel with a certain velocity,
carrying certain electromagnetic effects along with them.
In free space, where there is no matter and nothing but ether,
this velocity would be independent of the frequency, and
Maxwell showed that, if his theory were correct, the velocity
could be expressed in terms of certain quantities that could
be determined by electromagnetic measurements. This ve-
locity (v) is the ratio of the electromagnetic to the electro-
static unit charge of electricity. Maxwell's electromagnetic
theory of light consists in the statement that light-waves
are merely electromagnetic waves that have a frequency
lying within certain limits determined by the structure of
the eye. If this be true, the velocity of light (V) in free
space should be equal to the quantity that we have de-
noted by v. V and v can be measured by direct experi-
ment. Here are some of the results expressed in millions
of centimeters per second, with the names of the experi-
menters responsible for them. The variations in the table
F (OPTICAL)
v (ELECTRICAL)
Foucault
. 29,836
Ayrton and Perry .
29 600
Cornu
. 29,985
Klemencic . .
30 150
Michelson . ...
. 29 976
Rosa . . .
29 993
Newcoml) . . . .
. 29 962
Thomson and. Searls
29 955
show that it is difficult to measure these quantities with
very great precision, but there is no evidence that shows
LIGHT AND ELECTRICITY 233
that one is bigger than the other. The presumption is,
therefore, that they are equal, and this is the corner-
stone on which the electromagnetic theory of light is
based.
After Maxwell, the next great step was made by Hertz
about twenty years ago. He succeeded in setting up
electric waves (some of them about a foot in length,
others a yard or more), and investigated their properties.
His famous experiments furnish, perhaps, the most strik-
ing evidence that can be adduced in support of Maxwell's
theory, as he showed that these electric waves obeyed
exactly the laws of light, as Maxwell had predicted they
should. He found that they were reflected so that the
angle of reflection was equal to that of incidence. He
passed them through a large prism of pitch about a yard
and a half high, and showed that they were refracted ac-
cording to SnelFs law. He found, too, that, just as with
light- waves, he could get polarization and also diffraction.
The determination of the speed with which the waves
were propagated was a matter of some difficulty, and at
first it appeared that they did not travel with the same
velocity as does light, but later researches have shown
conclusively that they do. Much has been done since
Hertz's first experiments to clear away doubts and diffi-
culties, and now an almost complete analogy between
electrical and optical phenomena has been proved by ex-
periment. Perhaps I should say in passing that these
electric waves that Maxwell saw with his powerful mind,
and whose properties he predicted, and that Hertz made a
commonplace in every physical laboratory, are the same
waves that we have all heard so much about in more
recent times as employed in wireless telegraphy. They are
234 LIGHT
popularly associated with the name of Marconi, whose
important discovery of the influence of a " grounded
wire/' immensely extended the range of their effective-
ness.
Let us turn now to other evidences of a relation between
light and electricity. It has been stated more than once
that in free ether ; where there is no matter, the velocity of
all waves must be the same, whatever be their frequency,
and we have already seen that there is a good agreement
between theory and observation as to the magnitude of
this velocity. When, however, matter is present, the speed
of the wave varies with the frequency, as was pointed out
at some length in the lecture on dispersion. In that lec-
ture a formula was given connecting the refractive index
(ri), which determines the speed, and the frequency (/),
and if we refer to that formula (p. 66), we see that if / is
zero, so that there are no vibrations at all, and everything
is steady, we then have n 2 =JL Now the electromagnetic
theory indicates that, under these circumstances, K should
be what is known as the specific inductive capacity of the
substance that is dealt with. This can be determined
from purely electrical measurements, and it is important to
see how this determination agrees with its value obtained,
in accordance with our theory, from optical observations.
The two substances that have been most carefully ex-
amined from this point of view are Rock-salt and Fluorite.
The values of K obtained by different observers from
electrical experiments on Rock-salt were as follows (the
name being that of the experimenter quoted) : Curie, 5.85;
Thwing, 5.81; Starke, 6.29; the mean being 5.98. The
corresponding numbers for Fluorite are : Curie, 6.8 ; Romich,
6.7; Starke, 6.9; of which the mean is 6.8. The values of
LIGHT AND ELECTRICITY
235
K, calculated from optical experiments in the two cases, are
5.9 and 6.8, so that we have the following comparison :
SUBSTANCE
K (OPTICAL)
JT (ELECTRICAL)
Rock-salt
5.9
5.98
Fluorite
6.8
6.8
Theory also indicates that there is a relation between
the reflecting power of a metal and its electrical conduc-
tivity, and shows that the reflecting power must depend
on the frequency. By observing the electrical conduc-
tivities of different metals, we are able to predict what
their reflecting powers should be for a given frequency,
and to test the theory by actual measurements of these
reflecting powers. The following table sets forth some of
the results, the numbers expressing the percentage of the
incident light that is reflected. The word " light" is used
in rather a wide sense, for the frequencies fi and / 2 that are
dealt with are so low that the waves are far outside the
range of the visible portion of the spectrum. The fre-
quencies are expressed in million millions per second. It
METAL
/i-
35
/-
i
OPTICAL
ELECTRICAL
OPTICAL
ELECTRICAL
Silver
98.85
98.7
98 87
98.85
98.4
98 6
98 83
98 73
Zinc * .
97 73
97.73
97 45
97.47
96.5
96 5
97 18
97 04
Nickel
95.9
96 4
96 80
96.84
236 LIGHT
will be observed that the agreement between the optical
and electrical estimates of the reflecting power is better
for / 2 than for / x . The explanation of this is that the
theoretical formula employed in the computation is only
approximately true, the approximation being closer for
small frequencies than for large ones.
The various types of evidence for an intimate relation
between light and electricity that have so far been referred
to are all of a somewhat indirect character, and it would
seem reasonable to suppose that there should be some
phenomena that would prove more directly that light and
electricity have something in common. I have now to
direct your attention to evidence of this class. The most
elementary knowledge of the science of electricity will
make it clear that there is a very close relation between
electricity and magnetism. It shows, for example, that
an electric current gives rise to a magnetic field, and that
a piece of iron can be magnetized by passing an electric
current round it. If, then, light and electricity are in any
sense one, we should expect a magnetic field to have some
influence on light, and one of Faraday's epoch-making
discoveries proved that this is the case. Faraday found
that when such a uniform transparent substance as glass
or carbon bisulphide is placed in a powerful magnetic field,
and a beam of plane polarized light is made to traverse
the field in the direction of the lines of magnetic force,
the plane of polarization is rotated. When we dealt in an
earlier lecture with a kindred phenomenon exhibited by
quartz, solutions of sugar, and other optically active media,
we saw that the rotation could be explained once we un-
derstood why a wave circularly polarized in the clockwise
sense should move through the medium with a different
LIGHT AND ELECTRICITY 237
speed than one polarized counter-clockwise. The same
problem presents itself in the explanation of the Faraday
effect; but the solution must be quite different, for here
we have no peculiarities of structure to deal with that can
distinguish the right hand from the left when rotations
are concerned. In this case the explanation is afforded
by the application of certain well-known laws of electro-
magnetism which deal with the mutual influence of a cur-
rent and a magnetic field, and show that different effects
are produced by currents flowing in opposite senses, clockwise
and counter-clockwise. A precise form is given to the
investigation by the adoption of the electron theory,
which has already been referred to. According to this
the atoms of a substance are made up of groups of
electrons, which constitute small charges of electricity,
and, when moving round an orbit, have some of the
characteristics of an electric current. A careful analysis
shows that a right-handed circularly polarized beam
should cross the magnetic field at a different rate than
a left-handed one, so that a rotation of the plane of
polarization is to be expected. It also appears that the
amount of the rotation is directly proportional to the
length of the field traversed, a law that is similar to that
which governs the behavior of optically active media, and
one that, like it, has been amply verified by experiment.
The theory also indicates that the amount of the rotation
depends upon the frequency, so that we have rotatory
dispersion, as in the case of active media. The following
table records the rotations produced by creosote and car-
bon bisulphide for different lines in the spectrum, and
compares the observed values with the predictions of
theory :
238
LIGHT
CREOSOTE
CAKIJON BISULPHIDE
T
SPECTRUM
ROTATION
ROTATION
ROTATION
ROTATION
(theory)
(observation)
(theory)
(observation)
c
0.573
0.573
0.592
0.592
D
0.744
0.758
0.760
0.760
E
0.987
1.000
0.996
1.000
F
1.222
1.241
1.225
1.234
G
1.723
1.723
1.704
1.704
Wood gives the following results for the rotations pro-
duced by sodium vapor for different frequencies in the
neighborhood of the natural frequencies of sodium. The
frequencies (/) are given in million millions per second, and
the rotations (R) are those observed, or calculated, to the
nearest degree :
/
R (THEORY)
R (OBSERVATION)
/
R (THEORY)
R (OBSERVATION)
501
5
5
510
93
90
504
10
10
511
43
43
505
23
20
512
41
40
506
38
40
513
20
20
507
59
66
514
9
10
508
89
90
516
5
5
Theory also indicates, and experiment verifies, that
rotation is in the same absolute direction when the light
is travelling from A to B as from B to A. Thus if, to a
person at A looking towards B, the rotation appears to be
clockwise when the light goes from A to #, then if the
light be reflected from B so as to return to A } the rotation
LIGHT AND ELECTRICITY
239
will still appear to A to be clockwise. This leads to a
somewhat curious result. The path of a ray of light, no
matter how crooked it may be, is usually reversible. If
A can see B, then B can see A, and this is true whether
they look at one another directly, or whether the light be
reflected and refracted at various points in the passage
from one to another. You
&
may not be able to see a per- {
son directly, and yet you
may have a clear view of him
by reflection in a mirror ; but
if this be so, you know that
he also can see you in the
mirror. Thus, by no ordi-
nary optical device can A see
B without B being able also
to see A. However, by util-
izing this power of rotating
the plane of polarization possessed by a magnetic field, it is
possible to think of an arrangement by means of which B
could see A, while A could not see B. Take two Nicol
prisms and set them with their principal planes ON 1 and
ON 2 (Fig. 69) inclined at an angle of 45. Place them in
a medium in a magnetic field that has just the necessary
strength to turn the plane of polarization counter-clockwise,
say, through an angle of 45. The light that goes from A
passes through the first Nicol and then is plane polarized,
the plane of its polarization being parallel to ON^ After
passing across the magnetic field, this plane is rotated
through 45, and so is parallel to ON%. The light is thus
polarized just in the right plane to pass freely through
the second Nicol, so that it reaches B, who will therefore
FIG. 69
240 LIGHT
have no difficulty in seeing A. Now think of the light
that sets out from B towards A. On passing through the
first Nicol that it reaches, it will be plane polarized, with
the plane of its polarization parallel to ON 2 . It then
enters the magnetic field and, in crossing it, has the plane
of its polarization rotated 45 in the direction indicated in
the figure. Thus the light is polarized in the direction Oa,
which is at right angles to ON V so that the light cannot
get through the Nicol to reach A. Hence B sees A with-
out A seeing B.
The Faraday effect with which we have been dealing
was the first thing of the kind discovered that exhibited
a direct action of magnetism on light, but there have
been several similar discoveries since. Thus, about thirty
years ago, Kerr found that plane polarized light is con-
verted into elliptically polarized light when it is reflected
from the polished pole of an electromagnet, under circum-
stances in which this change could not occur if the field
were not magnetic. A few years earlier the same experi-
menter had discovered another interesting relation between
optical and electrical phenomena. He found that a dielec-
tric, like glass, or even a liquid, such as carbon bisulphide,
behaves quite differently when in a powerful electric field
than when it is not so placed. It acquires the doubly
refracting properties of a crystal. This seems to indicate
that the electric field has the effect of arranging the elec-
trons in order, and so of producing something like the
definite structure that gives a crystal different optical
qualities in different directions, and accounts for its doubly
refracting power.
Even more interesting than the Kerr effect is that of
Zeeman, discovered in 1896. He found that a magnetic
LIGHT AND ELECTRICITY 241
field could alter the positions and the character of certain
lines in the spectrum. This is a very significant fact, if
you bear in mind what has been said as to the position of
a line in the spectrum and its relation to the frequency of
the vibrations going on within the atom. To alter the
frequency, you must interfere with the mechanism of an
atom, and Zeeman's discovery proves that you can do
this merely by placing the atom in a strong magnetic
field. In view of the well-known influence of magnetic
forces on electric currents, we may find in the Zeeman
effect a powerful support for the electric theory of matter
that is a leading feature of recent speculation, and it is
mainly because of this that the phenomenon has received
so much attention from the world of physical science.
Let us see, somewhat more clearly, what the Zeeman
effect is (at least in its simplest aspect), and then consider
the general outlines of the explanation that has been sug-
gested. We have been reminded that when light from a
luminous body in the form of vapor is viewed through a
spectroscope, the spectrum is crossed by certain bright
lines which have definite and fixed positions for any given
substance in a given condition. So well fixed and well
known are these lines that, as has been seen, we may
readily determine the nature of a substance by noting
carefully the positions of these lines. Zeeman's striking
discovery was that, when the luminous body was placed
in a strong magnetic field, a single line was replaced in
some cases by two lines, one on each side of the position
of the original line ; in other cases by three lines, one in
the position of the original, and one on each side thereof.
Later researches have revealed more complicated cases,
but we shall confine our attention to those that are simplest.
242
LIGHT
Without entering too much into technicalities, let me
indicate the explanation afforded by Lorenz of the simplest
case of the Zeeman effect. The fundamental idea is that
which lies at the root of the electric theory of matter. It
supposes that, in its last analysis, an atom of matter
would be found to consist of a number of moving charges
of electricity, which now usually go by the name of elec-
trons. Theory indicates and experience proves that a
FIG. 70
charge of electricity moving rapidly round a closed orbit
has an effect similar to that of an electric current flowing
in the same circuit. Now it is one of the most widely
known and most firmly established laws of electromag-
netism that a current is affected by the presence of a mag-
netic field, so that we have good reason to suppose that
an electron moving in an orbit would be affected by such
a field. Moreover, certain laws of electromagnetism that
are well grounded in experience enable us to predict how
the electron would be affected in any given circumstances.
Consider the simple case of an electron moving steadily in
a circle, say in the plane of this paper round as a center.
(Fig. 70.) As the electron might move round in two
senses, clockwise or counter-clockwise, there will be two
cases to deal with, and we may distinguish these electrons
by the letters E 1 and E z . If the magnetic force is at right
LIGHT AND ELECTRICITY 243
angles to the plane of the paper, it follows from the laws
of electromagnetism that E 1 will be driven along OE lt
away from the center, while E 2 will be pulled along E%0
towards the center. It is a simple deduction from this that
the frequency of the vibrations of E 2 will be increased,
while that of E l will be diminished. You know, doubt-
less, that if you make a stone describe a circle by whirling
it round at the end of a string, the force with which you
have to pull the string is greater, the greater the number
of revolutions per minute, i.e. the greater the frequency.
Thus an increased force towards the center means a greater
frequency and a diminished force towards the center means
a smaller frequency. Now when there are no external
magnetic forces present the electrons E 1 and E% are drawn
towards with a certain force that depends on the distri-
bution of the electrons in that neighborhood. The pres-
ence of a magnetic field adds a new force away from in
the case of E 1} and towards in the case of E z , so that
the total force towards is diminished for E 1 and in-
creased for $2, and thus the frequency is diminished
for E 1 and increased for E 2 . It thus appears that the
effect of placing a number of rotating electrons in a mag-
netic field would be that those electrons whose planes of
motion were at right angles to the lines of magnetic force
would have their frequencies increased or diminished
according to the sense (clockwise or counter-clockwise) in
which their orbits were described. Thus the original single
line in the spectrum would be replaced by a doublet, the
members of which would be on opposite sides of the original
line. At the same time those electrons that were mov-
ing in the same plane as the lines of magnetic force would
not be affected, so that their frequency would be un-
244 LIGHT
changed. Not only does Lorenz's explanation account for
the main feature of the phenomenon, that is, for the pro-
duction of two or of three lines from a single line, accord-
ing to the direction of the lines of magnetic force, but it
also indicates the state of polarization of the different lines.
It shows that the two lines of a doublet should be circu-
larly polarized, one being right-handed and the other left-
handed. It shows also that with a triplet the middle line
should be polarized in a plane perpendicular to the direc-
tion of the magnetic force, and the two outer lines polar-
ized in a plane parallel to that direction. All these de-
tails with reference to the nature of the polarization of the
different lines were first predicted by Lorenz's theory, and
later observation proved them to be correct.
It should perhaps be stated that later researches have
proved that in many instances the influence of a magnetic
field on the character of the spectral lines is much more
complex than what was first observed by Zeeman. There
are many indications that if an atom be rightly regarded
as a group of electrons, the distribution and motion of
these must constitute a mechanism that is far from simple,
and the complexity of certain aspects of the Zeeman effect
is what might well be expected. It would be out of place
to enter into such questions here, but before taking leave
of the Zeeman effect I should like to call your attention
to a very interesting application of the theory that has
been made quite recently by Hale. It has long been
known that there is an intimate relation between electricity
and magnetism. You have been reminded within the last
few minutes of the influence on a current of a magnetic
field, and you know probably that a current by itself sets
up a magnetic field, that is, that there are certain mag-
LIGHT AND ELECTRICITY 245
netic effects due merely to the presence of an electric
current. If, then, a moving charge of electricity is, under
any circumstances, equivalent to a current, it should also
give rise to a magnetic field, as Maxwell anticipated and
as, in fact, Rowland proved by experiment as long ago
as 1876. Now the ingenious device of Hale referred to on
p. 88 of the lecture on Spectroscopy, by means of which
he takes photographs of the Sun with light from a single
line in the spectrum, e.g. one of the lines of hydrogen,
quickly led in his hands to many interesting discoveries.
It made it clear, amongst other things, that there are
numerous vortices or whirlwinds in the solar atmosphere,
and such is the detail in some of the photographs that it
seems possible to determine, from the form of the streamers
round the whirlwind, in what sense (clockwise or counter-
clockwise) the vortex is rotating. These whirlwinds are
characteristic of Sun-spots, and it seems probable that all
such spots are vortices spinning in the solar atmosphere.
We know from numerous terrestrial experiments that at
high temperatures carbon and many other elements that
occur in the Sun send out large numbers of corpuscles
charged with electricity. It is natural to suppose that the
same thing will happen under similar circumstances in the
Sun. Let us suppose, further, that in any region near a
Sun-spot a preponderance, say, of negative charges exists.
These will be whirled round in the vortex, and as they
move round will constitute effectively an electric current,
and so give rise to a magnetic field. We should expect,
then, that if our hypotheses be justifiable, a Sun-spot
should be characterized by the presence of a magnetic
field. One way of detecting this presence is to make care-
ful observations of the features of the lines of the spectrum
246 LIGHT
in this region, and see if we can find evidence of the Zee-
man effect. It had been known for some time that the
spectrum of a Sun-spot differs in several respects from the
ordinary solar spectrum. Amongst the peculiarities of a
Sun-spot spectrum are two that are specially significant in
view of the Zeeman effect : in the first place, a large num-
ber of doublets, or double lines, exist ; and secondly, many
of the lines are unusually broad. These are just the
features that we should expect, from our knowledge of the
Zeeman effect, provided we see the force of the reasons
that have been adduced, or of any other reasons, for ex-
pecting a strong magnetic field near a Sun-spot rather
than in other regions of the Solar atmosphere.
Prompted by some such reasons as these, Hale recently
devoted the resources of the Mt. Wilson Observatory to
the problem of examining the spectral lines in Sun-spots,
keeping an especially sharp lookout for evidences of the
Zeeman effect. He found that the light from the two edges
of certain lines was circularly polarized in opposite direc-
tions. He found that right- and left-handed polarizations
were interchanged in passing from a vortex spinning clock-
wise to one spinning in the opposite sense. He found also
that the displacements of the widened lines had just the
same features as those detected by Zeeman. With the
caution of a man of science he concluded that the existence
of a magnetic field in Sun-spots was "probable." By ex-
perimenting in his laboratory on the strength of field
necessary to produce a shift of the spectral lines of the
same amount as those observed in the Sun-spots, he was
enabled to form some estimate of the strength of the
magnetic field in these spots.
Here, then, we have a striking example of the breaking
LIGHT AND ELECTRICITY 247
down of barriers that earlier thinkers have set up be-
tween different fields of knowledge. Astronomy, chemis-
try, electricity, magnetism, and light have each had fences
raised around them. In these researches of Hale's yoiT
have observations that seem to deal only with light, obser-
vations, namely, of the varying intensity of the light in
different places. Some portions of the field of view are
very bright, others seem relatively dark, and present the
appearance of dark lines of different widths in different
positions. From these you are enabled to determine cer-
tain facts of astronomy, to learn something definite as to
the physical condition of the Sun. You also learn some-
thing of chemistry, for you can tell, with practical certainty,
that you are looking at iron, or chromium, or manganese,
or vanadium. Electricity, too, is brought before your
view, for you are forced to consider the effect of electric
charges caught up in the whirl of the great solar vortices.
Finally, these observations on light lead you inevitably
into the field of magnetism, and even enable you to esti-
mate the strength of the magnetic forces that play about
the surface of the Sun, although they are nearly a hundred
million miles away.
Thus science is, after all, a unity, and in this key I
may appropriately bring this course of lectures to a close.
Science strives to bring all things, with whatever names
they may have been labelled in the past, into harmony
with some all-pervading principle or law. "Give me
extension and motion/' exclaimed Descartes, "and I will
construct the world !" "Give me ether and electrons and
the fundamental laws of mechanics," says the modern
physicist, "and I will give you a picture of the world that
is beautiful in its simplicity and in its faithfulness. I will
248 LIGHT
not, however, pretend to explain the world, and I will
leave questions of reality and of purpose for others
to dispute over." Perhaps it should be remarked that
this method of the modern man of science differs essen-
tially from what is sometimes called the metaphysical
method. I have no intention of saying anything against
metaphysics. It would be an impertinence to do so, and
I am ready to admit that the remarks of scientists about
metaphysicians are often quite as valueless as those of
metaphysicians about science. All that need be said is
that physicists do not even attempt to evolve the laws
that govern the world from their own consciousness.
Their knowledge is strictly empirical, their hypotheses and
"laws" are valued only so far as they harmonize experi-
ences and fit the facts together. Everywhere these laws
must be put to this test, and if they fail to satisfy it, they
must be ruthlessly abandoned. My aim throughout has
been to show you how well the modern theory of light
serves its purpose and actually fits the facts, and I hope
that I have succeeded in giving you some conception of its
comprehensiveness and power, even if I have not revealed
its true nature as a noble work of art.
INDEX
Aberration, spherical, 148.
Absorption, 48-58; of energy, 53;
in lenses, 150; dark lines due to,
80 ; spectra, 81 ; Hartley on, 83.
Abstractions, 123-125.
Amplitude, defined, 26, 122 ; and in-
tensity, 127.
Arago, 99.
Aristotle, 9.
Art and Science, 1, 4-6, 45, 46, 248.
Atom, nature of, 53; vibrations
within, 55, 79; arrangement in
space, 83, 110-113.
Autochrome plate, 42.
Balmer, 56.
Biot, 109.
Brewster, law as to polarizing angle,
129 ; objection to wave theory, 207.
Bunsen, spectrum analysis, 77.
Cauchy, on dispersion, 62-65.
Chromatic effects in telescopes, 148,
151.
Color, relation to frequency, 26 ; equa-
tion, 27 ; primary, 27 ; vision, 28-
32 ; photography, 33-46, 170-174.
Conical refraction, 185.
Critical angle, 16, 120.
Crookes, spectrum analysis, 177.
Crystal, index surface in, 179; opti-
cal properties of, 175201 ; optic
axis of, 178; ordinary and ex-
traordinary rays in, 180; positive
and negative, 179; rings and
crosses with, 190-201 ; rotatory
power, 104 ; structure of, 104, 107.
Dark lines in spectrum, due to ab-
sorption, 54, 55.
Darwin, 4, 93 ; his Origin of Species,
91.
Descartes, 247.
Diffraction, 202-228 ; dynamical
theory of, 209; Fresnel on, 212,
213; Lommel on, 216-218; grat-
ings, 220.
Dispersion, meaning of, 47; theory
of, 59-69; anomalous, 69; appli-
cations of, 88.
Doppler's principle, 84-87.
Double refraction, 176.
Doublets, 57.
Elastic solid theory, 125.
Electricity, its relation to light, 229-
248.
Electric waves, 232.
Electrons, 53, 242, 247.
Energy, 53.
Ether, nature of, 99, 100, 121, 124,
125 ; in a crystal, 175 ; in electrical
science, 231.
Evolution, 91-93.
Extraordinary ray, 180.
Eye, as optical instrument, 141.
Eye-piece, 152.
Faraday, 23; electrical researches,
231 ; effect of magnetism on light,
236, 237.
Fischer, on optical activity, 114, 115.
Fraunhofer, 80.
Frequency, defined, 26; relation to
color, 26 ; natural, 48-51 ; forced,
4851 ; of vibrations within atoms,
55 ; relation to period and wave
length, 155; limits of eye's sensi-
tiveness, 70.
Fresnel, idea of ether, 99, 100; on
interference, 161, 162; biprism,
162; on diffraction, 212, 213.
Geometrical shadow, 205.
Gernez, on optical activity, 110.
Greek science, 7-9.
249
250
INDEX
Hale, method of photographing prom-
inences and flocculi, 88-91 ; his
spectroheliograph, 88; his investi-
gations on Sun-spots, 244-247.
Hamilton, on conical refraction,
185.
Hartley, 83.
Helmholtz, 23; on color vision, 28-
31 ; on Young, 157.
Hering, on color vision, 28, 31.
Herschel, on rotatory power, 104.
Hertz, on electric waves, 233.
Huggins, on nebulae, 76 ; method of
viewing solar prominences, 87.
Huyghens principle, 208, 209.
Index surface, 179.
Intensity of reflected light, 127;
ratio of intensities, 132 ; influence
of layer of transition on, 130, 131 ;
from metals, 136 ; reflecting power
and electrical conductivity, 235.
Interference, Principle of, 34, 154-
174; Young on, 157-160; Fresnel
on, 161, 162; Lloyd on, 161; color
due to, 163, 166-170; stationary
waves produced by, 172, 173; ap-
plication to diffraction, 209; to
gratings, 222.
Kayser and Runge, 56.
Kerr effect, 240.
Kirchhoff, 80, 81.
Least action, 140.
Le Bel, 112.
Lippman, color photography, 34,
170-174.
Lommel on diffraction, 216-218.
Lorenz, on Zeeman effect, 242-244.
Lumiere, color photography, 42-44.
Magnetism and light, Faraday effect,
236-239; Kerr effect, 240; Zee-
man effect, 240-246.
Marconi electric waves, 234.
Maxwell, 23; theory of color vision,
28; color photography, 34; on
Saturn's rings, 87; electromagnetic
theory of light, 231, 232 ; on mag-
netic effects of a moving electric
charge, 245.
Method of science, 10, 13, 14, 206,
207, 247.
Michelson, spectroscope, 75; visi-
bility curves, 78, 79 ; wave-lengths
as standards, 226.
Morse, 58.
Nebula, nature of, 76.
Newton, on color, 9; greatness of,
13, 21-23; his "Opticks," 13, 20,
166, 205 ; his method, 13, 14 ; his
experiments, 14-21 ; on soap-
bubbles, 164; his rings, 166-169;
on diffraction, 205, 206; on
shadows, 205, 206; objection to
wave theory, 205.
Nicol's prism, explanation of its
action, 177, 178; used, 95, 99, 102,
103, 116, 177, 191.
Objective, 149, 152.
Optical activity, 104-117; Biot, 109;
Gernez, 110; Pasteur, 110; Van't.
Hoff and Le Bel, 112; Fischer,
114, 115.
Optic axis, 178.
Ordinary ray, 180.
Pasteur, on optical rotation, 110.
Period, 155.
Phase, meaning of, 122; difference
of, 122; for reflection from trans-
parent substances, 134 ; for total
reflection, 134, 135; for reflection
from metals, 137; influence on
interference, 156.
Photography, ordinary, 35-37 ; color,
33-46; direct methods, 33; in-
direct methods, 33; Maxwell on,
34; difficulties of, 41; Lippman's
process, 170-174; Lumiere 's
process, 42-44; defects of, 44, 45;
relation to art, 45, 46.
Pickering, 57.
Plato, 8.
Polarization, 95-117; different kinds
of, 97, 98; mechanical analogues,
100, 101, 177 ; effect on intensity of
reflection, 127 ; plane of, in crystals,
188; rotatory, 102-117, 236-239.
Polarizing angle, 129 ; Brewster's law,
129 ; quasi, 137 ; in crystals, 187.
INDEX
251
Rays in crystals, 184.
Reflection, fact of, 10, 11; laws of,
10, 11, 118-153; from metals, 136;
illustrating principle of least action,
139, 140; total, 10, 11, 120, 135.
Refraction, fact of, 10, 11; laws of,
9, 11, 118-153; illustrating princi-
ple of least action, 139, 140;
double, 176.
Refractive index, meaning of, 120 ;
in crystals, 179-182; measured
electrically, 234.
Reversal, 81.
Rings and crosses formed with
crystals, 190-201.
Rotatory polarization, structural,
102, 103; magnetic, 236-239.
Rowland, grating, 75; map of
spectra, 80; on magnetic effect of
moving electric charge, 245.
Ruskin, 4-6.
Saturn's rings, 87.
Science, aim of, 118, 121, 123, 186,
248; alleged inhumanity, 3; rela-
tion to art, 1, 4, 5, 6; early, 7-12;
language of, 24 ; divisions of, 229 ;
method of, 10, 13, 14, 206, 207,
247.
Secondary spectra, 151.
Shadows, geometrical, 205; Newton
on, 205, 206.
Singular points, 185.
Snell, 9.
Soap-bubbles, 164, 165.
Solar prominences, 85, 87.
Solar vortices, 245.
Spectrograph, 76.
Spectroheliograph, 88, 89.
Spectroscope, 74, 75.
Spectroscopy, 70-94.
Spectrum, 15; dark lines in, 54-57,
80; bright lines in, 71, 74; con-
tinuous, 72, 73, 76; band, 57;
produced by gratings, 227.
Spherical aberration, 148.
Stellar evolution, 91-93.
Stokes, 23 ; on absorption lines, 80 ;
theory of diffraction, 209.
Sun-spots, 85, 245, 246.
Superposition, principle of, 155, 156.
Telescope, purpose of, 142; form,
143; material, 144; size, 145;
arrangement of parts, 147 ; defects,
148-150; objectives, 149, 152;
eye-piece, 152.
Transition from one medium to an-
other, 126, 127, 129, 134.
Turner, 5.
Van't Hoff, 112.
Vibrations, transverse, TS, 99; longi-
tudinal, 98, 99 ; confined to wave-
front, 97, 99.
Visibility curves, 78, 79.
Vision, limits of, 27, 30, 70; theory
of color, 28-32.
Watts, Marshall, 58.
Wave, 25; length, 154, 220-228;
front, 96; theory, 121, 205, 207;
surface, 182-185 ; different theories,
123, 154 ; stationary, 173 ; electric,
232-234.
Wood, 238.
Wordsworth, 21.
Young, on color vision, 28-31 ; on
interference, 157-161.
Zeeman effect, 240-246.
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