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With numerous Illustrations. Small crown 8vo, 3.5. ' ' The book is a trustworthy guide to the manufactiu-er of lenses, suitable alike for the amateur and the young workman." —Nature. " The author is both a sound practical optician and is able to convey liis knowledge to others in a clear manner." — British Journal of Photogrttplqi. THE OPTICS OF PHOTOGRAPHY AND PHOTOGRAPHIC LENSES. By J. Traill Taylor, Editor of "The British Journal of Photography." With 68 Illustrations, ^s. M. "An excellent guide, of great practical wsq"— Nature. " Personally we look upon this book as a most valuable labour-saving invention, for no questions are so frequent, or take so long to answer, as those abont lenses."— Proefim? Photofjrapher. "Written so plainly and clearly that we do not tliink the merest tyro will have any difficulty in mastering its contents." — Amateur Photographer. MODEEN ^^' OPTICAL INSTRUMENTS AXB THEIR COXSTRUCTIOX BY HENRY ORFORD AUTHOR OF "LEXS -WOEK FOE AMATEUES ' WHITTAKER AND CO. 2, WHITE HART STREET, PATERXOSTER SQUARE, LONDON A^'D 66, FIFTH AVENUE, NEW YORK 1896 [All rights resirced'] Richard Clay & Sons, Limited, London & Bitngay. QC PEEFACE The main object of the author in compiling the follow- ing book has been to place before the reader a descriptive outline of a few of what may safely be termed the more popular optical instruments in use. Taking the human eye as the most important, most instructive, and certainly the most valuable optical instrument known to science, its construction and properties are first of all dealt with in detail, and are followed by an ex^Dlanation of the defects and aberrations to which our eyes are not infrequently subject. It is believed that the succeeding chapters, which deal with the theory and practice of ophthalmoscopic examin- ation, too-ether with the fullv-illustrated remarks on spectacles and their various forms, and of the principles governing their use and selection, will be appreciated as an endeavour to constitute this part of the work of direct utility and information. 523422 vi PEE FACE Although subsidiary to the principal theme of the work — Ophthalmoscopy — the chapters on the Stereoscope, the Optical Lantern, the Spectroscope, and Stereoscopic Pro- jection will, it is hoped, be welcome to tlie reader as affording him an introduction to the study of several branches of optics, as interesting as they assuredly are full of possibilities in the way of practical application. CONTEXTS CHAP. I. THE EYE AS AX OPTICAL INSTRUMENT II. PROPERTIES AND ABERRATIONS OF LENSES III. ABERRATIONS OF THE EYE IV. EXAMINATION OF THE EYE THE OPHTHALMOSCOPE V. OPHTHALMOSCOPES AND THEIR USES YI. THE MORTON OPHTHALMOSCOPE YII. VARIOUS FORMS OF OPHTHALMOSCOPES VIII. RETINOSCOPY IX. SPECTACLES AND THEIR SELECTION X. VARIOUS FORMS OF SPECTACLES ILLUSTRATED AND DESCRIBED XI. STEREOSCOPIC PROJECTION — ANDERTON'S SYSTEM XII. THE PRINCIPLES OF THE OPTICAL LANTERN XIII. THE STEREOSCOPE ... XIV. THE SPECTROSCOPE ... 1 12 28 36 42 50 57 63 72 77 81 87 92 98 MODEPiN OPTICAL INSTRUMENTS AND THEIR CONSTRUCTION CHAPTER I THE EYE AS AN OPTICAL INSTRUMENT The strides made in the construction of optical instru- ments has led me to compile the following chapters relating to the subject, which will, no doubt, prove inter- esting to many. I shall endeavour to explain the use of the different instruments for their especial purposes, and also their construction, and the object of each part ; but, before starting, it would be as well to examine Nature's optical instrument, and having seen the construction of that, we shall then see how many of the optical instru- ments are approximately the same in their construction. Description of the Human Eye. — The eye, Fig. 1, as an optical instrument, consists essentially of a series of refracting media bounded by curved surfaces, and a net- work of small nerve-fibres, forming part of the optic nerve. A pencil of light incident upon the eye is refracted at the curved surfaces, and brought to a focus on the network of B ^ MODERN OPTICAL INSTRUMENTS iierve-fibrcs, and the impression carried to the brain along the optic nerve. The human eye is nearly spherical in shajDe, except in front, where it assumes a shorter curve, and protrudes. It is invested in a tough coat, which, except in the part which protrudes, is opaque and white ; this is called the Fig. 1. sclerotic. This is commonly termed the white of the eye. The part which protrudes is covered with an extremely strong and thick transparent membrane, wdiich is called the cornea. The eyeball has also two other linings: just within the sclerotic is a thin membrane called the choroid, and within that there is another thin lining called the retina. The interior of the choroid is covered with a black ANI> THEIR CONSTRUCTION 3 pigment, which gives it a velvety appearance. Its use is to absorb rays of light which have passed through the retina, and prevent them from being reflected back on it, and interfere with the images there formed. The Iris. — The anterior portion of the choroid, separ- ating from the sclerotic, is thickened and forms the iris, which is a contractible curtain perforated by an aperture in the centre, called the pupil. The outer edge of the iris is fixed, but the centre may be contracted by a strong muscular band running round it, which allows the size of the pupil to be changed. The use of the iris is to regulate the quantity of light which falls on the sensitive parts of the eye. In strong light the pupil contracts automatic- ally, and in feeble light expands. The anterior surface of the iris is differently coloured in different persons, and the posterior surface is covered with black j^igment, which absorbs any light which may fall upon it, due to internal reflection, etc. Before separating from the sclerotic the choroid splits into two layers : the anterior goes to form the ij-is, while the posterior is gathered into a plaited curtain, Avhich surrounds the outer edge of the crystalline lens, like a collar. These plaits are seventy-two in number, and are called the ciliary processes. Beneath this dark collar, and therefore in contact with the sclerotic, is a muscular collar with radiating fibres, called the ciliary muscle. The Retina. — The retina is a delicate, semi-transparent membrane, resulting from the spreading out of the optic nerve, and is composed of the terminal fibres of this nerve and nerve-cells, and covers the whole interior of the ball Modern optical instrument.^ as far as the ciliary collar. Exactly in the centre of the retina is a yellowish, round, elevated spot, about ttV inch in diameter, having a minute indentation called the fovea centralis at its summit. This is the point of distinct vision, and the fovea centralis is the most sensitive part of the retina. About jV inch on the inner side of the yellow spot is the point at which the optic nerve spreads out its fibres to form the retina : this is the only spot on the retina 'which is not sensitive to light, and is therefore called the blind spot. The Crystalline Lens. — Within tlie eye, just behind the iris, is sus- pended a soft transparent body, called the crystalline lens, of the form of a double convex lens, whose anterior surface is much less curved than the posterior. The crystalline lens is contained in a transparent capsule, and is kept in its place by the ciliary processes. It is composed of successive layers, Fig. 2, whose refract- ive indices increase towards the centre, its solid nucleus, A, refracting light most powerfully. It is easy to see that the action of the lens is more powerful than if it were composed of homogeneous substance having the same refractive index as the nucleus. For it may be regarded as the combination of a double convex lens c, Fig. 3, with two concave lenses, a and k These concave lenses AND THEIR CONSTRUCTION will neutralize tlie effect of the lens c to a certain extent, but not so rniicb as it tlieir refractive indices were as biojli as that of c. The focal len^tli may be found by experiment; its shape being known, its total refractive index may be found — that is, the refracting index which the lens would possess if it were homo- geneous. The increase of refracting power from the outer portions to the inner portions of the lens serves partly to correct the aberra- tion by increasing the convergence of the central rays more than that of the extreme rays of the pencil. The space between the cornea and the crystalline lens is filled wdth transparent fluid resembling water, and is termed aqueous humour. The space between the cr3^s- talline lens and the retina is filled with another trans- parent fluid, somewhat more viscous than the former, and therefore called vitreous humour. These two humours are contained in delicate capsules like the crystalline lens. In these refractive indices the aqueous and vitreous humours differ very little from water, while the total refractive index of the crystalline lens is a little greater than that of water. Refractiox of the Eye. — To determine the manner in which a pencil of light incident on the eye is refracted by it, we must know the refractive indices of the different media of which the eye is composed, and the forms and positions of the bounding surfaces. The anterior surf\ice of the cornea is very nearl}^ that of a segment of an ellipsoid of revolution, the axis of revolution being the 6 MODEBN OPTICAL TNSTBUMENTS major axis. The form of tlie posterior surface is but indifferently known ; but the two surfaces of the cornea iuc very nearly parallel, and as the anterior surface is always moistened with water, whose refractive index is the same as the aqueous humour, the cornea acts like a plate of refracting medium, and produces no deviation on an in- cident ray. The cornea itself may, therefore, be entirely neglected, and we may suppose for optical purposes that the aqueous humour extended to the anterior surface of the convex. There are, therefore, three surfaces at which refraction takes place : the first surface of the convex and the two sur- faces of the crystalline lens. The centres of these curves are nearly in a straight line, called tlie optic axis. For ra3^s wliose deviations from the axis are not lars^e, the surfaces may be supposed to coincide with the spheres of curvature at their respective vertices. Gauss's theory of refraction at any number of spherical surfaces whose centres lie along an axis is therefore applicable to this case, and the positions of the focal points, the principal points, and the nodal points may be found by calculation as soon as the radii of curvature, the positions of the refracting surfaces, and the indices of refraction of the media are known. Listing has given the following numbers as representing very closely the constants of an average eye. In reckon- ing refractive indices the refracting index of the air is taken to be unity. The radii of curvature of the bounding surfaces have the followinoj values : — 1. The anterior sur- face of cornea 8 millimetres. 2. The anterior surface of the lens 10 millimetres. 3. The posterior surface of the AND THEIR CON^TBUCTION 7 lens 6 millimetres. The distances between the refractiurv o surfaces from 1 to 2, 4 millimetres ; from 2 to 3 (thickness of the lens), 4 millimetres; from o to the retina, lo millimetres. The indices of refraction are : — 1. For the aqueous humour, -W. 2. For the lens (total), \'{. 3. For the vitreous humour, yt^- From these data he calculates the positions of the cardinal points according to Gauss's theor}', and finds that the two principal points lie very close together, as do also the two nodal points, so that without introducing much error, we may regard them as coinciding in each case. The single principal point lies 2*3448 millimetres behind the cornea, and the nodal point '4764 millimetre in front of the second surface of the lens. Such an eye is exactly equivalent to a single-refracti no- spherical surface, wdiose vortex is at the principal point and centre of the nodal points, the refractive index being -W, as before. A point and its image on the retina will lie on a line passing through the nodal points, and there- fore if we wish to find in what direction lies a point whose image is in a given position on the retina, we have only to join the image to the nodal point, and produce the line outwards. When the eye is passive, it is clear that only the points which lie in a single surface will have images falling exactly on the retina. The form of this surface and its position may be determined from the optical constants of the eye. Any object lying on this surface will have an imao'e on the retina similar to the orioinal figure, but inverted, the lines joining corresponding points of the object an(l the image, all passing through the nodal 8 MODERN OPTICAL INSTRUMENTS point. But if a point does not lie on this surface, its image will not be on the retina, but in front of or behind it. In both cases the retina cuts the pencil of refracted rays, not in a single point, but in a circle of diffused light. Hence it follows that an immovable eye can only see distinctly objects lying in one surface, and if we consider only rays of light making small angles with the axis of the eye, this surface may be considered plane. All objects, or portions of objects, not lying in this plane give in- distinct images, in which circles of diffusion correspond to luminous points of the object. Experience teaches us, however, that an eye is capable of seeing distinctly at almost any distance; there must, therefore, exist an arrangement for altering the eye, and adapting it for seeing different distances at will. Accommodation. — The changes which occur as the re- sult of this arrangement are included under the term ac- commodation. It is not known with absolute certainty for what distance an eye is adjusted when it is not actively accommodated ; but it is almost universally supposed that a normal eye, when passive, is adjusted for objects at an infinite distance, so that the second focal point of the eye at rest is on the retina. It has been found by experiment that accommodation is effected by change of form in the refracting surfaces of the eye. When the ejQ is accommo- dated for near objects, the anterior surface of the crystalline lens becomes more strongly curved, and approaches nearer the cornea. This is especially the case with the part not covered by the iris, which arches forward through the pupil. It has been seen that when the eye is at rest in ANT) THEIB CONSTRUCTION 9 any position, and accommodated for an object, tliere is one point, the fovea centralis, where the vision is distinct, but that the vision is distinct only for a small area about this spot. But the eye is usually in very rapid motion, and in an incredibly short space of time brings the various points of an object into distinct view. We are thus enabled to form a clear conception of a considerably extended surface. This is aided also by the duration of the impression produced by a light. It has been found by experiment that this duration depends on the character of the light. For strong lights, Helmholtz gives one twenty-fourth of a second, and for weak lights one-tenth of a second, as the duration of the impression ; Lissajous and others assign about one-thirtieth of a second as the lowest limit of the duration. If a spot on the retina be stimulated by a regular periodic light whose period is sufficiently short, there will arise a continuous impression, which in intensity is equal to what would be produced were the wdiole incident light of any period uniformly distributed over the whole period. Binocular Visiox. — The retinae of both our e3^es receive impressions. When Ave look at any external object, and in certain positions of our eyes, we see two imao'es, arisino- from the two retinae, while in other positions we only see one image. To each point to one retina there is a corresponding jDoint on the other, and when the images of an external point, formed by the two eyes, fall on corresponding points of the two retinae, the point is seen single ; but in other cases it is seen double. The points on the retina of an eye may be referred to two 10 MOT)ERN orTIOAL INSTRUMENTS meridians formed on the retina by two planes throngli the axis of the eye. Wlien the eye is directed forwards in a horizontal position, the points on the liorizon have images lying on a meridian, which Ave may call the retinal horizon. Similarly certain lines appear vertical to an eye ; the retinal image of these vertical lines is a meridian, which we may call the apparently vertical meridian. By experiment Helmholtz concludes that the retinal horizon is actually horizontal for both eyes ; but that the apparently vertical meridians are not quite perpendicular to the retinal horizon, they diverge outwards at their upper extremity. The inclination of each of these meridians to the real vertical is tlie same, and they include between them an angle varying from 2° 2V to 2° 33'. Hehnholtz also finds that in normal eyes the points of direct vision, as well as the retinal horizons and apparent verticals in the two eyes, correspond ; and, further, that corresponding points are equally distant from eacli retinal horizon, and from each apparently vertical meridian. Our most accurate estimate of the distances of visible objects depends upon us having two eyes. As we fix our gaze successively upon points at different distances, we have to chanoe the converofence of the axis of the two eyes, and from the degree of convergence to these axes, when we look at any point we form an estimate of the distance of the point. Our idea of solidity also depends upon vision with two eyes. The views presented to the two eyes are slightly different, because the eyes have slightly different positions, and it is by the blending of the AND THEIR OON^TBUCTTON 11 two impressions received upon tlie two retinae that we receive the idea of solidity. This can be Avell shown by the aid of the stereoscope. This instrument was invented by Wlieatstone for the purjDOse of combining t^vo photographic pictures, one of which is presented to each eye. These pictures are not exactly alike, but are taken by a camera, with two lenses placed a small distance apart, so that they represent two different views, such as might be presented to two e3'es observing the scene. By means of mirrors or prisms the pictures are seen superimposed, and the impression produced on the mind by these superimposed views is exactly the same as if we were looking at the real scene, each object appearing in relief, as in nature. For a perfect stereoscopic representation the points at an infinite distance must fall on corresponding points of the two retina?, where the axes of the eyes are parallel. If the pictures are brought nearer to each other in the same plane than in the positions thus determined, the impres- sion is exactly that of a relief picture. 12 MODERN OPTICA L INSTRUMENTS CHAPTER II PROPERTIES AND ABERRATIONS OF LENSES The instruments that have been constructed for the eyes are divided into two classes : the first for the correction of aberrations of the eye itself; and, secondly, the class for the detection and examination of those aberrations. The first are called spectacles, and the second ophthalmoscopes. If we first thoroughly examine the elements which constitute a spectacle- lens (the most common optical instrument), it will be comparatively easy to understand how the aberrations of the eyes may be almost counteracted by their judicious use. Refraction. — Pencils of light are deviated or refracted when they pass from one transparent medium into another of different density. If the deviation in passing from vacuum into air be represented by the number 1 that for crown glass is I'o, and for rock crystal 1*66. Such a number is the refractive index of the substance. Every ray is refracted except those which fall perpendicular to the surface, as the ray a a in Fig. 4. In passing from a less into a higlier refractino: medium, the deviation is AXD THEIR CON^TRUCTIoX 13 always towards the perpendicular of tlic refracting surface ; in passing from a higher into a low^er refracting medium, it is always and to the same extent away from the perpendicular (see ray h h, Fig. 4, and the angles x and Fig. 4. y). Hence, if the sides of the medium be loarallel, as in Fig. 4, the rays on emerging are restored to their original direction, but in a different path, and the thinner the medium, the less the deviation from their path will be. If the medium be formed as a prism, the sides of m, Fior. 5, form an anofle, the angles of incidence and emerfr- ence x and y still being equal, h' must also form an angle with h. The angle a is the refracting angle or edge of the prism ; the opposite side is the base. As seen in Fig. 5, the light is always deviated tow^ards the base. The devi- ation shown by the angle d is equal to about half the refracting angle a if the prism be of crown glass. The 14 MODERN OPTICAL INl^TRUMENTS relative direction of the rays is not cbanged by a prism, and if parallel or divergent before incidence, they are Fig. 5. Fig. 6. parallel or similarly divergent after emergence, as shown in Fig. G. An object seems to lie in the direction which the rays have as they enter the eye ; oh in Fig. 6, seen by AND THEIR CONSTRUCTION 15 the eye at a or h\ seems to be at o h', where it would be if the rays a V had not deviated. With very thin prisms the deviation a and 5 (Fig. 7) remains the same for varying Fig. angles of incidence. For thin lenses, this is expressed by saying that the angle cl (Fig. 8) is the same for the rays a Fig. 8. «', Jj h', c 0, incident at different angles, but at the same distance from the axis. 16 MODERN OPTICAL INSTRUMENTS An ordinary lens is a segment of a sphere, or of two spheres whose centres are joined by the axis of the lens. We can resfard a lens as formed of an infinite number of minute prisms, each with a different refracting angle. Fig. 9 shows two such elements of a convex lens, the angle Fig. 9. a of the prism at the edge of the lens being larger, and therefore, in accordance with the statement of the action of the prism (Fig. 5), refracting more than /3, the angle of the prism nearest the axis. If two parallel rays, a and h, traverse this system, a will be more refracted than h, and the rays will meet at/. Fig. 10 shows the corresponding facts for a concave lens by which the parallel rays are made divergent. The only ray not refracted by a lens is the one passing through the centre of each surface, which is the principal axis. Secondary axes are rays as sax, Fig. 11, entering and emerging at points on the lens parallel to each other, and hence not altered in direction. All rays which pass through the central point of a lens are secondary axes, AND THEIR CONSTRUCTION 17 except the principal axis. Fig. 12 shows spherical aberration, which increases with the curvature of the re P J Fig. 10. Fig. 11. lens ; but if stopped off, which is done in the eye by the iris, is not so apparent at the same time with a corre- sponding loss of light. c 18 MODERN OPTICAL INSTRUMENTS The principal focus of a lens, /, Fig. 13, is the point where the rays a a, that were parallel before they entered the lens, meet, after they have passed through it, the deviation of each ray varying directly with its distance from the principal axis. If parallel rays are incident from the side towards/, Fig. 13, they will be focussed at /' at the same distance from the lens as /; hence every lens has two principal foci, anterior and posterior. The path Ficx. 12. of a ray passing from one point to another is the same, whatever its direction. The path of the ray hh', Fig. 13, is the same, whether it pass from cf to c f or the ojDposite. Referring to Fig. 7, it follows that in Fig. 13 the angles a and a are equal, and hence the ray h, diverging from cf, will not meet the axis at /, but at c'f. c/and c'/ are conju- gate points, and each is the conjugate focus of the other, the angle a or a! remaining the same ; then if cf be further from the lens, c f will approach it, a ray c directed towards the axis will be focussed at c" f'\ it will, on taking AND THEIB CONSTRUCTION 19 the direction c, appear to have come from V f, which con- sequently is the virtual focus of c"f". Foci of Lenses. — All the foci of concave lenses are virtual. In Fig. 14 tlie ray d, parallel to the axis, is made di- vergent, its virtual focus being at /; similarly c f is the virtual conjugate focus of the point emitting the ray h in lenses equally bi-con- cave or bi-convex of crown glass. The principal focus is at the centre of the curvature of either surface of the lens. The image formed by a lens consists of foci each of which corresponds to a point on the object; given the foci of the boundary points of an 20 MODERN OPTICAL INSTRUMENT object, we liave the size and position of its image. In Fig. 15 the object a h lies beyond the focus/ From the terminal-point a takes two rays, a and a, the former a secondary axis and therefore unrefracted ; the latter parallel to the principal axis and therefore passing, after refraction, through the principal focus/'. These two rays will meet at A, the conjugate focus of a. Similarly the focus of the point h is found, and the real inverted ^-c^ 77 <7 1 1-:^::-^ . J I A Fig. 14. conjugate of a h is formed at A B. The relative sizes of a h and A B vary as their distance from the lens. If a h be so far off that its rays are virtually parallel on reaching the lens, its image A B will be at /', and very small. If a h be at / its rays will become parallel after refraction and form no image ; \i ah lies between/ or /' and the lens, the rays will diverge after refraction, and form no image. But in the last two cases a virtual image is seen by an eye so placed as to receive its rays. In Fig. IG two rays from a take after refraction the course shown by a and a, virtually meeting at A, and an observer at x will see at A B a virtual masfnified erect imacre of a h. The enlargfe- AND THEIR CONSTRUCTION 21 ment (Fig. 16) is greater the nearer a h \^ to/', and greatest ^vllen it is at /' ; but as A B has no real existence, its apparent size varies with the estimated distance of the surface against which it is projected. A uniform distance of projection of about 12 in. is taken in comparing the magnifying f)Ower of dif- ferent lenses. When a h is at/, Fig. 16, we shall find on trial, that the image A B can be seen well only by bringing the eye close up to the lens ; at a greater dis- tance only part of the im- age will be seen, and this part will be less brightly illuminated. This is im- portant in direct ophthal- moscopic examination. In Fig. 17 an observer placed anywhere between the lens and x receiving rays from the path of a h will see the whole image ; but if he withdraws to ^, his eye will 22 MODERN OPTICAL INSTRUMENTS receive only the rays from the central part of a h, and will only see the centre of the object. It is shown by similar constructions that the images formed by concave lenses are always virtually erect and diminished. Whatever the A^W THEIR CONSTRUCTION 23 distance of the object (Fig. 18), the size of the image \ varies, first, by the focal lengths of the lens, and, second, tlie distance of the object from the principal focus. First, 24 MODERN OPTICAL INSTRU3IENTS tlie shorter the focus of the lens, the greater is its effect : the refractive power of a lens varies inversely as its focal length. Secondly, for a convex lens the image is larger the nearer the object is to its principal focus. All objects Fig. 19. viewed through a prism seem displaced towards the edge of the prism, and to a degree which varies directly as the size of the refracting angle. The eye is directed towards the position which the object now seems to take, and this may be utilized for several purj^oses : (1) To lessen the AND THEIR CONSTRUCTION 25 of the visual lines, without removing the object further from the eyes. In Fig. 19 the eyes E, and L are looking at the object o h, with a convergence of the Fig. 20. visual lines represented by the angle a ; if prisms be now added with their edges towards the temples, they deflect the light so that it enters the eyes under the smaller angle 26 MODERN OPTICAL INSTRUMENTS j3 as if it had come from o h', and towards this point the eyes will be directed, though the object still remains at h. The same effect is given by a single prism of twice the strength before one eye, though the actual movement Fig. 21. is limited to the eye in question. If spectacle lenses be placed so that the lines do not pass through the centres, they act as prisms, thougli the strength of the prismatic action varies with the power of the lens, and the amount ANV THEIR CONSTRUCTION 27 of tins decentration. In Fig. 20 the visual lines pass outside the centres of the convex lenses a, and inside those of the concave lenses h. Each pair, therefore, acts as a prism with its edge outwards. (2) To remove double vision caused by slight degrees of strabismus. The prism so alters the directions of the rays as to compensate for the abnormal direction of the visual line. In Fig. 21 R is directed towards x instead of towards o h as seen. The prism j; deflects the rays to y, the optic nerve, and single binocular vision is the result. The prisms remove the diplopia. 28 MODERN OPTICAL INSTMUMENTS CHAPTER III ABERRATIONS OF THE EYE Emmetropia- AMETROPIA. — When the length of the eye is normal, and the accommodation relaxed (see Chapter II), only parallel rays are focussed on the retina, and conversely only pencils of rays emerging from the retina are parallel on leaving the eye, and this, the condition of the normal eye in distant vision, is called Fig. 22. emmetropia. Fig. 22 shows pencils of parallel rays entering or emerging from an emmetropic eye. All permanent departures from the condition in which, with relaxed accommodation, the retina lies at the principal AND THEIB CONSTRUCTION 29 focus, are known as ametropia. In emmetropia rays from any near object are focussed behind the retina at/ (Fig. 22), every conjugate focus being beyond the principal focus. Reaching the retina before focussing, such rays ^^ Fig. 23. will form a blurred image, and the object o h, Fig. 28, will only be seen dimly. Myopia. — But by using accommodation, the convexity of the crystalline lens can be increased and its focal length shortened, so as to make the conjugate focus ofoh coincide exactly with the retina, as in F, Fig. 24. Under the Fig. 24. condition shown in Fig. 24-, the object will be seen distinctly, whilst the focus of a distant object, which in Fig. 28 was formed on the retina, will now lie in front of it, F, Fig. 24, and the distant object will appear indistinct. In Fig. 28, if the retina was at C F instead 30 MODERN OPTICAL TNi^TRUMENTS of at F, a clear image would be formed of an object at h without any effect of accommodation, whilst objects farther off would be focussed in front of the retina. This state, in which the posterior part of the eyeball is too long, so that, with the accommodation at rest, the retina lies at the conjugate focus of an object at a comjDaratively small distance, is called myopia. In Fig. 25, the inner line at R is the retina, and F the Fig. 25. principal focus of the lens system. Rays emerging from R will, on leaving the eye, be convergent, and, meeting at the conjugate focus R', will form a clear image in the air; conversely, an object at R' will form a distinct image on the retina. The image of every object at a greater distance than R' will be formed more or less in front of R, and every such object must be indistinct. But objects nearer than R' will be seen clearly by accommo- dating just as in the normal eye, Fig. 23. The distance of T (R', Fig. 25) from the eye will depend on the distance of its conjugate focus R — that is, on the amount of the elongation of the eye. The greater the distance of R beyond F the less will be the conjugate focus R', and the more indistinct distant objects will become. If the elongation of the eye be very slight, R nearly coinciding AND THEIB CONSTRUCTION 31 with F, R' will be at a greater distance, and distant objects will be more distinct. All images in a myopic eye arc of larger magnification than in the normal eye. Consequently myopic persons can distinguish smaller objects at a greater distance than can people with normal eyes. The eye presents three refracting surfaces : the front of the cornea, the front of the lens, and the back of the lens, and in the normally formed or emmetropic eye with the accommo- dation relaxed, the principal focus of those combined dioptric media falls exactly upon the layer of rods and Fig. 26. cones of the retina — that is, the eye in a state of rest is adapted for parallel rays. The point at which the secondary axial rays (see n. Fig. 26) cross the posterior nodal point lies, in the normally-formed eye, at 15 milHmetres in front of the yellow spot of the retina, and nearly coincides with the posterior pole of the crystalline lens. The angle included between the lines joining n, Fig. 20, with the extremities of the object o 5 is the visual angle v. If the distance d from n to the retina remains the same, the size of any image 1 in, Fig. 26, on the retina will depend on the size of the angle ^^ and this again on the size and 32 MODERN OPTICAL INSTRUMENTS distance of the object. But if the distance d alters, the size of the image is altered without any change in v. Now if tlie length of d varies with the posterior segment of the eye, it is greater in myopia and less in hypermetropia, and hence the retinal image of an object at a given distance is larger in myopia and smaller in hypermetropia than in the normally-formed eye. The length of d also varies with the position of n, and this is influenced by the positions and the curvatures of the several refractive surfaces ; n is slightly advanced by the increased convexity of the lens during accommodation, and much more so if the same change of refraction be induced by a convex lens held in front of the cornea; hence convex lenses, by lengthening d, enlarge the retinal image. Concave lenses put n further back, and thus shortenino^ d, lessen the image. If the lens which corrects any optical error of the eye be placed at the anterior focus of the eye, 13 millimetres, or half an inch in front of the cornea, n moves to its normal distance, 15 millimetres from the retina, and the images are, therefore, reduced or enlarged to the same size as in the emmetropic eye. The length of the visual axis, a line drawn from the yellow spot to the cornea in the direction of the object looked at, is about 23 millimetres. The centre of the rotation of the eye is rather behind the centre of this axis, and 6 millimetres behind the back of the lens. The focal length of the cornea is 31 millimetres, and that of the crystalline lens varies from 43 miUimetres, with accommodation relaxed, to 33 millimetres during strong accommodation. AND THEin CONSTBUrriOX 33 Optical Coxditioxs of Clear Sight.— Many of the previous diagrams are similar to those in Mr. Nettleship's Student's Critidc to Diseases of tlic Eye, and which I shall employ to show the uses of the different ophthalmoscopes, to be described hereafter. The optical conditions of clear sight are as follows: — 1. The image must be clearly focussed on the retina. 2. It must be formed at the centre of the yellow spot. 3. It must have a certain size, and this is expressed by the size of the correspond- ing visual angle. 4. The cornea, lens, and vitreous humour must be clear, o. The illumination must be sufficient. NuMERATiox FOR CoRRECTiox. — 111 the numeration of spectacle lenses for the correction of the aberrations of the eyes, some system of numbering is required which should indicate the refractive power of the lenses used for spectacles. Two systems are current (Nettleship). In the first system, which was till latterly universal, the unit of strength is a strong lens of 1 in. focal length. As all the lenses used are weaker than this, their relative strengths can be expressed only by using fractions. Thus a lens of 2 in. focus, being half as strong as the unit 1 in., is expressed as \. A lens of 10 in. focus yV of 20 in., is ttV> ^^^ so on. The objections are inconvenient in practice, that the intervals between the successive numbers are very unequal, and that the length of the inch is not the same in all countries — so that the glass of the same number has not quite the same focal length when made by the Paris, English, and German inches respectively. The English inch equals 25*o millimetres; the French inch equals 3t MODEBN OPTICAL INSTRUMENTS 27* millimetres ; the Austrian inch equals 20*3 millimetres ; the German inch 2G*1 millimetres. In the second system, which has displaced the old one, the metrical scale is used. The unit in a weak lens of one metre (100 centimetres) is 10 D, and so on. The weakest lenses are •25, '5, and "To D, and numbers differing by '5 or '2o D are also introduced between the whole numbers. A slight inconvenience of the metrical dioptric system is that the number of the lens does not express its focal length. This, however, is obtained by dividing 100 by the number of the lens in D ; thus the focal length of 4 D = ^^ = 25 centimetres. If it be desired to convert one system into the other, this can be done, provided that we know which inch (whether English, French, etc.) was used in making the lens, whose equivalent is required in D. The metre is equal to about 87 in. French and 39 in. English or German ; a lens of 36 in. French (No. 36 or ^V olJ scale) or of 40 in. English or German (Xo. 40 or ■^\y) is nearly the equivalent of 1 D. A lens of 6 in. French (1- = y«^) will therefore be equal to 6 D. A lens of 18 in. French (yV = y^^.) = 2 D, etc. The following lenses are used for spectacles, and are therefore necessary in a complete set of trial glasses. The first column gives the number in D, the second the focal length in centimetres, the third the approximate numbers on the French i7ich scale, the denominator of each fraction showing the focal length in French inches. It will be seen that some metrical lenses have no exact equivalents on the inch system, AND THEIR CONSTRUCTION 25 D. Dioi.trcs. Focal Length in CM. No. and Fcc.il Length in Paris Inches. 0-25 400 _ 0-5 0-75 1 1-25 1-5 200 133 100 80 66 1/72 1/50 1/36 1/30 1/24 1-75 2 57 50 1/22 1/18 2-25 44 1/16 2-5 2-75 40 36 1/14 1/13 3 33 1,12 3-5 4 4-5 28 25 22 1/10 lis 5 5-5 20 18 '1 6 7 8 16 14 12-5 1/6 1/4 9 11 1 4 10 10 \H 11 9 — l-I 8-3 1,3 13 7-7 14 7 1 2| 12^ 15 6-7 16 6-2 l/2i 18 5-5 1/2 20 5 36 MODERN OPTICAL INSTRUMENTS CHAPTER IV EXAMINATION OF THE EYE — THE OPHTHALMOSCOPE In the examination of tlie eye b}^ lenses and mirrors, the focal or oblique illumination of the anterior part of the eye can be examined by concentrating the light of a lamp on the part by a convex lens. The method is used to detect or examine opacities of the cornea, etc. Such an examin- ation is generally used in every case before bringing in the aid of the ophthalmoscope. To make a preliminary examination of an eye, we shall require a convex lens of 3 in. focus, which is supplied with all ophthalmoscopes, and a naked lamp-flame. The lens is held between the finger and thumb at about its own focal length from the eye and the lamp, which should be 24* in. away from the eye to be examined. The lens being in the line of light, you will be enabled to throw a bright pencil on the front of the eye at an angle with the observer's line of sight. In this way, all parts of the eye — the cornea, the iris, or the anterior or posterior surfaces of the crystalline lens — may be examined, as is shown in Fig. AND THEIR CONSTRUCTION 37 27. By varying the position of the lens, and causing the eye to be moved, all parts can be thoroughly examined. F:g. 27 Rays of light entering tlie pnpii in a given direction are partly reflected back by the choroid and the retina, and on emerging from the pupil, take very nearly the same course 38 MODERN OPTICAL IN^'^TliUMENTS inches they liad on entcriug. There- fore, if tlie observer wishes to make a close examination of tlie eye, it is obvious that he would have to be placed so as to cut off the entering rays, and therefore no light would enter the eye at all, and for any use- ful examination of the eye the observer must be in the central path of the entering or emerg- ing rays. The ophthalmoscope. —The r: end wanted is gained by look- : ino[ through a small hole in a ^ mirror, the surface of which re- flects light into the eye. This mirror is the oplithalmoscope. By an indirect method an image of the fundus can be formed in the air between the eye of the observer and the observed, and is effected by taking two con- vex lenses of about 2 in. focal length each ; hold one in the left hand about 2 in. from any object you wish to \ie\\, take the other in the right hand, and moving your head a few lold the second lens at its focal length in 39 40 MODEllN OFTICAL IXSTllUJIENTS r-—--^-^^-^ front of the first one, you will tlicn see an inverted image slightly magnified. Fig. 28 will explain the phenomena. To thoroughly explain the action of the ophthal- moscope, the two preced- ing diagrams are sufficient. One shows the method of examination by the indi- rect method. You will see that in Fig. 29 only one . lens is made use of, and ^ to get an image of the ;i; retina we use the crystal- line lens of the eye to be examined instead of the lens, «, of Fig. 28. In the ordinary course, as stated before, no light could enter the eye to be examined because of tlie observer being in the course of the rays which should enter, so in front of the observer's eye is placed a perforated mirror, vt, Fig. 29. The light being to the right or left of the patient, the mirror is moved so that AXJJ THEin CONSTRUCTION 41 11 ray of light incident from the frame to the mirror is reflected into tlic patient's eye, the lens, /, Fig. 29, is moved to a suitable position, and a magnified image of the retina is formed between this and the observer. In the examination of virtual erect image, the lens, /, in Fig. 29, is dispensed with, and the ophthalmoscopic mirror placed very near the eye. The rays, r r, Fig. 30, entering the eye divergent would be focussed behind the retina as at /, and hence illuminate the fundus diffusely. The returning pencils, parallel or divergent, on leaving the eye appear to proceed from a highly-magnified erect image at or behind the eye. 42 MODERN OPTICAL INSTRUMENTS CHAPTER V OPHTHALMOSCOPES AND THEIR USES In using the ojDLtlialmoscope by the direct metliod, the examination is made by the mirror aL)ne or with the addition of a lens placed behind it between the back of the mirror and the eye of the observer, but with no lens between the mirror and the eye to be examined. These are called refraction ophthalmoscopes, and are made fiom the simple Liebreich to almost any degree of complication in con- struction, many of which I shall describe. By the method previously stated, the parts are seen in their true positions, and are used to ascertain the condition of the patient's refraction — the relation of his retina to the focus of his lens system ; to detect opacities in the vitreous humour ; for the minute examination of the fundus by the highly- magnified, erect image illustrated; for examining the iris, cornea, and crystalline lens with magnifying power. When usino- the mirror alone to ascertain the refraction at a distance of 12 in. to 18 in. from the eye, we see some of the retinal vessels, the eye is either myopic or AND THEIR COXSTRUCTIOX 4:3 hypermetropic. If when the observer's head is moved slightly from side to side the vessels^ seem to move in the same direction, the image seen is a virtual one, and tlie eye hypermetropic. The eye is myopic if the vessels seem to move in the contrary direction. The image in myopia is formed and seen in the same way as the inverted image seen by the indirect method of examination; but, except in highest degrees of myopia, it is too large and too far from the eye to be observed to be useful for detailed examination. In low degrees of myopia this image is formed so far in front as to only be visible when the observer is 3 ft. or 4 ft. distant, whilst in emmetropia and in tlie lower degrees of hypermetropia the erect image will not be easily seen at a greater distance than 12 in. to 18 in. If, therefore, the examiner has to go very near to or a great distance from the eye to get a clear image, no great error of refraction can be present. In emmetropia the erect image can be seen only if the observer be near to the patient and relax his accommodation. In hypermetropia, where the retina is within the focus of the lens system, the erect image is seen when close to the patient's eye only by an effort of accommodation in the observer, just the same as in the experiment with the lens within its focal length of an object. As in that experiment the object was seen as well with the head withdrawn, so in liypermetropia the erect image is seen at a distance as well as close to the patient. Now if the observer, instead of increasing the convexity of his crystal- line lens by an etibrt of accommodation, place a convex 44 MODEllN OPTICAL IN^TllUMENT^ lens of equivalent power behind his mirror, this lens will be the measure of tVe patient's hypermetropia ; it will be the lens Avhicli, when the patient's accommodation is in abeyance, will be needed to bring parallel rays to a focus on his retina. If a higher lens be used it will be the same as the experiment of the convex lens being placed beyond its proper focus — the fundus will be indistinct. To measure hypermetropia the accommodation of both ob- server and observed must be relaxed. The observer must go as close as possible to the patient, and place convex lenses behind the mirror of his ophthalmoscope, beginning with the weakest and increasing the strength till the highest is reached, which still permits the details of the yellow spot to be seen Avith perfect clearness. In the same way myopia can be measured by means of concave lenses, the lowest lens with which a clear, erect image is obtained being slightly more than the measure of the myopia. It is sometimes useful to know how much lengthening or shortening of the eye corresponds to a given neutralizing lens, the distance between the eye of the observer and that of the patient not being more than 1 in. Hyperinetr Dpia of 1 D = sliurtening of '3 mill. ")•> 2 5> *"3 » ?' 3 ,, 1-0 „ 5 ,, 1-5 „ >) ,, '2-0 „ 5> >5 1) IS )) 5J 3-0 „ 4-0 „ (5-0 „ AND THEIE (VNSTBUCTION 45 Myopia of 1 D = leniitheniiio- of -3 mm. 2 .. ' .. ' -5 „ 3 „ „ -i) .. 5 „ ., 1-3 „ « „ M 1-T5 „ 9 „ „ 2-6 „ „ 12 „ „ 3-5 „ 18 .. .. 5-0 .. Astigmatism. — Astigmatism of tlie eye may also be measured by this method, the refraction being estimated successively in the two chief meridians by means of appro- priate retinal vessels. Any horizontal running vessel is seen by means of rays which pass through the meridian of the cornea at a right angle to its courses. Thus if a vertical vessel be seen clearly through a convex 2 D lens, there is hypermetropia 2 D in the horizontal meridian, etc. The Liebreich Ophthalmoscope. — We have seen what the ophthalmoscope has to do, and the conditions under which it is used. It remains, therefore, to describe some of the most prominent types. The simplest ophthalmoscope is after Liebreich. Fig. 31 shows it with a lens in the clip at the back, and Fig. 32 a section of same, showing mirror on one side and lens the other. With this instru- ment are supplied two convex lenses, of 2J in. and 4 in. focus, and four or five lenses concave and convex. When using it the lenses have to be placed in the clip in rotation. It will be seen that the hole in the mirroi' (which should be not less than two millimetres, and not over three, in diameter) being small, a very small part of the lens is used — only the extreme centre, and all the rest waste ; but the small part required being separate would very 46 MODE UN OPTICAL INSTRUMENTS soon be lost, so it is obvious that if a few lenses could be placed in a disc that would revolve in front of the hole in front of the mirror, it would be a great advantage over continually moving the different correctors from their case to the clip, so that when a small disc was attached to the mirror, as Fig. 33, which could be swung on one side when necessary, it was a decided improvement. An instrument, as we can see by Fig. 34, can be built AND THEIB CONSTRUCTION 47 up of two discs, being as large as convenient, and having as many lenses as wanted, and intermediate powers being Fig. 33. obtained by an extra disc, with the odd plus and minus lenses in, each disc having a plain aperture ; one could be 48 MODIRBN OPTICAL INSTHUMENTS fastonod whilst tho other was used. This is the basis of J- M A t' lany constructions of oplithahuoscopes. The mirrors can AND THEIR CONSTRUCTION 49 be more than one on the principle of a swivel, as in Fig. 35, and can be canted to any angle, as shown in the section. These are the important parts of the instrument, and we shall see how they have been used to obtain the maojnificent instruments now extant. 50 MODERN OPTICAL IN^THUMENT^ CHAPTER VI THE MORTON OPHTHALMOSCOPE It is Jiot for me to say which is the best ophthahnoscojoe, as good results can be got in efficient hands from the simple Liebreich, but to describe the principles and con- struction of them. Those parts hitherto illustrated consist essentially of lenses in a disc ; but the one I shall now describe is altogether on another i^rinciple. Imagine a continuous chain of discs running round a ai'oove, and w^e have the idea of the instrument. Now it should be obvious that this should be one of the best instruments that could be devised, for however small you made your lenses in the disc you could not have very many, unless you had your wheels so large that the ophthalmoscope would be very unwieldy and heavy ; but by lengthening the magazine any amount of lenses may be used. Fig. 37 will show a magazine containing a number of small brass cells, and it will be seen that they will travel round and round, each one in its turn getting to the eye-hole, and with" the addition of the other disc with the extra lenses in, you can get an enormous number of dif- AXD THEIR CONSTRUCTION 51 ferent magnifications, contained iu a very limited this principle is the Morton ophthalmoscope. The magazine is made from thin sheet metal, knocked over to form the edge on a tem- plate. This is easily done if you anneal the metal from time to time. Knocking over is more certain than milling out, as it is impossible to vary in size, for it must be borne in mind that the cells, to work round, must be in a certain proportion to the body. If such is not the case, they will not perfectly fill up the channel, and a shake is the result. If this occurs, the lens that is supposed to be centred with the eye-hole will drop on one side, and the observer will be looking through the lens near its edge ; or if very much so, the edo"e of the cell will even o be visible. The cells being perfect, that is, sliding round without any shake any way in the channel, the next thing to do is to aroi On Fig. 3; 52 Modern optical instruments find a method of driving them. This is accomphshcd by filling to a template or milling out on the lathe a small Avheel with recesses in it to grasp each cell in rotation, carry it round, and then send it onwards by bringing an- other cell in its next claw. Fig. 38 will show it in its place.- Fig. 38. Now if a milled head was fastened on the piece A (Fig. 38) and rotated, the cells must w^ave backwards and for- wards at the will of the operator. In all ophthalmoscopes on the wheel principle, the number of the lens is engraved on to the wheel itself, and each shown in an aperture cut in the keeper disc ; but in this case it is not practical to have the number of the lens on the cell itself, so a toothed wheel is geared on to the milled head that revolves once to every revolution of the Avhole of the discs, no matter how many times the milled head itself revolves. This register disc is marked off to as many spaces as there are lenses in the magazine, and each number engraved on the space pro- vided for it. This disc is covered with a thin shield of AND THEIR CONSTBUrjTTON 53 metal that has a perforation that only allows the number of the lens to be shown that is central with the eye-hole (see Fig. 39). Each of the cells that is to have a lens in Fui. 40. Fig. 39. is either stamped or turned to the shape of Fig. 40, so that the lens rests on a shoulder, and the eye-hole of the ophthalmoscope being rather smaller than the diameter of the lens, even if they should become uncemented and 54 MODERN OPTICAL INSTRUMENTS loose ill tlie cell, it is impossible for them to be lost. Each cell has its own number marked on, so it is a very easy matter to get tlie cells in their pi'oper order. Once in and the top plate screwed down, it is almost impossible for them to get damaged. At the top of the ophthalmoscope Fig. 41. is an extra disc, with four additional lenses, which im- mensely increase the number by containing four lenses of different strengths. The magazine, say, contains 24 convex lenses. Now, if the disc of Fig. 41 contains a concave lens of rather higher power than the highest convex lens in tlie magazine, and is placed before the eye-hole, you can "Per-? M z?/"^ w 7^ ^ ^ f^^ 56 MODERN OPTICAL INSTRUMENTS hvm(i: the various lenses before it in rotation, thus ofcttinsf a scries of 40 powers in all. So with a magazine instru- ment with 24 convex and 24 concave lenses, and the extra disc, it is possible to get a total of 196 different powers. Fig. 42 shows a magazine ophthalmoscope in section, and the following are the parts : M, the magazine ; L, lens in centre of eye-hole ; E D, extra disc, with four powers ; R, D, register discs ; G W, gear wheel ; D, driving disc ; M H, the milled head for driving the whole ; P C M, plane and concave mirror, fitted in a gimbals so as to be easily chans^ed ; A M, ans^le mirror, set at angle to obviate the necessity of looking through the edge of the lenses whilst reflecting the light in the patient's eye ; H, the handle. This instrument, with the two convex lenses, forms one of the most complete to be had. AND THETB CONSTBUrTIOX CHAPTER VII VARIOUS FORMS OF OPHTHALMOSCOPES With the Morton, the registering was effected by gearing the register wheel on to the driving milled head ; Fia. 43. but a later improvement does away with this arrangement. The cells are so 'formed that each has a lug ^on the side 5S MODERN OPTICAL INSTRUMENTS that can have the number of the lens enc/raved on it, and by an opening in the case each is read in its turn. Downs' ophthal:\ioscope. — The Fig. 43, which is Down Bros.' patent, represents an improvement on the well- FiG. 44. h II 1 ■ 1 1 / Fig. 45. known Morton ophthahnoscope. It consists of a new form of lens-holder, which forms a link in the chain of lenses, and answers the double purpose of holding a lens and indicating the power of a lens. This is effected by a number engraved on the lug attached to the lens-holder, AND THETR COKSTRUCTWK 59 A, Fig. 43. This wing does not at all impede the passage of the chain of lenses along the trough or link-race, and it is impossible for the order in which tlie chain travels to become by any means disarranged. The number engravetl Fig. 4G. on the wing is shown at the sight-hole B, and represents the power of the lens appearing at the sight-hole C, thus dispensing with the complicated arrangement of a time- wheel, used to indicate the power of the lenses in the older form of the oplithalmoscope. 60 MODEBN OPTTCAL TN^'^TBUMENT,'^ AXD THEIR C(JX>STRUMENT^'< a thorough training in the more difficult ' direct method/ for in retinoscopy we see nothing, or think nothing, of the condition of the fundus of the eye. Accurate retinoscopy is not quicker than measurement by this direct method ; indeed, with a good instrument, the hitter method certainly has the advantage in rapidity. I think there is reason to fear that the free use of retinoscopy by students before they have mastered the more difficult ' direct method' may tend to lower the present high quality of English ophthalmic work." By examination with mirrors for retinoscopy the refraction is determined by noticing the direction of movements of the light thrown on to the retina by the mirror where the latter is rotated. The degree of error of refraction is measured by the lens, which, jDlaced close to the patient's eye in a case of ametropia, renders the movement and other characters of the illumination the same as in emmetropia. The test is most accurate. When used at a great distance from the patient in practice, a distance of between three and four inches is chosen. The observer, seated in front of the patient, throws the light from an ophthalmoscopic mirror into the pupil of the eye to be examined. He will then see the area of the pupil illuminated, and on slightly rotating the mirror, will notice a movement in this lighted area, which movement will have a direction either the same as, or opposite to, that in which the mirror is turned. The lighted area is bordered by a dark shadow, and it is to the edge of this shadow that attention must be directed. Retinoscopy may be practised with a plane or concave AND THETR CONSTRUCTION 65 mirror. With the latter the shadow moves against the mirror in emmetropia, hypermetropia, and low myopia, and with the mirror in myopia of more than 1 D. With the former this is entirely reversed. The light should be thrown as nearly as possible in the direction of the visual axis, and the lamp should be placed immediately over the patient's head. In Fig. 50, with a concave mirror of about 22 cm. focus, the mirror M forms an inverted image, 1, of the light, L, at its principal focus, and 1 becomes the source of light for the eye E. A second image of 1 again inverted is formed at 1' on the retina of E. If the far point of E be at 1, this retinal image V will be clear and distinct; but in every other case it will be more or less out of focus and indistinct. On rotating M to M', 1 will move to 1-, and V to 1-, and these movements (of 1 and 1') will occur, no matter what the refraction of E may be. The observer placed behind M sees an image of 1' formed in the same way as the image of the fundus seen by the direct method, and, therefore, either inverted or real, or erect and virtual, according as the refraction of the eye is myopic or hypermetropic. If the observer's eye be accurately adapted for this image of 1', he will indeed see not only the light and shadow, but also the retinal vessels. If E be myopic, Fig. 51, the image of 1' is real and inverted and formed at 1", the far point of E. On rotating the mirror, 1' will move to 1-, and 1" will move to V-. If the eye be hypermetropic (Fig. 62) or emmetropic, rays reflected from its retina leave the eye divergent or parallel, and are not brought to a focus after emerging : the observer therefore F CC MODEBN OPTICAL INSTRUMENTS sees a virtual image erect at V\ tlie virtual focus of 1, and sees its movements exactly as they occur, against the movements of the mirror. The above statement for myopia is true only if the AND THEIR CONSTRUCTION 67 observer be beyond the far point of the observed eye. In myopia of 1 D the rays, returning fi-om the patient's eye, are focussed at a distance of one metre, and if the observer intercept these rays before they meet Fig. 53, he will refer them towards 1 ' and 1"-, and obtain an erect, virtual 08 MODERN OPTICAL INSTRUMENTS but imfucussed image of 1', the movements of which will be the same as those in hypermetropia or emmetropia asainst the mirror. Hence at a distance of about one metre movement against the mirror may indicate myopia of about 1 D, or emmetropia, or hypermetropia. With a plain mirror (Fig. 54) the source of light for the observed eye is an erect and virtual image of the flame formed at the same distance behind the mirror as the light is in front of it. In Fig. 54 this image is at L, the virtual focus of L ; a second and inverted image of L is formed on the retina of E at 1. The movements of these images on rotation of the mirror are the reverse of those of the image 1, and its retinal image 1" (Fig 50) obtained when the concave mirror is used. When the mirror M is rotated to M', / will move in an opposite direction to /', but its retinal image 1 will move to 1' in the direction with the mirror. These movements of L and 1 occur in every eye, whatever may be its refraction. In emmetropia and hypermetropia, however, the move- ment of the retinal image is seen as it occurs, and there- fore with the mirror ; but in myopia (Fig. 55) the observer sees an inverted image of 1 formed at the far point of E, and its movements are exactly the reverse of those of the retinal image. Therefore, on rotating M to M', 1 moves to 1', the image, 1\ seen by the observer, moves to 1'- against the mirror. If the plane mirror be used at a distance of more than 1 metre, a movement of the shadow with the mirror will occur with myopia of 1 D or less, but if the observer be about 2 metres, or 7 ft., away, the movement against the mirror will be obtained, unless the AND THEIR CONSTRUCTION 69 -^ ut- ^- 70 MODERN OPTICAL INSTRUMENTS myoi^ia be less than 5 D, and therefore the image seen is at 2 metres. The plane mirror gives at a long distance a better illumination than a concave one ; it can be used at a greater distance from the eye, and by this means low ametropia may be accurately measured. When examining by retinoscopy the patient is supplied with a trial frame, into which lenses are successively put until one is reached which just reverses the movements of the shadows. This lens nearly indicates the refraction of the eye under observation. In hypermetropia subtract about 1 D from the lowest convex lens which reverses the shadow. In myopia 1 D must be added to the lowest concave lens which reverses the shadow. Astigmatism is easily detected, and its amount measured by observing, on rotating the mirror, first from side to side and from above downwards, whether the shadow has the same movement and characters in each direction, or by noting that when the shadow in one meridian is corrected by a lens, the meridian at right angles to it still shows ametropia: the lens is then found which corrects the latter meridian, and the astigmatism equals the difference between the two lenses. Apart from the direction in which the image moves, much may be learnt from the variation in its brightness, its rate of movement, and the form of its border. The image is brightest, its movement quickest and most extensive in very low myopia or in emmetropia. The higher the ametropia, whether myopia or hypermetropia, the duller is the illumination, the slower and less extensive its movement, and the more ill-defined its border. The AND THEIR CONSTRUCTION 71 briglitness of the image depends on liow clearly 1, Fig. 50, is fociissed on the retina. The more accurately 1' is an image of 1, the brighter and larger will V (Fig. 51) be, and as the flame is rectangular, the borders of the image will be nearly straight. These conditions occur when the eye is exactly adapted for the distance of 1, for instance, in myopia of 1 D or less. If the myopia be higher than 1 D, 1 will be out of focus, and, therefore, be spread over a large retinal area, and being formed by the same number of rays, it will be less bright. The image 1" (Fig. 51 J will be correspondingly diffused and dull, and being formed nearer to the eye being examined, as, for example, at X, it will move only from x to x in the same time as 1" takes in moving to 1"-; hence its movement is slower and less extensive. The same is true in hypermetropia (Fig. 52), because the higher the hypermetropia, the more diffused is 1' and the nearer is 1" to the eye being examined. In both cases, high myopia and high hypermetropia, the border of the shadow is crescentric, because the diffused image forms a nearlv round area on the retina. MODERN OPTICAL INSTBUMENTS CHAPTER IX SPECTACLES AND THEIR SELECTION Spectacles and their kindred, with the legion of shapes, sizes, and questionable capabilities, are suffi- ciently well known as to have merely a passing glance ; but being the best known of any optical instrument, and with the gigantic amount of benefit they confer on mankind, we cannot let them pass without a brief notice at least, if they do not warrant the description their more com- l^licated relations require. The different forms of lenses have been partly explained ; it is only necessary to give a descrijDtion of the mechanical contrivances for holding the same in position. A good frame is as vital to the wearer as the lenses, and certainly great care should be taken to insure their suitability to the case required. Measurement for Spectacles. — To obtain measure- ment from pupil to pupil, the prescriber is seated opposite the patient, in a good light, the latter looking straight before him at a fixed distant point. A measuring-rule is rested on the nose of the patient, the prescriber being as AND THEIR CONSTRUCTION 73 far away as he can comfortably reach. The zero of the scale being placed opposite the centre of the left pupil, the centre of the other may be marked with the nail (Fig 56). This distance does not vary much from 2g in. Fig. 56. An allowance must be made, as the prescriber's eyes are about 2 ft. away, and the rule is about J in. The marks upon the rule, though apparently opposite the pupils, are really a little within their actual centres. If two milli- metres are added to the distance previously marked, it will be approximately perfect. The Pupil Localizer. — If greater perfection should be needed, a pupil localizer can be slipped in the recesses of the trial frame, which has a graduated bar for measure- ment of interpupillary distance. This pupil localizer consists of a semicircle of metal, with a pointer some distance in front of it (see Fig. 57). The gaze of the observed and the observing eye being directed to each other's pupils, the two sights of the implement are brought into line between them. The same is gone through with the other eye, and the distance of the second pupil from 74 MODERN OPTICAL tNtiTRUMENTii the median of the face, as registered by the trial frame, is added to that of the first to obtain the distance. The Fig. 57. frames must be vertically central as well as laterally, and this is also done by measurement, as in Fig. 58. Decentring. — Lenses are decentred sometimes for special purposes, and the following table, which is approxi- mately correct, can be relied on, and is equivalent to a given refracting angle, index of refraction being 1'54— Lens. V 2° 3° 4^ o"" 6' 8^ 10^ 1 E . 9-4 18-8 28-3 37-7 47-2 56-5 75-8 95-2 2 . . 4-7 9-4 14-1 18-8 23-6 28-2 37-9 47-6 3 . . 31 6-3 9-4 12-6 15-7 18-8 25-3 31-7 4 . .2-3 4-7 7-1 9-4 11-8 14-1 18-9 28-8 5 . . 1-9 3-8 5-7 7-5 9-4 11-3 15-2 19-0 6 • • 1-6 31 4-7 6-3 7-9 9-4 12-6 15-9 . 1-3 2-7 4-0 5-4 6-7 8-1 10-8 13-5 8 . . 1-2 2-3 3-5 4-7 5-9 71 9-5 11-9 9 . . 10 21 31 4-2 5-2 6-3 8-4 10-5 10 . . -9 1-9 2-8 3-8 4-7 5-6 7-6 9-5 11 . . -9 1-7 2-6 3-5 4-3 5-1 6-9 8-7 12 . . -8 1-6 2-4 31 3-9 4-7 6-3 7-9 13 . . -7 1-4 2*2 2-9 36 4-3 5-8 7-0 14 . . -7 1-3 2-0 2-7 3-4 4-0 5-4 6-8 15 . . G 1-3 1-9 2-5 31 3-8 5-1 6-3 10 . . -6 1-2 1-8 2-4 30 3-5 4-7 6-0 17 . . -6 11 1-7 2-2 2-8 3-4 4-5 5-6 18 . . '5 1-0 1-0 21 2-G 31 4-2 5-3 19 . . '5 1-0 1-5 2'0 2-5 3 4-0 5-0 20 . . '5 •9 1-4 1-9 2-4 2-8 3-8 4-8 AND THEIR CONSTRUCTION Bifocal Glasses. — Where glasses of a different focus- sing power are required for near or distant vision, the trouble of frequently changing them is obviated by bifocal glasses ; that is, the lower part of the spectacle eye which is used for near work is made to differ in focus from the upper part that is used for distant vision. This may be done in several ways. In the first patterns each eye contained two half-oval straight edges too-ether. pieces (see Fig. 58), with their This was improved by making the line of conjunction a curved one (Fig. 59), givmg Fig. greater ange of distant vision. They were also made in one piece, called ground bifocals (Fig. 60) ; but the difficulty of approximately centring the different curves was great, and they generally gave a prismatic effect. The others (Fig. 61) are cemented bifocals, and to the back of the distant glass is cemented a small lens whose power, added 76 MODERN OPTICAL INSTRUMENT}^ to that of the distant lens, equals the strength required for near work. For cylindrical lenses this form is best, as Fig. 60. Fm. 01. the cylinder need only be ground on the distant lens, the other being simply a segment of a sphere. AND THEIR CONSTEUCTION CHAPTER X VARIOUS FORMS OF SPECTACLES ILLUSTRATED AND DESCRIBED The most perfect vision with spectacles is produced when the e3^e looks in the direction of the axis of the lens, and imperfection always attends oblique vision through them, which imperfection increases with the oblicj^uity. Persons using spectacles are obliged to turn Fig. G2. the head, whilst people who do not require their assistance merely turn the eye. To diminish this inconvenience, meniscus lenses were introduced instead of the double concave or convex lenses hitherto used. The effect of these lenses, as compared with the double-concave or double-convex, is that objects seen obliquely through them are less distorted, and consequently there is greater 78 MODERN orTTCAL INSTRUMENTS freedom of vision by turning the eye without turning the head. These glasses are termed periscopic spectacles. Spectacles are various in shapes, but those illustrated will be amply sufficient to show the different forms com- AND THE IB rONHTBUCTION 79 monly used. Fig. 62 shows a spectacle frame with turn- pin sides; Fig. Go, spectacles with oval eyes; Fig. C4, pantoscopic eyes ; Fig. G5, a frame with twisted joints, no solder being used in their construction ; Fig. 66, spectacles with round eyes; Fig. 67, oblong eyes; Fig. 68, spectacles 80 MODERN OFTICAL INSTRUMENTS with crank bridge ; Fig. 69, spectacles with a K-bridge ; Fig. 70, spectacles with half-moon eyes; Fig. 71, spectacles with a X-bridge ; Fig. 72, spectacles with octagonal eyes ; Fig. 74. Fig. 73, spectacles with an arch bridge ; Fig. 74 will show the different forms of folders and protectors ; Fig. 75 shows the standard sizes of the lenses ; and Fig. 76 the springs, placqiiets, etc., the frames are built up with. 3 &: ^£^^M.. \ / lillipiiin i i i o^l ^ i ** r ^UMJUlmi!! !; n ^ 13 1 II pp JIM I mil I i II I, II' III III iiTi~tf1 It)! III! I I ai IM^ IfTT I I d| iT- AXJJ THE IE CON^-iTUUCTWN 81 CHAPTER XI STEREOSCOPIC PROJECTION — ANDEKTOX's SYSTEM Optical lanterns and stereoscopes forming the subjects of the next few chapters, a description of the two combined will no doubt be interesting. This method is the invention of Mr. Anderton. In devising his system of stereoscopic projection, the inventor has carefully steered, clear of apparatus of a delicate or intricate character, and has aimed at producing the effect without calling on the lantern operator to put forth exceptional care and skill. An ordinary biunial lantern is utilized; the jets are turned on ; the two slides forming the stereoscopic pair are placed in position and approximately registered, and, these having received attention, all the demands of the system have been fully met by the manipulator. Over half a century has passed since Prof. Wheatstone advanced his theory of binocular vision, and proved its truth by the invention of the reflecting stereoscope, and during the fifty odd years that have elapsed since his great discovery many attempts have been made to produce stereoscopic effects by means of pictures projected by 82 MODEBN OPTICAL INSTRUMENTS optical lanterns. At first sight it does not appear to offer any great difficulties to the adapter ; but bringing to bear upon the matter a little consideration, we find the seeming simplicity takes to itself wings and soars out of sight, and difficulties bristle up formidably in its place. In the stereoscope we have a pair of j^ictures and a pair of lenses in practically fixed positions, and near to the latter the eyes of the observer must be placed. Move any one of the three and the others must follow. Obviously a lantern stereoscope, constructed on a similar principle, would be a scientific curiosity, and nothing more, and an expensive one to work withal, for a pair of 10 ft. pictures to each observer Avould be a luxurious form of entertain- ment. Therefore, to be effective, one pair of projected pictures must serve for any number of persons, irrespective of their position with respect to the screen upon which they are focussed. It will at once be seen that the pictures could not be placed side by side if the above requirements are to be fulfilled, and it is equally clear that the pictures must be superposed. This being so, we have on our screen two equally bright pictures, and the problem to be solved is to convey one of these pictures to the right eye of each observer, and the other picture to each left eye, and these irrespective of position. Mr. John Anderton has solved the problem by taking advantage of the properties possessed by light when polarized. Light can be obtained in this condition either by absorption, as when passed through a plate of tourma- line by double refraction, by reflection from glass and other substances, and by transmission through a number AND THEIR CONSTRUCTION 83 of plates of thin glass. As the last-named method is the one used by the inventor, both for obtaining polarized light in his lantern, and for analyzing it, we ^Yill turn for a brief space from the consideration of the lantern stereoscope to perform a simple experiment. Taking, say, forty pieces of thin glass, we divide into two parts, and mount each twenty at an angle on a separate piece of short tube or other convenient form of holder. Upon looking through either of these we are conscious that objects appear less bright than before, no other change being apparent. Holding one in the right hand and one in the left, we will again look through them, and we find that if t^vo "bundles" of thin glass be held in the same plane no change is observable. Now if we turn eitlier round even a quarter of a revolution, we find we can see little or nothing^ throuQ-h them; turn on throusjh another quarter, and objects are seen as clearly through them as before. We can now turn to our biunial lantern again, and, turning on its bottom jet, focus a slide upon a screen. If we slip into our objective tube one of our bundles of thin glass the pictures will be on the screen as before, the only apparent difference being that it is not so bright as formerly ; in every other j^articular it is seemingly the same, but appearances are proverbially deceptive, and in the present case we shall see that they are strikingly so, for if we look through our second little bundle we shall find that our screen picture behaves strangely, disappear- ing and reappearing as the bundle is revolved. To make this quite clear we will hold it in the same plane as is its fellow in the lantern, and upon looking through it we 84 MODE UN OFTICAL INlSTJiUMENTS sliall see the pictures as clearly as without it. Now we turn it through a quarter of a circle, and find that the picture has practically disappeared ; turning on through another quarter it re-appears. Another quarter-revolution accomplished and it again disappears, and when the revo- lution is completed it has re-appeared. If, instead of turning the bundle held in the hand, we will revolve that in the lantern, we shall find that exactly the same changes will occur. We will go a step farther, and make two more bundles, and place one of these in the top lantern of our biunial, set with its plane at right angles to the bundle in the bottom lantern. Upon the screen w^e now have two pictures sujDerposed, and if we look through one of our bundles we find we can see only one of the pictures at a time, and each in turn, as we revolve. To make this quite clear, we place in the bottom lantern a slide of a bear, and in the top lantern an interior view of the House of Commons. Upon looking through the bundle, we shall see one only of the super- posed pictures, that of the bear, when the bundle is held in a similar plane to that of the bundle in the top lantern ; wdiilst the interior view of the House of Commons will become visible when the bundle is in a position corre- sponding to that in the bottom lantern. If we take a bundle in each hand and hold them in the positions in- dicated, we find that through one the bear will be seen, and through the other the interior will be visible. If, therefore, we substitute a stereoscopic jmir for the two dissimilar slides, we have fulfilled the conditions re- quired to obtain stereoscopic effect, for one picture of the AND THEIR CONSTRUCTION 85 pair falls upon the right eye, and upon the corresponding portion of the retina of the left eye the other picture falls, and these two pictures coalesce in the brain, and the irresistible impression is conveyed to the mind of one picture possessing the attributes of relief and solidity. I have assumed that the screen used is a suitable one, and it is necessary to state that had we made our experi- ments with any of those ordinarily used, "whether linen, paper, or a whitened wall, no effect could be obtained, for the simple reason that they depolarize the light falling upon them, and the analyzers (bundles) become powerless. The screen devised by the inventor is faced with dead silver leaf, and this material, in addition to answering the purpose, is far before any other for giving a brilliant picture with an ordinary lantern, although it is perhaps not quite so agreeable in colour as those in ordinary use. The bundles of analyzers are mounted in the form of a miniature opera-glass, and, as they contain no lenses, they need no adjustment, and the instant they are raised to the eyes the blurred pictures, with here and there double outlines, are resolved into one clear and distinctly solid picture. I have said nothing of the difficulties of obtaining ar clear and well-defined picture through a bundle (polarizer) consisting of many plates of thin glass ; but the result of almost countless experiments is an arrangement that pro- duces a picture of good definition. A similar difficulty arose with respect to the analyzers, and recourse to a pair of Nicol's prisms would have saved the inventor a large amount of experimental labour. There are, however, two formidable objections to the use of Nicol's prisms that 86 MODERN OPTICAL INf^TIiUMENTS could not be overcome or removed. The first is the small angle of view they allow, and the second is the compara- tively large cost. Those who are familiar with the subject of polarized light will naturally imagine that the lantern stereoscopic picture must inevitably be dark and dim, from the large amount of light reflected by the j^olarizers ; and were an ordinary screen used, the picture would undoubtedly suffer severely from want of brightness ; but in the dead silver- faced screen we have the best irregular reflecting surface known, and, therefore, the loss of light occasioned by the polarizers is practically the only loss. I stated at the beginning of this chapter that the two slides forming the stereoscopic pair need only be approxi- mately registered upon the screen. It should be mentioned that as the pictures have necessarily been taken from a different point of view, they are not identical, and there- fore 23erfect registration is impossible. Fortunately, this is in no sense a drawback, for the stereoscopic effect is obtainable if the pictures are purposely separated to some 6 in. or so from one another. A peculiar effect is seen when the observer moves across before the screen, as the objects in the foreground appear to follow him in which- ever direction he moves. The polarizers can be fitted to any limelight, biunial, or pair of lanterns. ANT) THEIB CONSTRUCTION 87 CHAPTER XII THE PRINCIPLES OF THE OPTICAL LAXTERX The primitive lantern consists of a luminant, a condenser, an objective, and a reflector, fitted in a box to carry them, and the principle cannot be altered. The luminant has been wonderfully increased in its intensity, the condensers made double or triple, the objective achromatic and spherical and chromatic aberration reduced to a minimum, and consequently larger and brighter pictures are pro- duced, the size of which is only limited by the power of the light produced. When the picture is largest on the screen, then also are all errors at their worst. Fig. 77 will show the section of a lantern of modern construction ; H is a square metal box, with an opening at the top and a door at the side; I is an electric light, G is a reflector, O 0' are plano-convex lenses, a and h two achromatic pairs of lenses, S a milled head, by means of which the achromatic sj^stem may be made to approach or recede from the transparent slide, which is placed in the opening K. The rays of light from the carbons reinforced by the reflection from G, and falling upon the lenses O 0', are 88 MODERN OPTICAL TNSTBUMENTS made almost parallel. These two lenses are consequently called the condensers. The rays next pass through the more or less transparent object placed at K, and by means of the lenses a, h, an image is formed on a screen placed at a suitable distance to receive it. The image is, of course, inverted, and to be seen erect the object must be necessarily placed in the carrier in an inverted position. Fig. 77. Erecting Prisms. — The erection of the object can be easily done by introducing an equilateral rectangular prism in front of the lens tube, so that the hypothenuse surface is horizontaL The parallel rays, falling on the prism, are inverted in consequence of refraction at the sides, and reflection from the hypothenuse surface, so that an erect image is obtained instead of the inverted one. The dotted lines. Fig. 78, ah c d and cfgli will show the path of the two rays. The magnifying power of a lantern is obtained by dividing the distance of the lens from the image by its distance from the object. If the image is 100 or 1000 times farther from the lens than the object, ANT) THEIR CONSTBUCTION 89 tlie image will be 100 or 1000 times as large. Hence an objective of sliort focus will produce a very large image, Fig. 7^. provided the screen be large enough, and the illuminant sufficiently powerful. The Solar Lantern. — Using the sun as a source of light, we get the solar lantern ; this serves to produce highly-magnified images of very small objects. The apparatus, of which Fig. 70 is a section, is fixed in a Fig. 79. shutter of a room, and as the direction of the sun's light is continually varying, the position of the reflector outside the shutter must be changed, so that the reflection is 90 MOREEN OPTICAL INSTBUMENT>< always in the direction of the axis of the microscope. A heliostat is the most accurate apparatus for this purpose, and the light of the sun can only be sent in a constant direction by making the mirror movable. It must have a motion which compensates for the continual change in the direction of the sun's rays, produced by the apparent diurnal motion of the sun. The result is obtained by means of a clockwork motion, to which the mirror is fixed, and which causes it to follow the sun. The sun's rays falling on the mirror M, a?e reflected towards a condensing lens, L, and thence to a second lens, O, by which they are concentrated at its focus. The object is placed at this point, which is identical to the stage of an ordinary microscope, and clamped by means of spring- clips. The object being thus strongly illuminated, the image is formed by a system of lenses, a, and projected on to a screen, the lenses focussed accurately by means of the rack-and-pinion motion D. The Solar Microscope. — The solar microscope labours under the objection of concentrating great heat on the object, which soon alters or spoils it. This can be obviated to a great degree by interposing a saturated solution of alum, which has the power of taking up 88 per cent, of the heat, thus cutting off a considerable portion. The magnifying power may be deduced experimentally by substituting for the object a micrometer. The division being known as to their distance apart, the magnifying power may be calculated. An electric microscope can be formed by taking the front combination from Fig. 77, and substituting an apparatus like Fig. 70, of course without AXD THEIB CONSTPJJCTIOX 91 tlic reflector. The image from this can either be received on a screen, or by the introduction of a j^rism at H. Fig. Fift. 80. 80 siiows a system by which an image can be thrown on a table for class demonstration. The electric light, or oxy- hydrogen, which can be produced at any time of the day, is far preferable to solar light. 92 MODERN OPTICAL INSTRUMENTS CHAPTER XIII THE STEREOSCOPE The stereoscope is an instnimeut by which the effect of binocular parallax creates impressions of perspective and relief, and the principles are as follows : — Let any solid object, such as a small box, be supposed to be held at some short distance in front of the two eyes. On whatever point of it they are fixed, they will see that point the most distinctly, and other points more or less clearly. But it is evident that, as the two eyes see from different points of view, there will be formed in the right eye a picture of the object different from that formed in the left; and it is by the apjDarent union of these two dissimilar pictures that we see the object in relief If we delineate the object first as seen by the right eye and then by the left, and afterwards present these dis- similar 2:>ictures again to the eyes, taking care to present to each eye that picture which w^as drawn from its point of view, there would seem to be no reason why w^e should not see a representation of the object as we saw the object itself in relief. If the object held before the eyes were a AND THEXIl CONSTMUCTION 03 truncated pyramid, r and / woidd rej)resent its principal lines (Fig. 81) as seen by the right and left eye respectively. Fig. 81. If a card is held between the figures, and they are steadily looked at, r by the right eye and / by the left, for a few seconds, there Avill be seen a single picture having the appearance of relief. Even without a card between, the eye, by a little practice, can be taught to combine the two and form a solid picture. Three pictures will in this case be seen, the centre one solid and the outside one flat. Let r and /, Fig. 82, be any two corresponding points — say the points marked by an x in the figures ; R and L the positions of the right and left eyes. Then the right eye sees the point r in the direction K o, and the left eye the point I in the direction L o, and accordingly each by itself judging only by the direction; they together see both points as one, and imagine it to be situated at o. But the right eye, though looking in the direction R r, also receives an image of / on another part of the retina, and the left eye an image of r, and thus three images aie seen. A card 04 MOUEBN OPTICAL INSTRUMENTS placed between, where the dotted line is seen in Fig. 82 will cut off the two side pictures. The Reflecting Stereoscope. — In the reflecting stereo- scope, plane mirrors are used to change the apparent posi- tion of the pictures, so that they are seen in the sam6 direction, and their combination by the eye is thus ren- dered easy. If a l, Fig. 83, are two plane mirrors inclined <- ^h Fig. 82. Fig. 83. to one another at an angle of 90 , the two arrows x y would both be seen by the eyes situated at R and L in the position marked by the dotted arrow. If, instead of the arrows, we now substitute such a pair of dissimilar pictures as we have spoken of above of the same solid object, it is evident that if the margins of the pictures coincide, other points of the picture will not. The eyes, however, without effort will bring such jDoints into coincidence, and in so doing make them appear to recede or advance as they are AXD THEIR CONSTRUCTION 95 farther apart or nearer together than any two correspond- ing points of the margins when the pictures are placed side by side, as in Fig. 83. It will be plain, also, on considering the position for the arrows in Fig. 83, that to adopt such figures as those in Fig. 82 for use in a re- flecting stereoscope, one of them must be reversed or drawn, as it would be seen through the paper if held to the light. Fig. 84. The Refeactixg Stereoscope. — In the refracting stereoscope the rays of light passing through a convex lens are always bent towards the thicker part of the lens. Any segment of such a lens may be adapted to change the apparent position of any object viewed through it. If (Fig. 84) two segments be cut from a double convex lens and placed with their edges together, the arrows x y would both be seen in the position shown by the dotted 96 MODERN OPTICAL INSTRUMENT;^ arrow, the ejes being at E, and L. If we substitute for the arrows two dissimilar pictures of the same solid object, or the same picture, we shall then, if an opaque screen, a h, be placed between the lenses to prevent the i^ictures being- Fig. 85. seen crosswise by the eyes, see but one 23icture, and that in the centre magnified as before. If the margins are brought by the power of the lenses to coincide, other corresponding points will not be coincident until combined by an effort of the eyes, which, however, is very slight. Any pair of corresponding points which are farther apart than any other pair will be seen farther back on the picture. It will be noticed that there is ako a second point on this side of the paper, at which, if a person looks steadily, the diaoframs in Fio\ 85 will combine and form a different AND THEIB CONSTRUCTION 97 stereoscope picture ; instead of a solid, a hollow, pyramidal box will be seen, and the two external images will also be seen. If we wish to shut these out and see only the central stereoscopic effect, we must use a screen held parallel to the plane of the picture with a square hole in it. This screen must be so adjusted that it may conceal the right-hand figure from the left eye, and the left-hand figure from the right eye, while the central stereoscopic picture will be seen through the central hole. It will be plain from the diagram (Fig. 85) that o is the point to which the eyes must be directed, and at which they will imagine the point to be situated, which is formed by the combination of the two points r and /. An achromatic combination, balsamed together and then slit through the centre, can be easily made and fitted to anv suitable case. 98 MODERN OPTICAL INSTEUMJENTS CHAPTER XIV THE SPECTROSCOPE The spectroscope, which is an iastrument employed in the study of the spectrum (Fig. 86), is composed of three telescopes mounted on one foot, the axis of each converging a prism of flint glass, the telescope A having a circular AXD THEIR CONSTRUCTION 99 motion, the other two being rigid. The rays emitted by the flame G fall on the lens a, and are caused to converge to a point, 1), which is the principal focus of a second lens, c. Thus the pencil of light on leaving the tele- scope B is made parallel, and enters the prism P. On leaving the prism the light is decomposed and falls on the lens ox By this lens x a real and reversed image of the spectrum is formed at i. This imao^e is seen throug^h a lens which forms at S S a virtual image of the spectrum magnified. The tele- scope C serves to measure the dis- tances of the lines of the spectrum, and is provided with a micrometer placed at m. In the direct-vision spectroscope prisms are combined so as to get rid of the dispersion without entirely destroying the refraction (Fig. 87). They may conversely be combined, so that the light is not refracted, but decom- posed, and produces a spectrum. A system of two flint and three crown-glass prisms is placed in a tube, which slides in a second one. At the end of this is an aperture, o, and inside it a slit, the width of which can be regulated by turning the ring 100 MODERN OPTICAL INSTRUMENTS r. A small achromatic lens is placed at a a, the focus of which is at the slits, so that the rays pass parallel through the five prisms, and the spectrum is viewed at e. By having two equal systems of direct-vision prisms ^f. Fig. 88. arranged close to each other, the spectrum is reversed, and by movement of a split lens the position of the spectra may be moved apart or nearer to each other, and bringing together any two lines so that they may be in the same vertical line. The slit of the spectroscope can be made in two halves (Fig. 88) for quantitative spectrum analysis. THE END. Richard Clay d: Sons, Limited, London d: Bun(iay. INDEX Accommodation, 8 Ametropia, 28 Astigmatism, 45 Bifocal glasses, 75 Binocular vision, 9 Clear sight, optical conditions of, 33 Correction, numeration for, 33 Crystalline lens, 4 Decentring, 74 Emmetropia, 28 Erecting prisms, 88 Eye as an optical instrument, 1 — aberrations of, 28 — description of, 1 — examination of, 36 — refraction of, 5 Iris, the, 3 Lantern, solar, 89 Lenses, decentring, 74 foci of, 19 Lenses, properties and aberra- tions of, 12 Microscope, solar, 90 Myopia, 29 Ophthalmoscope, the, 36, 38 Downs', 59 its uses, 42 the Liebreich, 45 the Morton, 50 various forms of, 57 Optical lantern, principles of 87 Pupil localizer, 73 Refraction, 12 Retina, the, 3 Retinoscopy, 63 Spectacles and their selection, 72 Spectacles, measurement for, 72 various forms of, 77 Spectroscope, the, 98 Stereoscope, the, 92 reflecting, 94 refracting, 95 Stereoscopic projection, 81 This book is DUE on the last date stamped below NOV 2 4 ia4e MAY 1 l^i^ JAN 3 1 1967 QC 371 067m EBgDieering Library fmw JML72 ^ 3r/?-2,'45(3232) (4) Kapp's Electric Transmission of Energy, los. 6d. 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