EXCHANGE SPECTRAL PHOTOMETRIC STUDIES - BY DANIEL WILLIAM MURPHY A THESIS PRESENTED TO THE FACULTY OF LELAND STANFORD JUNIOR UNIVERSITY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY MAY, 1896 THE ASTROPHYSICAL JOURNAL AN INTERNATIONAL REVIEW OF SPECTROSCOPY AND ASTRONOMICAL PHYSICS JUNE VOLUME vi j LJ i> L iw/ NUMBER i SPECTRAL PHOTOMETRIC STUDIES. By D. W. MURPHY. DETERMINATION BY MEANS OF THE ROTATING SECTOR OF THE RELA- TION OF SPECTRUM INTENSITY TO THE WIDTH OF THE COL- LIMATOR SLIT. AMONG the different methods of comparing the intensities of two spectra that of Vicrordt is the most common. The instru- ment used, in its simplest form, differs from the ordinary spec- trometer only in the arrangement of the collimator slit. When the apparatus is to be used for photometric purposes the col limator slit is replaced by two separate slits located one directly above the other. The width of each slit is measured by means of a micrometer screw, and each in turn may be lighted from either of the sources whose intensities arc to be compared. 1 The spectra thus formed are situated one above the other, and are separated by a narrow dark band. The observations are made by means of an ocular which, being supplied with an adjustable slit, allows all the spectrum to be cut off except that part in which the comparisons are to be made. The two fields are brought to the same intensities by varying the widths of the two parts of the double collimator 1 When measuring the amount of absorption both spectra are lighted from the same source, and the absorption medium is placed between the light and one of the slits. 239402 2 /). ir. slit. From the relations of the slit widths for equal intensities in the different parts of the spectrum, the intensity for different colors is found. According to Vierordt we assume that the intensity of a spectrum so lighted is directly proportional to the width of the collimator slit. When the two spectra are of the same intensity the lights are inversely proportional to their respective slit widths. We shall investigate under what conditions this principle introduced by Vierordt is correct, both for unilateral and for bilateral slits. We know for both cases that when the width of the slit is doubled, twice the amount of light comes to the field of the observer. The question which we are then called upon to solve is, does the doubling of the amount of light in this manner double the intensity of every part of the spectrum ? Let us imagine, first, an infinitely narrow slit ; the spectrum from such a source may be called a pure spectrum, since any point in it will contain light of but one wave-length. If this slit be moved in a direction perpendicular to the edge of the prism the spectrum will travel in the same direction ; and a stationary point, as the light traveled over it, would be illuminated by light of different colors. Next, let us consider a wide slit, and think of its being divided into infinitely narrow ones ; we recognize that every part of the spectrum from such a source will consist of lights of different wave-lengths superposed upon each other. Such a spectrum we will call an impure one, and it is with such that we are required to deal in practical measurements. With a unilateral slit only waves that are either greater or less, depending upon the direction of the opening of the slit, than the fundamental wave, will be superposed upon it. If a bilateral slit is used the extra waves which are brought to a given point, due to the opening of the slit, will be both greater and less than the fundamental wave. From the above consideration it follows: that with a uni- lateral slit the law of proportionality holds only when the inten- sities of the adjacent parts of the spectrum arc the same ; or, SPECTRAL PHOTOMETRIC STUDIES 3 where the curve of intensity is parallel to the one axis of coordinates. With the bilateral slit the law holds where the curve of intensity is a straight line, and may be true for other curves in the region of inflection points. In the latter case the differentials of the increase in intensities due to the light from the opposite sides of the slit, must be equal and of opposite signs. According to the measurements of Fraunhofer, Koenig, Brodhun and others, the distribution of intensity in the spectrum of the Sun and other incandescent bodies corresponds approx- imately to the curve shown in Fig. I. FIG. i. The abscissae represent the wave-lengths, and the ordinates the corresponding intensities. From this curve it follows that the unilateral slit is to be used only in those parts of the spec- trum where the curve of intensity is parallel to the axis. This is true for only a small part of the spectrum in the region cd. The bilateral slit, on the other hand, will give true results not only at cd, but in the vicinity of the two points b and e. When the curve is convex to the axis, as at ab and ef, the increase in inten- sity must be more rapid than the increase in the slit width. If the curve is concave to the axis, as at be t the increase in intensity is less rapid than that of the slit width. In order to prove the correctness of these inferences, and to determine the magnitude of the deviation from the law of proportionality, the following observations were made. Method of observation and apparatus used. The photometer measurements were made with the Lummer-Brodhun spectral />. //'. MURPHY photometer, a complete cleseription of which may be found in the Zcitsclirift fiir Instntmentenkunde for April 1892. This instru- ment differs in two respects from the spectrometers of Vicrordt and others. First, it is supplied with two collimator tubes, C and C ', placed perpendicular to each other (sec Fig. 2); and, second, the observations are made, not by means of an ocular, but by bringing the eye directly before the slit o. The plane FIG. 2. ad, which is the hypotenuse of the photometer cube W, passes through the axis of the instrument. The field iki< n 0. At the ends of the spectrum just the opposite is observed. These results agree with those deduced from a consideration of the form of the intensity curve. The amounts of the deviations are different for the different wave-lengths, and, in general, are smaller for blue than for green, yellow, and extreme red. It is further shown, that for a given wave-length the deviation changes with the size of the slit used. Heretofore the measurc'ments have been made through the entire length of the spectrum with nearly the same width of slit, and each particular series gave the results for that width of slit only. In order to study more fully the change for varying slit widths the experiments were repeated in another form. Particu- SPECTRAL PHOTOMETRIC STUDIES 9 lar colors were examined for different slits, from the smallest to the largest size with which the measurements were possible. In this manner results were obtained for the wave-lengths 540, 590, and 690 />t/Lt. In Tables V to VII, inclusive, the results are shown. In these results g, b, and 8 have the same significance as in the results previously given. TABLE V. (X= & *b 8 zb S 13.0 14.4 -9.8 68.t 67.0 + I-.7 17.7 19.0 -6.8 82.7 81.6 + 1-4 27.7 28.2 -1.8 103-3 101.6 + 1-7 38.0 37-8 +0.5 123.4 122.0 + 1.2 53-2 52.0 +2.3 I43-I 140.0 +2.2 TABLE VI. \ = g zb & f *b a 13-1 14.4 9.0 68.5 67.0 +2.2 1 8.0 19.0 5-3 84-3 82.0 +2-9 27-9 28.6 2.4 104.3 101.8 +2-5 38.6 38.0 +1.6 124.0 I20.O +3-6 53-8 52.2 +3-1 145-9 I40.I +4.1 TABLE VII. (X = g 2b B g 2l> 1 13-3 14.6 9.0 69.4 70.2 I.I 18.1 19.2 6.0 86.7 88.4 1.9 28.5 29.0 1-7 107.2 1 10.2 2.7 38.4 38.8 i.o 126.6 135-0 6.2 54-4 54-6 0.4 147.8 159.6 7.4 These tables show, in the first place, a concordance with the former ones ; at least they lead to the same general conclu- sions. Beyond this they teach, that for slit widths below a certain value, for every wave-length g2 b becomes K THE INTENSITY OF REFLECTED LIGHT, AND THE DEPENDENCE OF THIS INTENSITY ON THE COLOR OF THE LIGHT USED. Since Fresnel, from a theoretical consideration, gave his celebrated formula for the amount of light reflected from the surface of a transparent medium, the experimental verification of it has been a problem of interest to investigators in optical SPECTRAL PHOTOMETRIC STUDIES I I science. And of all the methods used, the photometer the simplest in principle was applied relatively very late. This is probably due in a large degree to the hitherto inexactness of photometric measurements which, with the small amount of light reflected, gave rise to serious errors. It is for this reason that Professor Rood, 1 who was the first to investigate the subject, prefers measuring the amount of light transmitted by thin plates of glass, and from these results to compute the reflection at the first surface. Lord Rayleigh, 2 and shortly after him Sir John Conroy 3 were the first to choose the experimentally difficult, but decidedly less objectionable, method of measuring directly the amount of the reflected light. In order to prevent the great loss of light by diffusion which takes place in the ordinary photometers, Rayleigh dispensed with the use of diffusion screens and used only direct reflection from the light source to the eye. He observed from the amount of light reflected from the surface of glass prisms that only those sur- faces which had been freshly polished gave results consistent with theory. Conroy measured not only the light reflected, but also that transmitted by glass plates, hoping in this manner to find an explanation for the differences which so often exist between observed and computed results. He concluded that the amount of light reflected from a glass surface varies with the kind of polish to which the surface has been treated. Even though a sufficient reason for taking up the subject anew might be found in the variations of results heretofore obtained, I had still another purpose in so doing. Rayleigh and Conroy in their investigations used white light, and as a basis for their calculations used the refractive index of the color of greatest intensity. They further used ordinary unpolarized light, while the Fresnel formula is deduced from a consideration of lights polarized in and perpendicular to the plane of incidence. A much more complete test of the formula would, therefore, be 1 American Journal oj Science, 50, I. *Proc. A'. Sot., 41, 275. 3/VhV. Trans., Vol. A 1889, p. 245. 12 D. W. MURPHY . obtained by working with light polarized at different angles to the plane of incidence. So far as I know, no investigations had been made on the amount of the reflection for lights of differ- ent colors, and no experiments that have been carried on in a purely photometric way, show that the amount of reflection is different for the different wave-lengths of the light used. 1 By means of the linear bolometer, Rubens has investigated the Fresnel formula in the ultra-red part of the spectrum, and has found that the amount of energy reflection varies for different wave-lengths. In the following I shall show, that with the aid of the Lum- mer-Brodhun spectral photometer, in connection with a rotating sector for measuring the weakening of the light, and a second- ary spectrometer for determining the angle of incidence of the reflected ray, we can measure the amount of reflection for any wave-length and for any desired angle of incidence. By using a Nicol placed in the path of the ray it is possible to extend those measurements to light polarized in .any desired plane. The measurements to be made with special care, however, are those which show the relations of the intensities of the different colors in the spectra of the direct and reflected light. Method of investigation and description of the apparatus. In Fig. 3 is shown a horizontal cross section of the apparatus giving the arrangement of the different parts. The spectral photom- eter consists of the tubes C, C and T t the photometer cube W t and the refracting prism P. C and C' are the collimators 1 The Fresnel formula, nM*'+r) tan* (* in which 7 r is the amount of light reflected, I\ the incident, i the angle of incidence, and r the angle of refraction. This formula shows that as n (the refractive index) increases, sin (i r) becomes larger, and, up to a certain point, where (i -f- r ~ 90), sin (/ -j- r) becomes smaller. The same is true of the second term. The formula then says that for a given angle of incidence the amount of reflection will be a func^ tion of the refractive index, and if this index be increased the amount of reflection will be increased. We can further deduce, that since the change in the amount of reflection is a transcendental function, it will be different for different :ingk-s of inci- dence. SPECTRAL PHOTOMETRIC STUDIES \ 3 by means of which the light rays from the sources L and L' are rendered parallel before reaching the photometer W. T is the observing telescope and is provided with a variable ocular slit o. When the apparatus is in adjustment an eye placed before o sees the photometer fields lighted from the illuminated slits s and s r . The light sources used, L and L' , consisted of incan- descent electric lamps of approximately fifty candle power each. The lamps were joined in series to a circuit, and supplied with a SP- FJG. 3. current from a storage battery, having an E. M. F. of thirty-two volts. The light source L is firmly fastened to an arm of the spectral photometer, and always lights in the same manner the one field of the photometer W. The other light source, L r , is mounted upon a separate piece of apparatus, Sp. This appa- ratus, which is a form of spectrometer, consists essentially of the circular plate M to which are fastened the arms Q and R. The plate M, whose diameter is about 5O cm , is turned from a heavy slab of slate, and its edge, being graduated, serves as the 14 D. W. MURTHY spectrometer circle. The metal arm R, which carries the lamp L' , is so mounted that it turns about an axis through the center of M) and its position is read by means of the graduated circle. The arm Q is firmly fastened, and always retains the same posi- tion relative to the spectrometer disk. The lamp L' is enclosed so that the only light emitted from it is through the slit z. The slit s and the collimator slit s are covered with milk glass plates p and/', the purpose of which is to give a more uniform field than could be got from the lamp direct. The lenses a and b are mounted so as to slide along the arms Q and R in the path of the ray. These lenses are so adjusted that the light from z passes in parallel rays from b to a, and is brought to a focus again on the slit s' . The spectrometer as a whole is so placed that when the arm R is at its zero position, that is, making an angle of 1 80 with Q, the axis of the spectrometer cuts the straight line passing through the center of IV and the slits s' and z. The pencil of light between b and a will then be concentric with the line of collimation of C' , and will cut the spectrometer axis at right angles. When viewed with an ocular placed before o the images of s and s' will be seen to exactly coincide, and the color of the two fields will, with this adjustment, be the same for all positions of the observing telescope. In order to compare the intensities of light of any desired wave-length, it is only necessary to turn the telescope T until that color is brought into view. The surface whose reflecting power is to be measured is placed upon the table of the spectrometer in such a position that it lies in the plane passing through the axis. By rotating the table the reflected light may be made to fall upon s r for all positions of the arm R. In order to compute by means of the Fresnel formula the amount of the reflected light, one face of a Steinhcil prism was used as a reflecting surface. The refractive indices of the prism for the desired wave-lengths had been carefully measured. The light from the source L was weakened to the same inten- sity as that of the reflected portion from L' by means of a rotating SPECTRAL PHOTOMETRIC STUDIES I 5 sector 5 placed between L and the slit s. The size of the sector opening could, during rotation, be changed at will from 180 to O, and by means of a vernier read to an accuracy of O.O2. Upon the arm Q, and between the reflecting surface and the lens a, a Nicol prism N could be mounted. By revolving the Nicol in its mountings the light which fell upon s' could be polarized at any desired angle with the plane of incidence. Dependence of the amount of reflection on the wave-length. The method of finding the variation in the amount of reflection for different wave-lengths was as follows: The relation of the inten- sities of the light sources L and L' for two colors, first for the direct and then for the reflected light, was measured. A com- parison of these ratios gave the excess of reflection for one color over that of the other. The method of observation for this is very simple in form. First, the slits s and s' are set at approximately the same widths. With the arm R at its zero position and the sector open to nearly 180, the lamps are adjusted until the fields are of nearly the same intensity for one color ; all other conditions remaining the same, equal intensities are obtained by opening or closing the sector. After a series of ten settings has been made, and readings on the size of the sector opening taken, the observ- ing telescope is turned so as to observe the light of the other wave-length, and a second series of sector readings for equal intensities of this color is taken. The ratio -y, of the sector readings tor the two colors, which is denoted by 7 d , is the relation of the intensities of these colors in the spectrum of the direct light from L' . This rela- tion is in terms of the spectrum from L, which may be con- sidered of unit intensity for every wave-length. The arm R is next moved from its zero position, and the reflecting surface placed on the table of the spectrometer. In order to bring the photometer fields to the same intensity when using only the reflected portion of the light from L 1 ', it would require a very considerable diminution of the sector. Measure- 16 D. II'. AWRI'HY ments made in this way do not possess the highest degree of accuracy on account of the smallness of the sector opening. To avoid this source of inaccuracy the sector was left at its original size, and the light source L removed until the intensities were approximately equal. The values of K ' and 0\ ' for the reflected ray were then obtained in the same manner as for the direct ray. The quo- O ' tient, ^y, is denoted by 7 r . Fr9m a consideration of the above we have as the relation of the reflection of light of wave- Al length \ to that of light of wave-length /. For example, the readings of the half-sector openings for wave-lengths 535/4/4 and 670/4/4, for the direct light were 0* = 8i.33 and 01 = 75. 76 (^ being considered as wave 535/4/4 and / as wave 670/4/4). The value of 7 d was therefore - ^ = 1.074. F r tne 75-76 light reflected at incidence angle of 20 the results obtained were K ' 8o.25 and 0\ ' 73. 35. From this 7 r = 1.094 and - = 1.019. This shows that for light of wave-length 535/4/4, *d 1.9 per cent, more light is reflected than for light of wave- length 670/^/4. TABLE I. Relations of the amounts of light reflected for X=535/*Ai and Incidence angle Observed Computed 20 I.OIQ I.OI5 40 60 I.OI9 I.OIO I.OI5 1.008 80 1.003 1.002 The results of these investigations for different incidence angles are given in Table I. The computed values are the ratios of the amounts of reflection taken from the results computed by the Fresnel formula for the corresponding angle of incidence SPECTRAL PHOTOMETRIC STUDIES 17 and for the refractive indices of the glass for wave-lengths 535/>t/Lt and bjo^p. [See Table III.] Character of light reflected from colored plates. Measurements were made on the intensity of the different colors of the spec- trum for lights reflected from different colored glass. For this purpose, glass plates, the reverse side of which had been cov- ered with asphalt black, were used. Red, as well as blue, glasses gave for the blue a stronger reflection than for the red rays, showing that the composition of the reflected light is not changed by the color of the reflecting medium. These results were not compared with theory, since the refractive indices of the plates for different wave-lengths of light could not be readily determined. Measurement of the amount of light reflected for different colors and at different angles of incidence. The problem of measuring the absolute amount of light reflected is in theory a very simple one. For its solution it is necessary only to compare the total incident light from L' with the reflected portion. This is done by taking the sector readings for equal intensities of the photo- meter fields with R at its zero position and at the position of the desired angle of incidence. The comparison of the direct with the reflected light, however, is attended with two experimental difficulties. First, the reflected portion is small, being, for the smaller angle of incidence, only about 4 per cent, of the total incident light. Second, the reflected light, more especially for large angles of incidence, is partly polarized at the reflecting surface. The first condition leads to the measuring of small sector openings, the adjustment and reading of which require especial care to prevent error. The polarizing of the light at the reflecting surface may lead to another source of error, since in the spectral photometer the refracting prism also produces polarization, and in this case acts as an analyser in destroying the light which has been polarized by reflection. It is for this reason that photometers consisting simply of diffusion screens have in some cases been brought into use for measuring the amount of reflected light. t8 r>. w. The error due to polarization may, however, be entirely avoided by placing a polarizer in the path of the ray, between the reflecting surface and the lens a. For this purpose a Nicol prism of 45 mm x45 mm opening was used. With this arrangement the measurements, for both the direct and the reflected rays, are made for light polarized in one plane whose position is identical with that of the Nicol. In order to compare the results obtained by measurements with those computed from the formula it is necessary to know accurately the polarizing plane of the Nicol. This may be found by computing from the refractive index with the help of the Brewster formula, ft=tan ;, the angle of inci- dence under which the reflected light is totally polarized. The position of L' is adjusted by means of the movable arm R until the light falls upon the surface at this angle ; the Nicol is then turned until the light which reaches the photometer from L' is a minimum. At this position the polarizing plane of the Nicol is perpendicular to the plane of incidence. By means of the graduated circle on the Nicol mounting I was able to bring the polarizing plane to any desired position and to read its position to an accuracy of 5'. Method of observation. After the Nicol had been adjusted the reflecting prism was removed and the arm A' placed at its zero position. By means of the rotating sector the photometer fields were brought to the same intensities, and a series of five readings on the size of the sector opening was taken. The arm was then turned to the position for the required angle of inci- dence, and the prism so placed that the reflected light fell upon the slit s' . Photometric equality was then brought about by closing the sector, and a series of readings on the size of the sector opening was taken. To avoid any error due to a change in the relative intensities of the light sources during the measur- ing process, the arm R was again placed in its zero position, the prism removed, and a second scries of five readings of the sector for direct light was taken. The ratio of the two sector openings gives the relation of the incident to the reflected light. If we consider the incident light SPECTRAL PHOTOMETRIC STUDIES equal to one hundred, which has been done in the following results, the amount of the reflection is given in terms of per cent, of the incident light. Measurements were made for light of wave-lengths 535 A^ and 670 ft//-, and for three positions of the polarizing plane, which were at angles of O, 45 and 90 with the plane of inci- dence. The results are given in the following tables. / is the angle at which the incident light falls upon the reflecting surface. The observed values are the results obtained from a single series of observations, and not the mean of several sets of readings. The computed results are deduced from the Fresnel formula: L 2 (* r) tan 2 (/- tan 2 ( / -f- T sin 2 (/ + r) The refractive indices were obtained by direct measurement, and were for wave-lengths 535 pp and 670 ft/A respectively, 1.56462 and 1.55896. The differences between the observed and computed results are given direct, and are not owing to the different values of the reflected light computed in terms of percentage. These tables show in general a close agreement between the observed and computed results, the differences being in every case but a small percentage of the total incident light, while in many cases they are almost perfectly concordant. The greatest discrepancy exists for light polarized perpendicular to the inci- dence plane, and in this case for the small angles of incidence. TABLE II. Light polarized in the incidence plane. \ = 670 fi/u. * = 535 MM I Observed Computed 5 Observed Computed 8 20 5.60 5-58 -j-O.02 5-61 5.66 0.05 40 9.24 8.94 +0.30 9.20 9.06 0.14 60 19.64 19.64 zhO.OO 20.19 19.80 + 0.39 80 55-73 56.04 -0. 3 I 56.72 56.24 -f0. 4 8 20 /). /K MURrilY TAHLE III. Light polarized at an angle of 45 to the incidence plane. A = 670 MM * = 535 MM I Observed Computed Observed Computed & 20 4.80 4.80 :O.OO 5.10 4.87 +0.23 40 5-60 5-38 -f-0.22 5-63 5.46 +0.17 60 9.62 9.87 -0.25 10.12 9-95 -0.17 80 39-07 39-65 0.56 39-04 39-73 0.69 TABLE IV. Light polarized perpendicular to the incidence plane. A = 670 MM * = 535 MM ' Observed Computed a Observed Computed a 20 40 60 4-43 2.03 4.02 1.82 O 10 +0.41 -|-0.2I 4-38 2.00 4.08 1.86 10 +0.30 -0.14 80 23-OS 23.16 O.I I 22.76 23.22 -0.46 If these many independent observations speak for the cor- rectness of the Fresnel formula, they also give evidence of the exactness of the photometric comparisons, and of the method of measuring by means of the rotating sector despite the small amount of reflected light. As the measurements for light polarized perpendicular to the plane of incidence could not be repeated, the spectral photom- eter being in use for other investigations, I am unable to give any explanation of the slightly greater variations between observed and computed results in this particular case. It is not probable that the Fresnel formula fails to give correct results in this particular case, but that the cause for these variations is to be sought for in some other source of inaccuracy. In Table V I have given the results obtained without using the Nicol at Q; this will show the magnitude of the error which may affect results when the polarizer is not used as a ray filter. SPECTRAL PHOTOMETRIC STUDIES TABLE V. A = 670 ft.fJL A = 535 W I Observed Computed 8 Observed Computed 8 20 4.70 4.80 O.IO 4-74 4.87 -0.13 40 4.60 5-3 0.78 4.62 5-46 0.84 00 7-77 9.87 2.IO 7-79 9-95 2.16 80 34-44 39.65 -5-21 34-41 39-73 -5-32 The calculated values for the reflection of ordinary light are the same as for light polarized at an angle of 45 to the inci- dence plane. [Compare Table III.] For small angles of incidence where the polarizing effect is small, the observed and computed results agree to within 2 per cent. When the angles of incidence are large this difference rises to 1 2 per cent, and over. In a second work, which I hope to be able to carry out, I shall use the method described above to study the influence which the treatment and character of the surface have on the amount of the reflected light. In conclusion I wish to express my thanks' to the Physikalische Technischen Reichsanstalt for the opportunities granted me for carrying out the above investigations, and to the members of the institution for the many courtesies shown me, especially to Professor Lummer and Dr. Brodhun, to whom I am indebted for much valuable assistance. STANFORD UNIVERSITY, April 1897. 507H-7,'16