Now from these readings to prove that the ratio of the sines of the angles of incidence and refraction is always constant and equal to the index of refraction. In the figure, the angle of incidence equals 90° - ADB, and the angle of refraction EDF. To find these angles, subtract the reading of C from that of G, which gives GC, and dividing by two gives EG, or CE, since ABD equals DEG. In the same way, subtracting the reading of C from that of F gives CF, and subtracting CE, found above, gives FE. Dividing EG and EF by DE gives the tangents of the angles of incidence and reflection, from which these angles may be found. The ratio of their sines, or the difference of their logarithmic sines, should then be constant, and give the index of refraction. This in the case of water equals 1.33. If preferred, AB need not equal BC, but it is more convenient to have them both equal to some simple number, as 10 inches.

74. LAW OF REFRACTION. II.

Apparatus. The instrument represented in Fig. 52 may, by a slight change, be employed to prove the law of refraction. The graduated circle is mounted vertically, the needle D replaced by a narrow slit, the mirror B removed, and a test-tube attached to the index C. This test-tube is held by a strip of brass, whose top is just on a level with the centre of the circle. If, then, it is filled with water, so that the bottom of the meniscus is, just above the brass, the top of the water will be just on a level with the centre of the circle, even if the tube is inclined. To mark the direction of the ray in the liquid, two diaphragms with slits in them are placed in the tube, one at the bottom, the other in the middle. A piece of white paper, or a mirror, should be placed below to reflect light up through the tube, and the whole should be mounted on levelling-screws, and placed in a good light opposite the window.

Experiment. By the following method, the law of refraction, that the ratio of the sines of the angles of incidence and refraction is a constant, may be proved more directly than in the last experiment. Set the index C at 90°, so that the test-tube shall be vertical, and move the other index carrying the slit, to 270°. The three slits will now be in the same vertical line, and on looking through the upper one, light will be seen through the other two. If not, they must be brought into this position by moving the test-tube. Fill the latter with water until light is just visible

above the brass strip. If now the test-tube is inclined by moving its index, the other index must be moved by a larger amount to bring the three slits again apparently in line, owing to the refraction at the surface of the water. And the angles through which these indices have been moved will equal the angles of refraction and incidence, respectively. Before making the measurement, however, the line connecting the indices in their first position must be brought at right angles to the surface of the water. For this purpose turn the upper index 70° or 80°, or as far as readings can be conveniently taken, and turn the lower index until light passes through the three slits. Read its position and turn each index as much on the other side. If light is again visible through the slits, no further correction is necessary. If not, turn the levelling screws through one half the distance required to bring them apparently in line. By repeating this correction the adjustment may be made exact. Then take a number of readings of the two indices, moving the upper one a few degrees, and turning the lower one until light is visible through the slits. Subtracting from these readings 90° and 270°, gives the angles of incidence and refraction. The difference of the logarithm of their natural sines will equal the logarithm of the index of refraction.

75. INDEX OF REFRACTION.

Apparatus. The instrument devised by Wollaston to measure the index of refraction is represented in Fig. 58. A cube or rightangled prism of glass A, rests on a plate of glass in which a slight depression has been ground. The system of jointed bars BC, CE and DF, is attached to this, so that when Cis raised, F and B slide towards E. BC is exactly 10 inches long, and carries two sights through which A may be viewed. EC equals 10 inches multiplied by the index of refraction of the prism, and DC = DE = DF; hence is always vertically under C, because if a circle is described with centre D and radius DC, CFE will be a right-angle, being inscribed in a semicircle. EF is divided into inches, but the graduation need extend only from about 12 to 15 inches, if the index of refraction is 1.55. Bottles containing several liquids to be measured are also needed, as water, alcohol, turpentine and various oils, and some solids with polished surfaces, as mica, quartz, and marble.

Experiment. Place a drop of water in the hollow under the prism and raise C. On looking through the sights the spot where

E

Fig. 58.

the prism rests on the drop is at first bright, but after passing a certain position, becomes dark. The bounding line is marked by colors, and bringing it into the middle of the field of view and reading Fshould give 13.35, which divided by 10, or 1.335, is the index of refraction of water. The explanation is, that when C is low, total reflection takes place, and the spot appears bright; but when raised the light is mostly transmitted. The colored line appears at the angle of total reflection, in which case the sine of the angle of incidence equals the ratio of the indices of refraction of the two media. Call n and n' the indices of the glass and given liquid, i the angle of incidence of the ray through the sights upon the prism, r its angle of refraction, and 90° — r its angle of incidence on the reflecting surface of glass and liquid. Then ben'

ing at the angle of total reflection, sin (90° —— r) = cos r = n or n′ = n cos r, and the problem is to prove that this equals EF, calling CB, or 10 inches, equal to unity. Now sin CBE: sin CEB = CE : CB=n: 1. But CBE = i, hence CEB = i, hence CEB =r. Again, since F is vertically under C, EF = CE cos CEF = n cos r, or equals n'.

Wipe the drop of water carefully from under A, and replace it by other liquids in turn. Next measure the indices of one or more solids, by cementing them to the glass by a drop of some liquid of higher index, as balsam of tolu.

76. CHEMICAL SPECTROSCOPE.

Apparatus. A common chemical spectroscope with one prism, and a photographed scale to measure the position of the lines. Two Bunsen burners, an Argand burner, some platinum wires sealed. into the ends of glass tubes, and two stands to hold them a little lower than the slit of the spectroscope. A dozen small vials are set in a stand formed by boring holes in a block of wood, and filled with the substances to be tested. Part contain salts of sodium, lithium, strontium, calcium, barium, thallium, etc., and the remainder labelled A, B, C, etc., contain mixtures of these substances. In Fig. 59, the light enters the instrument through a slit in the end of the tube B. At the other end of this tube is a lens, whose

focus equals the length of the tube, so that the rays emerging from it are parallel, that is, the same effect is produced as if the slit were placed at an infinite distance. The width of the slit is varied by means of a screw acting against a spring, so that more or less light may be admitted. The rays next encounter the prism D, by which they are refracted, the different colors being bent unequally, and then enter the observing telescope A. A series of images of the slit are thus produced, one for each color, forming a continuous band of colored light, red at one end, and violet at the other. To measure the position of the different parts of this spectrum, a third tube, C, is employed, which carries at its outer end a fine scale photographed on glass, and the rays from it are rendered parallel by a lens, as in the case of B. C is set at such an angle that the image of the scale reflected in the face of the prism is visible through the observing telescope A, at the same time as the spectrum. To exclude the stray light, D must either be enclosed in a box, or covered with a black cloth.

Experiment. Turn B towards the window, or better, reflect a ray of sunlight through it, and nearly close the slit. A brilliant band of color becomes visible through A,

Fig. 59.

red and yellow at one end, and blue and violet at the other. Slide the eye-pieceof A in or out, until the edges are sharply marked, when fine lines will be seen at right angles to its length. These must be focussed with care, noticing that with a wide slit they disappear entirely, while with a very narrow one they are obscured by other lines at right angles to them, due to irregularities in the slit, or dust on its edges. Light the Argand burner and place it near C, drawing the scale in or out, until its image is distinctly visible through A. This adjustment is aided by closing the slit, or covering it up. Both the lines and scale. should now be distinctly visible, and the position of the former may be accurately determined by the latter. Record in this way the position of a number of the more prominent lines in the solar spectrum.

Turn the slit away from the window, so that the field of view shall be dark, and light one of the Bunsen burners, placing it opposite the slit, and three or four inches distant. Heat one of the platinum wires in it, until it ceases to color the flame. Then dip it in the vial containing soda, and place it on its stand in the

flame. On looking through A, a brilliant yellow line is visible, which, with a more powerful instrument, is seen to be double, or to consist of two fine lines very near together. This line is very characteristic, and by it an almost infinitesimal amount of soda may be detected. In fact, it shows itself in all ordinary substances. Record the position of this line, burn the wire clean, and repeat with lithia and the other substances. Most of them give several lines, which sometimes become more visible after the wire has remained in the flame for some time. Thus strontia gives a blue line, a strongly marked orange line, and six red lines, all of whose positions should be accurately recorded. To save time, it is best to use two wires, observing with one, while the other is being cleaned by heating it with the second Bunsen burner. It may sometimes be cleaned more quickly by heating it to redness, and dipping it in cold water, or by crushing the bead formed with a pair of flat-nosed pliers; but care must then be taken not to break the wire. If the salt will not adhere to the wire, the latter may be moistened with distilled water, or a loop made in its end. Having measured, and become familiar with these spectra, try some of the contents of vial A. See first if its ingredients can be recognized from its spectrum by the eye, and then measure all the lines, and compare with the measurements previously taken. The substances present may be found by the law that the spectrum of a mixture of any bodies contains all the lines they give separately.

All measurements made with a spectroscope must be reduced to some common scale, in order that they may be of real value, as the scales attached to these instruments are quite arbitrary, no two being alike. To make such a reduction, the lines measured in the solar spectrum must first be identified. The table given in Experiment No. 77, on p. 152, may be employed for this purpose. If the light used is only that of the sky, instead of sunlight, the visible spectrum will only extend from near B to G. Having identified the intermediate lines, construct points with ordinates equal to their observed position, and abscissas equal to their wavelengths. A curve is thus obtained, from which any readings of the spectroscope may be reduced to wave-lengths by inspection. Apply it to the lines of the metals measured above.