54
Light Waves and Their Uses
of the interferometer for this experiment1 is shown in Fig. 48. The films are introduced in the path AC, as indicated at
F. Yet even fifty films produced a displacement of only about half a fringe, as shown in Fig. 49. Since the light passed through each film twice, this displacement of half a fringe is what would be produced by a single passage through one hundred films. One film would therefore produce a displacement of one two-hundredths of a fringe. A simple calculation tells us that the corresponding distance between the water molecules is not greater than six millionths of a millimeter. It may be much less than this.
^The interferometer is especially useful whenever it is necessary to measure small changes in distance or angle. One rather important instance of such a measure is that of coefficient expansion. Most bodies expand with heat—certainly a very small quantity: one or two parts in ten thousand for a change of temperature of a single degree.
In some cases it may be necessary to experiment upon a very small specimen of the material in question, and in such cases the whole change to be measured may be of the order of a ten-thousandth part of an inch — IE. S. Jouonnott, Phil. Mag. (5), Vol. XLVII (1890), p. 301.
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FIG. 49
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immminmiilill!■ m«LirJC
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Application of Interference Methods 55
a quantity requiring a good microscope to perceive; but such a quantity is very readily measured by the interferometer. It means a displacement amounting to several fringes, and this displacement may be measured to within a fiftieth of a fringe or less; so that the whole displacement may be measured to within a fraction of 1 per cent. Of course, with long bars the attainable degree of accuracy is far greater.
Figs. 50 and 51 represent a piece of apparatus designed by Professors Morley and Rogers,1 based on this principle, b and c (Fig.
50) are the two plane-parallel plates of the interferometer, and the two mirrors are at a and a'. Each mirror is divided into two halves as at an, so that a motion of each end of the bar to be tested can be observed. The jackets gg serve to keep the bars at any desired temperatures. One side of the instrument, as aa, being kept at a constant temperature, a change in the temperature of a'a' will cause the fringes to move, and from this motion of the fringes the change in length, which is caused by the change in temperature, can be very accurately determined. Fig. 51 shows a perspective view of the apparatus.
Evidently the same kind of instrument is suitable for experiments in elasticity, and one of these was shown in the last lecture, where a steel axle was twisted (c/. Figs. 30 and
i Morley and Rogers, Physical Review, Vol. IV (1896), pp. 1,100.