Application of Interference Methods 53
film. It was also shown that at the top of the film, where the thickness was very small, a black band appears, its lower edge being sharply defined as though there were here a sudden change in thickness, as illustrated in Fig. 47.
Now, this “black spot” may be observed sufficiently long to measure the displacement produced in interference fringes when the film is placed in the interferometer. It is probable that over the area of the “black spot” the two surfaces of the film are as near together as possible; and if the water is made up of molecules, there are very few molecules in this thickness—possibly only two —so that a measurement of this thickness would give at least an upper limit to the distance between the molecules.
A soap solution of slightly different character from that used in the last lecture is more serviceable for this purpose.1 With such a solution the film lasts a remarkably long time. It is interesting to note that some time after the “black spot” has formed, portions of its surface reflect even less light than the rest, and these portions gradually increase in size and number till the whole surface almost entirely vanishes.
It is found on placing such a film as this in the interferometer that there is no appreciable change in the fringes. The film is so thin that we cannot observe any displacement at all; if we place two films in the interferometer, the displacement should be twice as great; but even then it is inappreciable. To obtain a measurable displacement it was found necessary to use fifty such films. The arrangement
1 This solution is made of caustic soda 1 oleic acid 7 grmM dissolved in 600 c.c. of water.
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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