Application of Interference Methods 51
passing from air into the medium in question. But if this number is identical with the ratio of the velocities, the index would evidently be determined if we knew the ratio of the wave lengths, since the wave lengths are also proportional to the velocities. This can be obtained by the interferometer. In fact, the original name of the instrument is ‘ ‘ interferential refractometer,” because it was first used for this purpose by Fresnel and Arago in 1816: This name, however, is as cumbersome as it is inappropriate, for, as we shall see, the range of usefulness of the instrument is by no means limited to this sort of measurement.
The interferometer being adjusted for white light, the colored interference fringes are thrown on the screen. If, now, the number of waves in one of the paths be altered by interposing a piece of glass, the adjustment will be disturbed and the fringes will disappear; for the difference of path thus introduced is several hundreds or thousands of waves; and, as shown in the preceding lecture, the fringes appear in white light only when the difference of path is very small.
The exact number of waves introduced can readily be
shown to be 2(n—1)|; that is, twice the product of the
index less unity by the thickness of the glass divided by the length of the light wave. Thus, if the index of the glass plate is one and one-half and its thickness one millimeter, and the wave length one-half micron, the difference in path would be two thousand waves.
Let us take, therefore, an extremely thin piece of mica, or a glass film such as may be obtained by blowing a
Light Waves and Their Uses
bubble of glass till it bursts. Covering only half the field with the film, the fringes on the corresponding side are shifted in position, as shown in Fig. 45, and the number of fringes in the shift is the number of waves in the difference of path, from which the index can be calculated by the formula.1
The interferometer is particularly well adapted for showing very slight differences in the paths of the two interfering pencils, such, for instance, as are produced by inequalities in the temperature of the air. The heat of the hand held near one of the paths is quite sufficient to cause a wavering of the fringes; and a lighted match produces contortions such as are shown in Fig. 4C>. The effect is duo to the fact that the density of the air varies with the temperature; when the air is hot its density diminishes, and with it the refractive index.
It follows that, if such an experiment were tried under proper conditions, so that the displacement of the interference fringes were regular and could be measured—which means that the temperature is uniform throughout—then the movement of the fringes would be an indication of temperature. Comparatively recently this method has been used to measure very high temperatures, such as exist in the interior of blast furnaces, etc.
In one of the preceding lectures an image of a soap film was thrown on the screen, and it was shown that the thickness of the film increased regularly from top to bottom, and that where the thickness was sufficiently small the interference fringes enable us to deduce the thickness of the
i For quantitative measurements it is necessary to employ monochromatic light. The shifting of the central band of the colored fringes in white light does not give even an approximately accurate result.