Application of Interference Methods 49
perhaps several miles; the first, after it had passed through only a few feet of wire. If the mirror in this interval had turned through a perceptible angle, the reflected light would have moved through double that angle; and, knowing the velocity of rotation of the mirror, and measuring this small angle, the velocity of electricity could be determined. Arago thought this same method might be adapted to the measurement of the velocity of light.
The principle of Arago's method may be illustrated as follows: Suppose we have a mirror R (Fig. 43), revolving in the direction of the arrows, s is a spark from a condenser, which sends light directly to the mirror R, and also to the distant mirror 31, whence it returns to R, and both rays are reflected in the direction sv If, however, the light takes an appreciable time to pass from s to M and back, this light will reach the mirror R later, and the mirror will have turned in the interval so as to reflect the light to
If the angle sxRs2 can be measured, the angle through which the mirror moves is one-half as great; and, knowing the speed of the mirror, we know also the time it takes to turn through this angle; and this is the time required for light to traverse twice the distance sM, whence the velocity of light.
The principle of Arago’s method is sound, but it would be extremely difficult to carry it into practice without an important modification, due to Foucault, which is illustrated
FIG. 43
50
Light Waves and Their Uses
in Fig. 44. Light from a source s falls on the revolving mirror R, and by means of a lens L forms an image of s at the surface of a large concave mirror JH- The light retraces its path and forms an image which coincides with s if the mirror R is at rest or is turning slowly. When the rotation is sufficiently rapid the image is formed at sx, and the displacement s*?! is readily measured.
If the distance LM is occupied by a column of water, the displacement would be less if the velocity of light is greater in water than in air, as it should be according to the corpuscular theory; and if the undulatory theory is correct, the displacement would be greater. Foucault found the displacement greater, and thus the corpuscular theory received its death-blow.
It remained for subsequent experiment to determine whether the undulatory theory was true, because it was not sufficient to show that the velocity was smaller in water; it was necessary to show that the ratio of the two velocities was equal to the index of refraction of the water, which is 1.33. Experiments showed that the ratio of the two velocities is almost identical with this number, thus furnishing an important confirmation of the undulatory theory.
Ordinarily the index of refraction is found by measuring the amount of bending which a beam of light experiences in