48
Light Waves and Theib Uses
accomplish this we must compare the velocities of light in air and in some denser, transparent medium—say water. Now, the greatest length of a column of water which still permits enough light to pass to enable us to measure the very small quantities involved is something like thirty feet.
We should therefore have to determine the time it takes the light to pass through thirty feet of water, at the rate of 150,000 miles a second. This interval of time is of the order of one twenty-millionth of a second. But we must measure a time interval even smaller than this, for we have to distinguish between the velocity in water and the corresponding velocity in the air, /. r\, to determine the difference between two time intervals, each of which is of the order of one twenty-millionth of a second. This, at first sight, seems beyond the possibility of any physical experiment; but, notwithstanding this exceedingly small interval of time, by the combined genius of Wheatstone, Arago, Foucault, and Fizeau the problem has been successfully solved. The method proposed by Wheatstone for measuring the velocity of electricity was this: A mirror was mounted so that it could be revolved about an axis parallel to its surface at a very high rate, and the light from the spark produced by the discharge of a condenser was allowed to fall on the mirror. The images of two sparks were observed in the revolving mirror; the second spark passed after the electric current which produced it had passed through a considerable length of wire —
FIG. 42
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