Albert A. Michaelson very carefully measured the speed of light using an alterna

Question

Albert A. Michaelson very carefully measured the speed of light using an alternative version of the technique developed by Fizeau. Light was reflected from one face of a rotating eight-sided mirror toward a stationary mirror 35.0 km away. At certain rates of rotation, the returning beam of light was directed toward the eye of an observer as shown, (a) What minimum angular speed must the rotating mirror have in order that side A will have rotated to position B, causing the light to be reflected to the eye? (b) What is the next-higher angular velocity that will enable the source of light to be seen?

Explanation / Answer

A.

the time for the light to travel to the stationary mirror back and forth will be given by

dt = 2*d/c

dt = 2*35*10^3/(3*10^8)

dt = 2.33*10^-4 sec

At the lowest angular speed the octagonal mirror will have rotated 1/8 rev in this time

Wmin = d(theta)/dt

Wmin = (1/8)rev/(2.33*10^-4 sec)

Wmin = 536 rev/sec

B.

At the next higher angular speed, the mirror will have rotated 2/8 rev in the elapsed time

w2 = 2*Wmin

w2 = 2*536 = 1072 rev/sec

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