In a Michelson experiment intended for measuring the speed of light, the total distance travelled by light between two successive reflections from the rotating mirror is 4.8 km . The rotating mirror is shaped as a regular octagon. Find the minimum non-zero angular speed of the mirror required for the image to be formed at the exact position where a stationary mirror would form it.

Step-by-step solution

The time taken by light to travel the given distance D is t = D c = 4.8 10^3 3 10^8 = 1.6 10⁻⁵ s For the image to be formed at the exact position as a stationary mirror, the regular octagonal mirror must rotate by an angle equal to the angle between its adjacent faces in time t . The angle between adjacent faces of a regular octagon is 1 8 of a revolution. The minimum non-zero angular speed f in revolutions per second is given by f = 1/8 t f = 1 8 1.6 10⁻⁵ f = 10^5 12.8 = 7812.5 rev/s