Speed-of-Light Demonstration Background The set of videos linked below animates

Question

Speed-of-Light Demonstration

Background
The set of videos linked below animates experiments done by Albert Michelson, over a span of nearly 50 years, to measure the speed of light. The ball in the animations represents a flash of light. The light first reflects off one of the faces of a rotating mirror and travels to a distant stationary mirror. There it is reflected back to the rotating mirror. If the mirror is rotating at just the right speed, the light will be reflected into the detector (tube).

Play the animations in the following order:

1. Mirror rotating too slowly http://crodog.org/animate/speed%20of%20light%20slow.html
2. Mirror rotating too fast http://crodog.org/animate/speed%20of%20light%20fast.html
3. Mirror rotating just right http://crodog.org/animate/speed%20of%20light.html

For a real treat, view the 3D animation.http://crodog.org/animate/mirrorball2.html

By knowing the distance, d, to the distant stationary mirror and the rotation period, T, of the mirror, it is possible to deduce a value for the speed of light, c = 16d/T. (Here it is assumed that the 8-faced mirror makes one eight of a revolution during the round-trip (2d) of the light flash. (Other time intervals t = (nT/8), where n is an integer, are possible if the mirror rotates faster.) In Michelson

Explanation / Answer

Light flash traves 2d distance with speed c. Time for travel is

t=2d/c

In this time the rotating mirror rotates 1/8th of a turn so the period of rotation is

T=8*t= 16d/c

Frequency is just F=1/T =c/(16d) =(186282*1609.34)*60/(16*35000)= =32120.5

(above c= 186282 mile/s *1609 (m/mile) and 60 from the denumerator comes from the fact that there are 60 secons in one minute so that the final result is obtained in rpm as asked. Of course you can take speed of light as Michelson found 186285 but in this case there is an error.)

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