The following data are utilized in an experiment to measure the speed of light using Fizeau's apparatus: Distance between the mirrors = 12.0 km , Number of teeth in the wheel = 180 . Determine the minimum angular speed of the wheel such that the image is not observed.

Step-by-step solution

Time taken by light to travel to the mirror and back is t = 2D c . For the image to be completely eclipsed (not observed) at the minimum angular speed, the wheel must rotate such that the light passing through a gap is blocked by the adjacent tooth upon its return. The angle between the center of a gap and the center of the adjacent tooth is = 360^ 2N . Given N = 180 , we get = 360^ 2 180 = 1^ . The time taken by the wheel to rotate by this angle is t = . Equating the two expressions for time: 2D c = = c 2D Substit