For an experiment using Foucault's apparatus, the setup distances are given as follows: Distance between the rotating and the fixed mirror = 16 m , Distance between the lens and the rotating mirror = 6 m , Distance between the source and the lens = 2 m . Upon rotating the mirror at a speed of 356 revolutions per second, a shift of 0.7 mm is observed in the image. Determine the speed of light from this data.

Step-by-step solution

In Foucault's rotating mirror experiment, the shift in the image is given by the formula: s = 4 R^2 a c (R+b) where: R = distance between the rotating and fixed mirror = 16 m b = distance between the lens and the rotating mirror = 6 m a = distance between the source and the lens = 2 m = angular velocity of the rotating mirror = 2 n n = frequency of rotation = 356 rev/s s = shift in the image = 0.7 mm = 0.7 10⁻³ m c = speed of light Rearranging the formula to solve for the speed of light c : c = 4 R^2 (2 n) a s (R+b