A beam of light is reflected by a rotating mirror onto a fixed mirror which sends back to the rotating mirror from which it is reflected and then makes an angle of 3.6° with the original direction. The distance between the two mirrors is 1 km and the mirror is rotating at 750 rev/s. Calculate the velocity of light.
1 Answer
Solution
Given,
Frequency pf rotating mirror (n) = 750 rev/s,
Deviation of the beam after reflection from the rotating mirror (2θ) = 3.6°,
∴ \(\theta=3.6^\circ\)
⇒ \(\theta=\frac{3.6^\circ}2=1.8^\circ=1.8\times\frac{\mathrm\pi}{}\)
Distance between two mirrors (d) = 1 km = 1000 m
Velocity of the light (c) = ?
We have the relation for the velocity of light as
\(c=\frac{4\mathrm{πnd}}\theta\)
Or, \(c=\frac{4\pi\times750\times1000\times180}{1.8\times\mathrm\pi}\)
∴ c = 3 x 10^8 m/s
Hence, the velocity of light (c) is equal to 3 x 10^8 m/s