Question

In a Michelson experiment for measuring speed of light, the distance travelled by light between two reflections from the rotating mirror is 4.8 km. The rotating mirror has a shape of a regular octagon. At what minimum angular speed of the mirror (other than zero) the image is formed at the position where a nonrotating mirror forms it?

Answer 1

Distance travelled by light between two reflections from the rotating mirror (D) = 4.8 km = 4.8 × 10³ m
Number of faces of the mirror, N = 8
Angular speed of the mirror, $\omega$ = ?

In Michelson experiment, the speed of light (c) is given by
$c=\frac{\omega DN}{2\mathrm{\pi }}$
where
ω = angular speed
N = number of faces in the polygon mirror

$\therefore \omega =\frac{2\mathrm{\pi }c}{DN}rad/\mathrm{s}$
$=\frac{c}{DN}\mathrm{rev}/\mathrm{s}$
$=\frac{3\times {10}^8}{(4.8\times {10}^3\times 8)}$
= 7.8 × 10³ rev/s
Hence, the required angular speed is 7.8 × 10³ rev/s.