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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?
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Solution
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 \[c = \frac{\omega DN}{2\pi}\]
where
ω = angular speed
N = number of faces in the polygon mirror
\[\therefore \omega=\frac{2\pi c}{DN}\text { rad/s }\]
\[= \frac{c}{DN} \text { rev/s }\]
\[= \frac{3 \times {10}^8}{(4 . 8 \times {10}^3 \times 8)}\]
= 7.8 × 103 rev/s
Hence, the required angular speed is 7.8 × 103 rev/s.
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