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Question
In an experiment to measure the speed of light by Fizeau's apparatus, following data are used: Distance between the mirrors = 12.0 km,
Number of teeth in the wheel = 180.
Find the minimum angular speed of the wheel for which the image is not seen.
Solution
Distance between the mirrors (D) = 12.0 km = 12 × 103 m
Number of teeth in the wheel (n) = 180
Now we apply Fizeau's apparatus
Speed of light, c = 3 × 108 m/s
\[\text { We know }, c = \frac{2Dn\omega}{\pi}\]
\[ \Rightarrow \omega = \frac{c\pi}{2Dn}\text { red/s }\]
\[= \frac{\pi c}{2Dn} \times \frac{180}{\pi}\ \text { deg/s }\]
\[\omega = \frac{3 \times {10}^8}{24 \times {10}^3}\]
\[ = 1 . 25 \times {10}^4 \deg/\sec\]
Hence, the required angular speed of the wheel for which the image is not seen is \[1 . 25 \times {10}^4 \deg/\sec\]
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