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.

Answer 1

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 \[1 . 25 \times  {10}^4   \deg/\sec\]