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
$$\begin{gathered} \mathrm{We}\mathrm{know},c=\frac{2Dn\omega }{\mathrm{\pi }} \\ \Rightarrow \omega =\frac{c\pi }{2Dn}\mathrm{red}/\mathrm{s} \end{gathered}$$

$=\frac{\pi c}{2\mathrm{D}n}\times \frac{180}{\pi }\mathrm{deg}/\mathrm{s}$
$$\begin{gathered} \omega =\frac{3\times {10}^8}{24\times {10}^3} \\ =1.25\times {10}^4\mathrm{deg}/\sec \end{gathered}$$

Hence, the required angular speed of the wheel for which the image is not seen is $1.25\times {10}^4\mathrm{deg}/\sec$