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

The minimum angular speed of the wheel is  $1.25 \times 10^{4} d e g / s$.

Explanation:

The data given in the question :  

Gap between the mirrors (D) = 12.0 km = 12 × 103 m

Teeth count in the wheel (n) = 180        

Now we're adding the Fizeau appliance ,

Speed  light , $c=3 \times 10^{8} \mathrm{m} / \mathrm{s}$

We know that,

$c=\frac{2 D n w}{\pi}$

$w=\frac{c \pi}{2 D n} r a d / s$

$w=\frac{c \pi}{2 D n} \times \frac{180}{\pi} d e g / s$

$w=\frac{3 \times 10^{8}}{2 \times 12 \times 10^{3} \times 180} \times 180 d e g / s$

$w=\frac{3 \times 10^{8}}{24 \times 10^{3}} d e g / s$

$w=\frac{10^{8}}{8 \times 10^{3}} d e g / s$

$w=\frac{10^{5}}{8} d e g / s$

$w=0.125 \times 10^{5} d e g / s$

$w=1.25 \times 10^{4} d e g / s$

Thus, the minimum angular speed of the wheel is $w=1.25 \times 10^{4} d e g / s$ .