Q.Describe Fizeau's method to determine the speed of light.

Hippolyte Fizeau's 1849 apparatus was the earliest successful terrestrial measurement of the speed of light. Light from a source $S$ falls on a partially silvered glass plate $G$ tilted at $45°$, passes through a rotating toothed wheel with $N$ teeth and $N$ equal cuts, travels a known distance $d$ (about 8 km) to a distant mirror $M$, reflects back through the same region of the wheel, and is viewed by an observer through $G$. As the wheel's angular speed $\omega$ is increased from zero, the returning light is eventually completely blocked by the tooth adjacent to the cut it went out through -- the observer sees darkness for the first time. At that instant the wheel has rotated through the angle $\theta$ between one tooth and the next slot in the light's round-trip time $t=2d/v$, where $\theta=2\pi/2N=\pi/N$ (total angle divided by teeth-plus-cuts), giving $\omega=\theta/t=\pi N/t$, so $t=\pi N/\omega$. Substituting into $v=2d/t$ gives Fizeau's formula $v=\dfrac{2d\omega N}{\pi}$. Increasing $\omega$ further, the light reappears at $2\omega$ (through the next slot) and disappears again at every subsequent odd multiple of the first blocking speed. Fizeau's value was close to, though less precise than, the modern value $c=2.99792\times10^{8}\ \text{m s}^{-1}$; later, Foucault and Michelson refined the method using rotating mirrors and introduced glass, water and evacuated tubes into the light path, establishing that light travels slower in every material medium than in vacuum, and that the speed in vacuum and in air are almost indistinguishable.