Fizeau's Method to Determine Speed of Light

Fizeau's apparatus for measuring the speed of light in air used a light source $S$, a partially silvered glass plate $G$ tilted at $45°$ to send light out towards a rotating toothed wheel with $N$ teeth and $N$ equal-width cuts (gaps), and a distant fixed mirror $M$ placed a known distance $d$ (about 8 km) away. Light passing through one gap in the wheel travels to $M$, reflects back, and (if the wheel had not rotated in the meantime) would pass back through the same gap to reach the observer looking through $G$. As the wheel's angular speed $\omega$ was increased from zero, at some speed the returning light became completely blocked by the tooth adjacent to that gap -- the light vanished for the first time. At that instant, the wheel had rotated through the angle $\theta$ between one tooth and the next slot ($\theta=2\pi/2N=\pi/N$) in the light's round-trip travel time $t=2d/v$; combining $\omega=\theta/t$ with $v=2d/t$ gives $v=\dfrac{2d\omega N}{\pi}$. Increasing $\omega$ further, the light reappears at $2\omega$ and vanishes again at …