Question 34.1: Measuring the Speed of Light with Fizeau’s Wheel Assume Fize...
Measuring the Speed of Light with Fizeau’s Wheel
Assume Fizeau’s wheel has 360 teeth and rotates at 55.0 rev/s when a pulse of light passing through opening A in Figure 34.2 passes through opening C on its return. If the distance to the mirror is 7 500 m, what is the speed of light?
Conceptualize Imagine a pulse of light passing through opening A in Figure 34.2 and reflecting from the mirror. By the time the pulse arrives back at the wheel, tooth B has passed by, and opening C has rotated into the position previously occupied by opening A.
Categorize The wheel is a rigid object rotating at constant angular speed. We model the pulse of light as a particle under constant speed.
Analyze The wheel has 360 teeth, so it must have 360 openings. Therefore, because the light passes through opening A and reflects back through the opening immediately adjacent to A, the wheel must rotate through an angular displacement of \frac{1}{360} rev in the time interval during which the light pulse makes its round trip.
From the particle under constant speed model, find the speed of the pulse of light, and use Equation 10.2 to substitute for the time interval for the pulse’s round trip:
\omega_{\text {avg }} \equiv \frac{\Delta \theta}{\Delta t} (10.2)
c=\frac{2 d}{\Delta t}=\frac{2 d \omega}{\Delta \theta}Substitute numerical values:
c=\frac{2(7 500 m)(55.0 \text{ rev} / s)}{\frac{1}{360} \text{ rev}}=2.97 \times 10^8 m/sFinalize This result is very close to the actual value of the speed of light.