Question

Fizeau’s method for measuring the speed of light using a rotating toothed wheel. The speed of rotation of the wheel controls what an observer sees. For example, if the light passing the opening at point A should return at the instant that tooth B had rotated into position to cover the return path, the light would not reach the observer. At a faster rate of rotation, the opening at point C could move into position to allow the reflected beam to reach the observer. Toothed Wheel Mirror A B C d Calculate the minimum angular speed of the wheel for light that passed through opening A to return through opening C to reach the observer. In an experiment to measure the speed of light using the apparatus of Fizeau, the distance between the toothed wheel and mirror was 10.72 km and the wheel had 671 notches. The experimentally determined value of c was 2.908 × 108 m/s . Answer in units of rad/s.

Answer 1

The minimum angular speed, w is 126.94 rad/s

Step-by-step explanation:

Given:

C = 2.908×10⁸ m/s

d = 10.72 km ⇒ 10.72×10³ m

There are 671 notches

⇒ Δθ =
`(2\pi)/(671)` ==> 9.359×10⁻³ rad

C = 2d / Δt ⇒ Δt = 2d/C

⇒

w = Δθ / Δt = CΔθ / 2d

substitute for given parameters

w = [2.908×10⁸×9.359×10⁻³] / [2×10.72×10³]

= 27.215972×10⁵ / 21.44×10³

= 1.2694×10²

w ⇒ 126.94 rad/s