In Fizeau's experiment to measure the speed of light, the wheel has 475 notches and rotates with a speed of 55.0 rev/sec. Light passing through one notch travels to the mirror and back just in time to pass through the next notch. If the distance between the wheel and the mirror is 8800 m, how much time does it take the wheel to rotate from one notch to the next? A) 11.9 s B) 24.8 s C) 3.83 × 10^-5 s D) 7.44 × 10^-5 s E) 8.44 × 10^-5 s

Question

Quizplus · Accepted Answer

The time it takes for the wheel to rotate one notch is equal to the time it takes for the light to travel the distance between two neighboring notches on the wheel. 
The distance between two neighboring notches is equal to the circumference of the wheel divided by the number of notches on the wheel. 
Circumference of the wheel = 2πr, where r is the radius of the wheel. 
The distance between two neighboring notches = circumference of the wheel/475 = 2πr/475
The time it takes for light to travel this distance is given by:
time = distance/speed = (2πr/475)/(3.00 × 10^8 m/s)
We can solve for r by knowing that the time it takes for the wheel to make one revolution is equal to 1/55.0 seconds. This gives us:
2πr/55.0 = πd, where d is the distance between the wheel and the mirror (8800 m), and solving for r gives: 
r = d/1092.5 
Substituting this value of r in the equation for time, we get:
time = (2π/475)*(8800/1092.5)/(3.00 × 10^8) = 3.83 × 10^-5 s.
Therefore, the time it takes for the wheel to rotate from one notch to the next is 3.83 × 10^-5 s or 38.3 microseconds.

In Fizeau's Experiment to Measure the Speed of Light, the Wheel