## Saturday, 6 September 2014

### SPEED OF LIGHT PROBLEMS

SPEED OF LIGHT

1. A wheel with 120 teeth is rotated at a uniform speed and light passing through one slot is reflected back along its own path from a mirror 20 km away. If the light is to return through the next slot, determine the speed of rotation of the wheel. (Velocity of light = 3.0 x108 ms-1)

2. In Fizeau’s rotating wheel experiment the first eclipse occurs when the angular velocity of the wheel is . Calculate the speed at which
(a) the light will be visible again
(b) the second eclipse will occur, and
(c) the third eclipse will occur.

3. A rotating mirror method was used to measure the velocity of light in a liquid.
Calculate the refractive index of the liquid using the following data:
Velocity of light in air                                    3.0x108 ms-1
Number of revolutions per second         600
Deflection of image                                       2.0 mm
Source to lens                                                   1.50 m
Lens concave mirror                                       20 m
Lens to plane mirror                                       10 cm

4. In a simple version of Foucault's apparatus for measur­ing the velocity of light the distance between the rotating mirror and the concave reflector was 1 km, the distance from the eyepiece to the rotating mirror was 5 m, the measured value of the velocity of light was 2.98x108 ms-1.
What was the speed of rotation of the mirror when the image was displaced through a distance of 20 mm?

5. In an experiment to measure the velocity of light using Michelson’s rotating eight-sided prism the distance between the prism and the distant reflector­ was 35 km.
If the speed of light is 3.0x108 ms-1, calculate the least possible speed of rotation of the prism to give a steady reflected signal at the eyepiece.
What is the next speed of rotation would give the same effect.

6. If the velocity of light in a vacuum is 3.0x108 ms-1 m calculate its velocity in:
(a) water (refractive index 1.33),
(b) glass (refractive index 1.45), and
(c) diamond (refractive index 2.42).