Michelson’s Method to Determine the Speed of Light

An American physicist Albert A. Michelson determined the speed of light for which he received a Nobel Prize in 1907.

The simplified version of his experiment is shown in the following figure.

Michelson's method to determine the speed of light

Let M1 be an octagonal steel mirror which can be rotated about a vertical axis through its centre with the help of a motor of variable speed. Light from a source S passes through a slit S1 which falls on the face 1 of the mirror M1 at an angle of 45˚. The mirror M1 reflects it to a distant concave mirror M2 at a point A. The beam is parallel to the axis of the mirror M2. Then, the mirror M2 reflects it to a plane mirror M3 which is at the focus of the mirror M2. The mirror M3 again reflects it to a point B of the mirror M2 from where it is reflected parallel to the axis of the mirror M2. If the mirror M1 is at rest, the beam falls to the face 3 and it will be reflected towards the observer who can see the image of the source through the eyepiece E.

The mirror is set into rotation with a low speed. In this case, the beam of light returning from the mirror M2 to the mirror M1 will not be incident at the angle of 45˚. As a result, the image will not enter the eyepiece. When the speed of the mirror is gradually increased and suitably adjusted, then the image will again appear in the eyepiece. This would happen when the speed of rotation is such that the adjacent face 2 of the mirror M1 is in position formerly occupied by face 1, during which light travels from the mirror M1 to mirror M2 and back to mirror M1.

Let the distance between the mirrors M1 and M2 be d, then, the time taken by the light to travel from M1 to M2 and back to M1 is,\[t=\frac{2d}{c}\text{ __(1)}\] During this time period, each mirror of octagonal is rotated through an angle θ. So, the total angle rotated by all the eight mirrors will be 8θ which will be equal to 2π i.e. \[8θ=2π\]\[θ=\frac{π}{4} \text{ __(2)}\] If f is the frequency of the rotation of the mirror, then, \[ω=\frac{θ}{t}\] \[t=\frac{θ}{ω}\] \[t=\frac{θ}{2πf} \text{ __(3)}\] From equation (2) and (3), \[t=\frac{π/4}{2πf}\] \[t=\frac{1}{8f} \text{ __(4)}\] \[\text{From (1) and (4),}\] \[\frac{2d}{c}=\frac{1}{8f}\] \[c=16fd\] This can be used to determine the speed of light. Michelson mounted the revolving mirror on Mount Wilson and placed a reflector on Mount San Antorio, 35 km away. He rotated the mirror with an air jet at 528 revolutions sec-1. He measured the frequency by comparing the rotating mirror with an electrically driven tuning fork.

Therefore, putting the value of f=528 rev/sec and d=35km=35×103m, c can be calculated. Michelson’s result for the speed of light in vacuum was 2.99910×108±50 ms-1.

Modern methods of measuring the speed of light use highly coherent and unidirectional laser beams. Because of this, the speed of light can be measured with very high degree of accuracy. The accepted value of the speed of light in free space is 2.99774×108 ms-1.

Advantages

  1. The distance (d) between two mirrors is very large (about 35 km). So, it gives an accurate measure of speed of light.
  2. The distance travelled by light and the rate of rotation of the mirror can be measured accurately.
  3. Light cannot reach the eyepiece directly from the source.
  4. It is a null deflection method so correction in the measurement of displacement is not required.
  5. The appearance of the image of the slit is abrupt which helps to determine the speed of light accurately.

Disadvantages

  1. The speed of rotation of the mirror needs to be very high which cannot be maintained for a long time.
  2. Due to the high speed rotation, the image remains in a place for a short time. So, observation has to be taken immediately.
  3. Since the mirror rotates very fast, there is a chance of the face being broken.

To remove the difficulties, Michelson used more than 8 faces of mirror and also reduced the rate of rotation.

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