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Michelson-Morley Experiment

The requirement to measure the speed of light necessitates the need of reference frame or coordinate frame with respect to which we can measure the velocity. It was assumed initially that ether is present in the space through which light travels. This ether is perfectly transparent to light and the material body may pass through it without any resistance. The orbital velocity of earth is 30 km/ s with respect to ether. If ether exists, the spinning and orbital motion of the earth should be through it. An observer on the earth would sense an ‘ether wind’ whose velocity is ‘v’ relative to the earth. Hence, as ether was assumed to be at rest, it was considered possible to measure absolute velocity of light moving through it. The experimental set up used for the verification of ether medium by Michelson and Morley is described below :

 

Michelson and Morley mounted the interferometer on a massive stone slab for stability and floated the apparatus in mercury so that we can rotate the apparatus smoothly about a central pin. The light path was increased by making it travel through mirrors on the slab to reflect the beam back and forth through eight round trips. Light from a monochromatic source S after being made parallel by a collimating lens L falls on semi-silvered glass plate G inclined at 45° to the beam. It is then divided into two parts. First part, ray 1 travels towards mirror M1 and second part ray ’2′ travels towards mirror M2. Then they reflected back along their original paths meet again at the semi-silvered face of G and enter a short focus telescope T. These two ray produce interference fringes in the field of view of T. A desired path difference can be introduced between the two reflected rays by moving M1. The optical distances of M1 and M2 from G are made equal by using a compensating glass plate G’. If the apparatus is at rest, the two reflected rays would take equal time to return the glass plate G. But actually the whole apparatus is moving along with the Earth.

Let us suppose the direction of motion of earth is in the direction of the initial beam due to the motion of the earth the optical paths traversed by both the rays are not the same. The reflections at M1 and M2 do not take place at A and B, but at A’ and B’ respectively. Thus the time taken by the two rays to travel to the mirrors and back to G will be different in this case.

 

Theory: Let M1 and