# Relativity Series-3: Michelson-Morley Experiment – Set Up and Results

Michelson interferometer, as it is famously called, is used in the Michelson-Morley experiment. Earth moves around the sun at a speed of around 108000 km/h so when a light beam is shone along the direction of this motion the light beam should take more time to travel certain distance compared to the one shone perpendicular to the direction of this motion. This time difference can be captured in the interference pattern formed from the two light beams.

The setup of Michelson-Morley experiment includes a light source, which emits radiation. The emitted radiation travels and reaches a beam splitter. A half-silvered mirror is used as a beam splitter. The light beam is now split into two beams. These two beams are initially coherent and have no phase difference. Each of these beams travel a length of L units towards a mirror which then reflects them back. The reflected beams interference at the point of meeting and the interference pattern can be observed at the detector.

In the experiment conducted, the two beams travel perpendicular to each other; one along the direction of motion of earth and the other perpendicular to the motion of earth. Each of these beams travels a distance of 2L before undergoing interference. Since earth is moving at a velocity ‘v’ (=108000 km/h), the beam travelling along the direction of earth should take longer to travel 2L distance. As described in the previous essay, if the time taken for each of the beams to travel these distances is different, then there is a phase difference between the beams. As we have learnt during our JC Physics tuition classes, this would result in an interference pattern. This interference pattern changes when the speed of earth is not taken into account and there is a shift in the interference fringes formed. Speed of earth does not play a role when the speed of light remains unaltered for a moving observer and an observer at rest.

Michelson and Morley observed that the fringes observed resemble the ones that are to be observed when speed of earth is not taken into account. Thus the experiment proves that the speed of light is constant irrespective of the motion of observer. Note that the speed of light depends on the medium and 3 x 10m/s is the velocity in vacuum. Michelson-Morley repeated the experiment at different locations on earth with different levels of sophistication and sensitivity only to observe that there is no change in the conclusion drawn. Einstein based his theory of relativity on this observation.