Geometric Evaluation of the Effect of Earths Rotation on Michelson Type Interferometers

The famous Michelson-Morley experiment used a setup of interferometer which consisted of a light source, beam splitter and mirrors, also known as Michelson interferometer. Similar Michelson-type interferometer is used to detect gravitational waves by setup used in LIGO-Hanford and LIGO-Livingston. Due to different inertial gravitational forces experienced by the two beams of light, the light in both arms should return at beam splitter at different times. This paper attempts to find the change in time of arrival and fractional fringe shift induced in Michelson-type interferometer due to the uniform rotation of the earth. It is found that the fractional fringe shift is proportional to the angular velocity of the earth, square of arm�s length and inversely proportional to the wavelength of light source and speed of light.