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Transcript

L e c t u r e 12 | 1 Michelson-Morley Experiment Suppose that light makes a round trip ABA between two points A and B separated by distance l. The velocity of light relative to the apparatus is to the left, and to the right. The effect of earth’s motion is to delay the return of the light signal by For earth in orbit and if we take then an interval much too small to be measured directly. Rather than measure the time of transit of one light beam, Michelson observed the difference between the transit times of two beams. M2 M1 A B E Time taken by beam 1 to travel BM1B Version 3.6 L e c t u r e 12 | 2 D B B Let us say time taken by light to travel from B during this time is to be hence distance travelled by earth Solving for Thus time taken to travel to Thus time difference for two beams to reach the same spot according to ether hypothesis The interference patter produced by the two beams will thus be shifted from the position it would have occupied if the earth were stationary with respect to ether, i.e., if . However, since this no-shift postion cannot be realized( the earch cannot be stopped from orbiting). Micheson and Morley rotated the interferometer through 900. This interchanged the role of two beams, causing a Version 3.6 L e c t u r e 12 | 3 path difference in two directions. Therefore as a result of rotation, the path difference would change by . It was expected that the effect would be graphable as a sine wave with two peaks and two troughs per rotation of the device. This is because during each full rotation, each arm would be parallel to the aetherial wind twice (facing into and away from the wind giving identical readings) and perpendicular to the wind twice. Additionally, due to the Earth's rotation, the wind would be expected to show periodic changes in direction and magnitude during the course of a sidereal day. Because of the motion of the Earth around the Sun, it was expected that yearly cycles would also be detectable in the measured data. The change in the delay between the two positions readily calculated. If and the corresponding fringe shift can be is the wavelength of the illuminating light, a time delay of pattern by one fringe. Thus the time delay of will shift the pattern by will shift the fringes. Since and c are constant the only factor which can be increased to incerase is which Michelson and Moreley did by reflecting beams back and forth through eight round trips. The eintire appratus was set floating on mercury in order to avoid any jerks due to rotation . A glass slab was also introudced in order to adjust the path length of the order of wavelength. But was observed experimntally which implies =0. In this experiment Michelson and Morely increased the effective length l to 11m by reflecting the beams back and forth several times. The wavelenght of light was . Taking and we have Thus , a shift of the pattern by 0.4 of a fringe was expected. Their apparatus was so sensitive that it could detect a shift of 0.01 of a fringe. However, no fringe shift was observed on rotating the interferrometer. The experiment has since been repeated by various groups at different palaces and times. Another scientist, Miller worked on increasingly larger interferometers, culminating in one with a 32 m (effective) arm length that he tried at various sites including on top of a mountain at the Mount Wilson observatory. Version 3.6