In the Michelson-Morley experiment, a null result, or a net fringe shift of Delt
ID: 1332755 • Letter: I
Question
In the Michelson-Morley experiment, a null result, or a net fringe shift of Delta N = 0 was obtained when the Michelson interferometer was rotated by90 degree. This implies there is no path difference between the two arms of the interferometer: i.e., Delta L = 0 . Consider the interferometer when arm AC is oriented parallel to the direction of motion [see lecture notes in Ch 1 Handout # 3], Use equations (1.8) and (1.9) without applying the binomial approximation to show that the length of arm AC, L2, has contracted and is given by L2 = L1 1 - beta 2, where beta = v/c and v is the speed of the interferometer (and Earth) through the ether.Explanation / Answer
the maximum path difference in path lengths for two light signals observed is
c (2 Lv2 / c3) = 2 L v2 / c2
but c2 = vrel2 + v2
if the interferometer arm is oriented parallel to the direction motion then
vrel = sqrt(c2 - v2)
= c sqrt(1 - (v2 / c2))