I am uncertain what I am suppose to be solving in this problem. Can someone expl

Question

I am uncertain what I am suppose to be solving in this problem. Can someone explain it and solve the problem?

A shift of one fringe in the Michelson-Morley experiment would result from a difference of one wavelength or a change of one period of vibration in the round-trip travel of the light when the interferometer is rotated by 90 degree. What speed would Michelson have computed for Earth's motion through the ether had the experiment seen a shift of one fringe? (The orbital speed of Earth is 29.8 km/s and the expected number of fringes in the Michelson-Morley experiment is 0.4.)

Explanation / Answer

A change of path deifference lambda causes a shift of One fringe. there fore number of fringes displaced across the cross-wire of the telescope when the whole apparatus is rotated through 90 deg. is given by

N = total path difference / wave length OR N=2d*(v^2 / (lambda*c^2))

the effective optical path d used by Michelson and morley in their experiment in 1881 was 11 metre. therefore

v= c x sqrt ( (N * lambda) / ( 2L) ) , take N= 0.4 as given in your question , L=11m , lambda = 590 nm , c = 3 x 10^8 m/s

v = 31071.76 m/s = 31.07 km/s

hope this might have helped you

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