Thank you in advance! The interferometer uses interference effects to produce an

Question

Thank you in advance!

The interferometer uses interference effects to produce an observable change with a small change in the optical path length of one path relative to the other. Michelson and Morley also used a telescope to zoom in to observe phase shifts of only 1% of the width of a fringe. Light source Detector a In the figure above, how far would mirror 2 need to move to shift the interference Pattern by 0% o the width of inge above when use with ianto wave en nm. nm (b) If Michelson and Morley tried to measure the difference in travel times for light traveling along paths A and B, what time resolution would they need? That is, how much extra time is needed for the light to cover the distance found in part (a)? Assume the speed of light is 3.0 x 108 m/s.

Explanation / Answer

in the given design of experiment

a. let distacne moved by mirror 2 be x

then

path difference = d

d = 3L - L - 2(L - d) = 2L - 2L + 2d = 2d

now, lambda = 693 nm

also, for fixed x, fringe width , w = 2*lambda/sin(theta)

number of fringes crossing the center = n = 2*x/lambda

now, given

n = 0.01

hence

0.01 = 2x/lambda

x = 0.01*693/2 = 3.465 nm

b. for c = 3*10^8 m/s

time resolution = dt

c = x/dt

dt = x/c = 11.55*10^-18 s

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