Question 2 (20 points)h Mirror-1 a) The Michelson interferometer shown is illumi

Question

Question 2 (20 points)h Mirror-1 a) The Michelson interferometer shown is illuminated by a plane wave of = 600 nm. Initially, the mirrors are at equal distances to the beamsplitter. As you move Mirror-2 to the right, you record the intensity at the detector and find that the intensity goes down and up 100 times. How far was the mirror moved? moving Mirror-2 Detector b) If the intensity of the plane wave entering the interferometer is lo, what is the intensity at the detector when the mirrors are at: equal distances to the beamsplitter when mirror 2 is moved to the right by 150 nm when mirror 2 is moved to the right by 300 nm when mirror 2 is moved to the right by 600 nm

Explanation / Answer

a. when the mirror in one arm of the interferometer is moved by distance d, the fricnges move a distance 2d

now, lambda = 600*10^-9 m

now mirror 2 is moved by distance d

the fringes move by a distance of 100*lambda = 6*10^-5 m

hence

2d = 6*10^-5

d = 3*10^-5 m

b. intensity of wave entering the interferometer is Io

a. intensity at detector when the mirros are equidistance form the center

I = 2Io

b. d = 150*10^-9 m

distance moved by fringes = 2*d = 3*10^-7 m = 3*10^-7*lambda/6*10^-7 = 0.5lambda

so the interfering waves have a phase difference of 90 deg ( lambda/2)

hence intensity = 0

c. d = 300 nm

distance moved by fringes = 2*300*10^-9 = 6*10^-7 m = lambda

hence intensity = 2Io

d. d = 600 nm

distance moved by fringes = 2*600*10^-9 = 2*lambda

I = 2Io

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