Two light sources can be adjusted to emit monochromatic light of any visible wav

Question

Two light sources can be adjusted to emit monochromatic light of any visible wavelength. The two sources are coherent, 2.04 um apart, and in line with an observer, so that one source is 2.04 um farther from the observer than the other.

a) For what visible wavelengths (380nm to 750 nm) will the observer see the brightest light, owing to constructive interference?

b) How would the answers to part a) be affected if the two sources were not in line with the observer, but still arrranged so that one source is 2.04 um further away from the observer than the other?

c)For what visible wavelengths will there be destructive interference at the location of the observer?

Explanation / Answer

a) path difference=2.05 um

==> for constructive

2.0 um=n*lambda=2000 nm

==> for n=3

lambda=2000/3=666.67 nm

for n=4

lambda=2000/4=500 nm

for n=5

lambda=2000/5=400 nm

so the costructive interferance if found for 400, 500, 666.67 nm

b) the answers will not change

c) for destructive

2.0 um=(n+0.5)*lambda=2000 nm

==> for n=3

lambda=2000/3.5=571.43 nm

for n=4

lambda=2000/4.5=444.44 nm

so the costructive interferance if found for 444.44, 571.43 nm

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