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Question

Young's double-slit experiment is carried out with two thin sheets of thickness 10.4 μm each and refractive index μ1=1.52 and μ2=1.40, covering the slits S1 and S2 respectively. If white light of range of wavelength 400 nm to 780 nm is used, which wavelength will form maxima exactly at point O, the center of the screen?


A
12480 ˚A and 3120 ˚A
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B
4160 ˚A and 3120 ˚A
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C
6240 ˚A and 4160 ˚A
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D
12480 ˚A and 4160 ˚A
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Solution

The correct option is C 6240 ˚A and 4160 ˚A
Path difference =(μ2μ1)t=(1.521.40)×10.4×106
=1.248×106 m=12480 ˚A

Now, for maxima, the path difference should be integer multiple of λ

i.e. nλ=12480 ˚A

λ1=12480 ˚A n=1
λ2=6240 ˚A n=2
λ3=4160 ˚An=3
λ4=3120 ˚A n=4

Therefore, only 6240 ˚A and 4160 ˚A will form a maxima at point O.

Hence, (C) is the correct answer.

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