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Question

Young's double-slit experiment is performed in a liquid. The 10th bright fringe in liquid lies where 6th dark fringe lies in vacuum. The refractive index of the liquid is , approximately,

A
1.8
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B
1.54
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C
1.67
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D
1.2
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Solution

The correct option is A 1.8
When the apparatus is immersed in a liquid, λ is reduced μ(refractive index) times.

i.e. μ=λvλl

Now, β=λDd

βvβl=λvλl=μ

βv=μ βl....(i)

Now, 6th dark band in vacuum coincides with 10th bright band in the liquid.

[β6,d]v=[β10,b]l

(2×612)βv=10 βl

From (i), we can write,

112 μ βl=10 βl

μ=2011=1.81

Hence, (A) is the correct answer.

Why this question?Since the fringe width depends on the wavelength of light, \ the fringe width decreases when the whole set up \ is put in a liquid of refractive index μ.

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