Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ is:

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Question

Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ is:

A

$\frac{3}{\sqrt{5}}$

B

$\frac{5}{\sqrt{3}}$

C

$\sqrt{\frac{5}{3}}$

D

$\frac{4}{3}$

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Sin 90° = μ sin θ

$\Rightarrow sinθ = \frac{1}{μ}$

μ sin θ = 1.5 sin r

μ tan θ = 1.5

$\Rightarrow tanθ = \frac{1 .5}{μ}$

$sinθ = \frac{3}{\sqrt{9 + 4 μ^{2}}} = \frac{1}{μ}$

9μ² = 9 + 4μ²

^{$\Rightarrow μ = \frac{3}{\sqrt{5}}$}

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