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

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Consider a tank made of glass (refractive index 1.5 ) with a thick bottom. It is filled with a liquid of refractive index &#956; . 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 &#956; is:

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Correct answer: A. 3 5

For reflected light not be completely polarized, tan ⁡ r ≠ μ g μ w = 1.5 μ For minimum μ r is maximum. r is maximum when i is maximum i.e. i = 90 o ⇒ sin ⁡ r = 1 μ ⇒ tan ⁡ r = 1 μ 2 - 1 ∴ 1 μ 2 - 1 = 1.5 μ ⇒ μ 2 = 2.25 μ 2 - 1 ⇒ 1.25 μ 2 = 2.25 ⇒ μ = 2.25 1.25 = 9 5 = 3 5

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