A monochromatic light is incident from air on a refracting surface of a prism of angle 75 o and refractive index n 0 = 3 . The other refracting surface of a prism is coated by a thin film of material

Question

A monochromatic light is incident from air on a refracting surface of a prism of angle $75^{o}$ and refractive index $n_{0} = \sqrt{3} .$ The other refracting surface of a prism is coated by a thin film of material of refractive index $n$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $θ \leq 60^{o} .$ The value of $n^{2}$ is_______.

TestHub · Accepted Answer

For T.I.R at coating sinc ⁡ = n 3 …(i) sin ⁡ C = n 2 n 1 Appling Snell's law at first surface sin ⁡ θ = 3 sin ⁡ 75 - c for limiting conduction, at θ = 60 o sin ⁡ 60 = 3 sin ⁡ 75 - c 3 2 = 3 sin ⁡ 75 - c 1 2 = sin ⁡ 75 - c ⇒ sin ⁡ 30 = sin ⁡ 75 - c ⇒ 30 = 75 - c ⇒ c = 45 o U s i n g i n 3 = 1 2 ⇒ n 2 = 3 2 = 1.50

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