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JEE Main 2015 · 4 Apr · Shift 1, Physics question 24

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided :

A triangular prism ABC with apex A; a ray strikes face AB at angle θ to the normal (dashed).
Choose one option
Answer and worked solution

Official answer: A

Let C be the critical angle, sin⁡C=1μ\sin C=\frac1\mu. To escape from AC the internal angle there must be r2<Cr_2<C, so the angle at AB must be r1=A−r2>A−Cr_1=A-r_2>A-C. Then
sin⁡θ=μsin⁡r1>μsin⁡(A−C),θ>sin⁡−1[μsin⁡(A−sin⁡−11μ)].\sin\theta=\mu\sin r_1>\mu\sin(A-C),\qquad\theta>\sin^{-1}\left[\mu\sin\left(A-\sin^{-1}\frac1\mu\right)\right].

Topics:Prism and dispersionTotal internal reflection
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