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) θ > cos ⁻¹[μsin (A+sin ⁻¹(1/μ))] (b) θ sin ⁻¹[μsin (A-sin ⁻¹(1/μ))] (d) θ < sin ⁻¹[μsin (A-sin ⁻¹(1/μ))]

Answer: (c). For emergence at AC: r₂ A - sin ⁻¹(1/μ). At AB: sin θ = μ sin r₁ > μ sin (A - sin ⁻¹1/μ). So the answer is (c) θ > sin ⁻¹[μsin (A-sin ⁻¹1/μ)].

Monochromatic light is incident on a glass prism of angle A. If the… | JEE Main 2015

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Prism, Dispersion & Scattering

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

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Answer: (c)

For emergence at $AC$ : $r_2 < C$ , where $\sin C = \dfrac{1}{\mu}$ .
Since $r_1 + r_2 = A$ : $r_1 > A - \sin^{-1}\left(\dfrac{1}{\mu}\right)$ .
At $AB$ : $\sin\theta = \mu \sin r_1 > \mu \sin\left(A - \sin^{-1}\dfrac{1}{\mu}\right)$ .
So the answer is (c) $\theta > \sin^{-1}\left[\mu\sin\left(A-\sin^{-1}\frac{1}{\mu}\right)\right]$ .

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