A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $δ = 60 °$ (see Figure-1). The angle of minimum deviation for red light from the same prism is $δ_{\min} = 30 °$ (see Figure-2). The refractive index of the prism material for blue light is $\sqrt{3}$ . Which of the following statement(s) is(are) correct?

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The blue light is polarized in the plane of incidence.

The angle of the prism is 45°.

The refractive index of the material of the prism for red light is $\sqrt{2}$ .

The angle of refraction for blue light in air at the exit plane of the prism is 60°

answer is A, C, D.

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Detailed Solution

brewstr’s angle $= \tan^{- 1} (μ) = 60^{0}$
$\begin{array}{l} δ = i + e - A \\ 60 = 60 + e - A \\ e = A \\ 1 \sin 60 = \sqrt{3} \sin r_{1} \Rightarrow r_{1} = 30 \\ \sqrt{3} \sin (A - r_{1}) = \sin A \\ \sqrt{3} \sin Acos 30 - \sqrt{3} \cos Asin 30 = \sin A \\ \frac{\sin A}{2} = \frac{\sqrt{3}}{2} \cos A A = 60^{\circ} \end{array}$
$μ = \frac{\sin (\frac{\sin + A}{2})}{\sin \frac{A}{2}} μ = \frac{\sin (\frac{30 + 60}{2})}{\sin (\frac{60}{2})} μ = \sqrt{2}$