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 (see Figure-1). The angle of minimum deviation for red light from the same prism is (se

Question

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 [2023]

Smart Achievers · Accepted Answer

(1, 3, 4)

Since for blue light ray, there is no reflection from the surface of the prism, so $\tan θ_{B} = μ_{B} = \sqrt{3}$

Angle of incidence, $i = θ_{B} = 60 °$

From Snell's law,

$1 \sin 60 ° = \sqrt{3} \sin r_{1}$ $\Rightarrow 1 \times \frac{\sqrt{3}}{2} = \sqrt{3} \sin r_{1}$

$∴$ $r_{1} = 30 °$ $∵$ $r_{1} + r_{2} = A$

$δ = (i + e) - A$ $∴$ $60 ° = 60 ° + e - A$ $\Rightarrow e = A$

Again, $\sqrt{3} \sin r_{2} = 1 \sin e$

$\Rightarrow \sqrt{3} \sin (A - 30 °) = \sin A$ $\Rightarrow \sqrt{3} \sin 30 ° = \sin A$

$∴$ $\frac{\sqrt{3}}{2} = \sin A$ $∴$ $A = 60 °$

So, $e = 60 °$

For red light,

$μ = \frac{\sin (\frac{A + δ_{\min}}{2})}{\sin (\frac{A}{2})}$ $= \frac{\sin (\frac{60 ° + 30 °}{2})}{\sin (\frac{60 °}{2})}$ $= \frac{\sin 45 °}{\sin 30 °}$

$= \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \sqrt{2}$

Therefore, options (1, 3, 4) are correct.

Solution

1 The blue light is polarized in the plane of incidence.

2 The angle of the prism is $45 °$ .

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

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

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Solution

1 The blue light is polarized in the plane of incidence.

2 The angle of the prism is 45°.

3 The refractive index of the material of the prism for red light is 2.

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

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2 The angle of the prism is $45 °$ .

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

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