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Q.

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 δmin=30° (see Figure-2). The refractive index of the prism material for blue light is 3. Which of the following statement(s) is(are) correct?

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a

The blue light is polarized in the plane of incidence.

b

The angle of the prism is 45°.  

c

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

d

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

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brewstr’s angle =tan−1⁡(μ) =600
δ=i+e−A60=60+e−Ae=A1sin⁡60=3sin⁡r1⇒ r1=303sin⁡A−r1=sin⁡A3sin⁡Acos⁡30−3cos⁡Asin⁡30=sin⁡Asin⁡A2=32cos⁡A A=60∘
μ=sin⁡sin+A2sin⁡A2 μ=sin⁡30+602sin⁡602 μ=2

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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 δmin=30° (see Figure-2). The refractive index of the prism material for blue light is 3. Which of the following statement(s) is(are) correct?