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← JEE Advanced 2023 · Paper 1
PhysicsMultiple correct+4 / -2Question 19 of 51

JEE Advanced 2023 · Paper 1, Physics question 2

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∘\delta = 60^\circ (see Figure-1). The angle of minimum deviation for red light from the same prism is δmin⁡=30∘\delta_{\min} = 30^\circ (see Figure-2). The refractive index of the prism material for blue light is 3\sqrt3. Which of the following statement(s) is(are) correct?

Figure-1: plane polarized blue light enters a triangular prism from the left and emerges on the right, deviated by δ = 60° (angle marked between the dashed extension of the incident ray and the emergent ray). Figure-2: plane polarized red light passes through the same prism at minimum deviation δ_min = 30°; a weak reflected ray is drawn going up from the first face.
Choose one or more options
Answer and worked solution

Official answer: A, C, D

No reflected ray. No light is reflected only when light polarized in the plane of incidence strikes at Brewster's angle. (A) true.

Blue light. tan⁡i=3\tan i=\sqrt3, so i=60∘i=60^\circ. At Brewster incidence the refracted and reflected rays are perpendicular, so r1=30∘r_1=30^\circ.

Prism angle. With δ=i+e−A=60∘\delta=i+e-A=60^\circ, take A=60∘A=60^\circ:

  • r2=A−r1=30∘r_2=A-r_1=30^\circ;
  • sin⁡e=3sin⁡30∘\sin e=\sqrt3\sin30^\circ, so e=60∘e=60^\circ;
  • δ=60+60−60=60∘\delta=60+60-60=60^\circ, which checks.

So A=60∘A=60^\circ: (B) false, and the exit angle is 60∘60^\circ: (D) true.

Red light.
μr=sin⁡A+δmin⁡2sin⁡A2=sin⁡45∘sin⁡30∘=2.\mu_r=\frac{\sin\frac{A+\delta_{\min}}2}{\sin\frac A2}=\frac{\sin45^\circ}{\sin30^\circ}=\sqrt2.
(C) true.

Topics:Prism and dispersionPolarisation and Brewster's law
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