JEE Main 2026 — Jan 21, Shift 2 — Physics solution

JEE Main2026Jan 21, Shift 2Physics

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is $2$ , the angle $θ$ of prism is.

A
60°
B
75°
C
90°
D
45°

Solution

Let the prism's apex angle be A, with base angles 45° (left) and $θ$ (right). Then $A = 180 d e g; - 45 d e g; - θ = 135 d e g; - θ$ .

The incident ray is parallel to the base and meets the left face (which makes 45° with the base), so the angle of incidence is $i_{1} = 45 d e g;$ . By Snell at the first face: $sin 45 d e g; = 2 sin r_{1}$ , giving $sin r_{1} = \frac{1}{2}$ , so $r_{1} = 30 d e g;$ .

Emergent ray grazes the second surface means $r_{2}$ equals the critical angle: $sin r_{2} = \frac{1}{2}$ , so $r_{2} = 45 d e g;$ .

Prism relation: $r_{1} + r_{2} = A$ , so $A = 75 d e g;$ . Therefore $θ = 135 d e g; - 75 d e g; = 60 d e g;$ .

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