The refractive index of the material of a glass prism is $\sqrt{3}$. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Geometrical Optics

The refractive index of the material of a glass prism is

3

. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

(A) $5 0^{\circ}$
(B) $6 0^{\circ}$ ✓ Correct
(C) $5 8^{\circ}$
(D) $4 8^{\circ}$

Answer: (B)

Solution

At minimum deviation,

μ = \frac{sin ( \frac{A + δ _{min}}{2} )}{sin \frac{A}{2}}

Given

δ_{min} = A

3 = \frac{sin A}{sin \frac{A}{2}} = \frac{2 sin \frac{A}{2} cos \frac{A}{2}}{sin \frac{A}{2}} = 2 cos \frac{A}{2}

cos \frac{A}{2} = \frac{3}{2} ⟹ \frac{A}{2} = 3 0^{\circ} ⟹ A = 6 0^{\circ}

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option

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