The refractive index of prism is μ = √3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism i s _________°.
Physics · Geometrical optics · prism and thin prism
JEE Mains 2024 06 Apr Morning Shift

Question

The refractive index of prism is μ = √3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism i s _________°.

G1 Physics · Accepted Answer

Given: δ(min)/A = 1 Therefore: δ(min) = A At minimum deviation: i = e r₁ = r₂ = A/2 Also: δ(min) = 2i - A So: A = 2i - A i = A Using Snell's law: sin i = μ sin r sin A = √3 sin(A/2) Using: sin A = 2 sin(A/2) cos(A/2) we get: 2 cos(A/2) = √3 Therefore: cos(A/2) = √3/2 A/2 = 30° Hence: A = 60°