A ray of light passing through a prism of refractive index 2 undergoes minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. The angle of the prism is

Question

A ray of light passing through a prism of refractive index 2 undergoes minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. The angle of the prism is, 60 °, 90 °, 75 °, 30 °

MARKS App · Accepted Answer

According to given problem, i = 2 r = A ∵ a n g l e o f p r i s m , A = 2 r Since, δ m = 2 i - A ⇒ δ m = 2 A - A = A We have, n = sin ⁡ A + δ m 2 sin ⁡ A 2 ⇒ 2 = sin ⁡ A sin ⁡ A 2 ⇒ 2 = 2 sin ⁡ A 2 cos ⁡ A 2 sin ⁡ A 2 ⇒ cos ⁡ A 2 = 2 2 ⇒ A 2 = cos - 1 ⁡ 1 2 ⇒ A 2 = 45 ° ⇒ A = 90 °

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