The refracting angle of a prism is A and refractive index of the material of the prism

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is

(a) 180⁰-3 A
(b) 180⁰-2 A
(c) 90⁰- A
(d) 180⁰+2 A

180⁰-2 A

Refractive index, μ = sin (A+Dm / 2) / sin (A/2)

cot (A / 2) = sin (A+Dm / 2) / sin (A/2)

cos (A/2) / sin (A/2) = sin (A+Dm / 2) / sin (A/2)

sin [(π/2) – (A/2)] = sin [(A + Dm) / 2]

(π / 2) – (A / 2) = (A / 2) + (Dm / 2)

Dm = π – 2A

Angle of minimum deviation, Dm = 180° – 2A

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