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The refractive index of a prism with apex angle A is c o t A 2 . The angle of minimum deviation is :

Options

  1. Aδ m = 180 ° - A
  2. Bδ m = 180 ° - 3 A
  3. Cδ m = 180 ° - 4 A
  4. Dδ m = 180 ° - 2 A

Correct answer

D. δ m = 180 ° - 2 A

Step-by-step solution

As we know, μ = sin A + δ m 2 sin A 2 ⇒ cos A 2 sin A 2 = sin A + δ m 2 sin A 2 ⇒ sin π 2 - A 2 = sin A + δ m 2 ⇒ π 2 - A 2 = A 2 + δ m 2 ⇒ δ m = π - 2 A = 180 ° - 2 A

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