JEE Main 2022 · 28 June · morning · Single correct · +4 / −1

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

  1. (a) 180 - 2A
  2. (b) 90 - A
  3. (c) 180 + 2A
  4. (d) 180 - 3A
Answer and solution

Answer (a) 180 - 2A

Solution

Physics sir · 4 steps

Write cot as cos over sin, and the prism formula turns into one sine equals another sine.

  1. Prism formula. At minimum deviation δₘ, the refractive index of a prism with refracting angle A is given by the relation below.

    μ = sin((A+δₘ)/2)/sin(A/2) = cot A/2 = cos(A/2)/sin(A/2)

  2. Cancel the denominator. Both sides have sin A/2 underneath, so sin((A+δₘ)/2) = cos A/2 = sin(90° - A/2).
  3. Compare the angles. So (A+δₘ)/2 = 90° - A/2. Multiply by 2 to get A + δₘ = 180° - A.
  4. So. δₘ = 180° - 2A, which is option (a).

The idea to keep. When μ is given as a trig function of A, put it into μ = sin(A+δₘ)/2 / sin A/2 and use cos θ = sin(90° - θ) to compare the angles.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 200 times in JEE Main since 2020. This question is from 2022.