JEE Main 2025 · 23 January · evening · Single correct · +4 / −1

The refractive index of the material of a glass prism is √3. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

  1. (a) 60°
  2. (b) 50°
  3. (c) 58°
  4. (d) 48°
Answer and solution

Answer (a) 60°

Solution

Physics sir · 4 steps

Put δₘ = A into the prism formula and the numerator becomes sin A, which simplifies neatly.

  1. Prism formula. At minimum deviation, the refractive index of a prism is related to its angle A and the minimum deviation δₘ by this formula.

    μ = sin((A+δₘ)/2)/sin(A/2)

  2. Use the condition. With δₘ = A, the numerator is sin(2A/2) = sin A = 2 sin A/2 cos A/2. Cancelling sin A/2 leaves μ = 2 cos A/2.
  3. Solve for A. 2 cos A/2 = √3 gives cos A/2 = √3/2, so A/2 = 30°.
  4. So. The angle of the prism is A = 60°, option (a).

The idea to keep. Whenever δₘ = A, the prism formula reduces to μ = 2 cos A/2. Remember this shortcut, because it comes up again and again.

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 2025.