A ray of light passing through a prism (μ = √3) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is _____________ (in degrees).

Solution

Physics sir · 4 steps

At minimum deviation the ray goes through symmetrically, so r = A/2. Find r and double it.

1. Minimum deviation. At minimum deviation the ray inside the prism runs parallel to the base. So the refraction angles at both faces are equal, and r₁ = r₂ = r with A = 2r.
2. Use Snell's law. At the first face sin i = μ sin r. The question gives i = 2r and μ = √3.

   sin 2r = √3 sin r ⇒ 2 sin r cos r = √3 sin r ⇒ cos r = √3/2

3. Find r. sin r is not zero, so it cancels from both sides. Then cos r = √3/2 gives r = 30°, and i = 2r = 60°.
4. So. A = 2r = 2 × 30° = 60°.

The common slip: 30. Stopping at the refraction angle gives 30, not 60. The prism angle is A = 2r.

The idea to keep. Minimum deviation means symmetry: r = A/2 and i = e. Any extra condition on i and r then goes straight into Snell's law at one face.

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