The refractive index of an equilateral prism is √2. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

Solution

Physics sir · 3 steps

At minimum deviation the ray passes symmetrically, so each refraction angle is half the prism angle.

1. Symmetric passage. At minimum deviation the ray inside the prism runs parallel to the base. So r₁ = r₂ = r and i = e. Since r₁ + r₂ = A, we get r = A/2.
2. Angle inside. An equilateral prism has A = 60°, so r = 30°.

   sin e = μ sin r = √2 × sin 30° = √2 × 1/2 = 1/√2

3. So. sin e = 1/√2 gives e = 45°. The angle of emergence is 45.

The common slip: 30. Reporting the angle of refraction inside the prism, or the minimum deviation δₘ = 2e - A, both give 30, not the angle of emergence.

The idea to keep. Minimum deviation means symmetry: r = A/2 and i = e. Find r from the prism angle first, then use Snell's law once to get i or e.

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