A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is √2. The angle of incidence (in degrees) is__________

Solution

Physics sir · 3 steps

At minimum deviation the ray goes through symmetrically, so the inside angle is just half the prism angle.

1. Symmetric path. At minimum deviation the ray inside the prism runs parallel to the base. The two refraction angles are then equal, r₁ = r₂ = r.
2. Find r. Since r₁ + r₂ = A, we get 2r = 60°, so r = 30°.

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

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

The common slip: 30. Stopping at the refraction angle inside the prism gives 30, not 45. You still need Snell's law at the first face to get the angle of incidence.

The idea to keep. Minimum deviation means a symmetric path: r = A/2 inside the prism. Then Snell's law at the first face gives the angle of incidence.

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