The refractive index of a transparent liquid filled in an equilateral hollow prism is √2. The angle of minimum deviation for the liquid will be ___________ °.

Solution

Physics sir · 4 steps

Equilateral means A = 60°, so plug it into the minimum deviation formula and read off a familiar sine.

1. Prism angle. The hollow prism is equilateral, so each angle is 60°. The liquid inside takes this shape, so the prism angle is A = 60°.

   μ = sin((A + δₘ)/2)/sin(A/2)

2. Put in numbers. sin(A/2) = sin 30° = 1/2. So sin((60° + δₘ)/2) = √2 × 1/2 = 1/√2.
3. Solve the angle. sin 45° = 1/√2, so (60° + δₘ)/2 = 45°. That gives 60° + δₘ = 90°.
4. So. δₘ = 90° - 60° = 30°.

The common slip: 90. Stopping at A + δₘ = 90° and reporting that sum gives 90. Subtract the prism angle 60° to get δₘ.

The idea to keep. For any prism at minimum deviation, use μ = sin(A+δₘ)/2 / sin A/2. With A = 60°, the denominator is always 1/2, so the sine on top is just μ/2.

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