The refractive index of prism is μ=√3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _________°.

Solution

Physics sir · 4 steps

Put δₘ = A in the prism formula, and sin A over sin A/2 collapses to 2 cos A/2.

1. Prism formula. At minimum deviation the ray passes symmetrically through the prism. The refractive index is then linked to A and δₘ by the relation below.

   μ = sin((A+δₘ)/2)/sin(A/2)

2. Use the ratio. The ratio δₘ / A = 1 means δₘ = A. The numerator becomes sin A = 2 sin A/2 cos A/2, so 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 = 2 × 30° = 60°.

The common slip: 30. Stopping at A/2 = 30° and reporting it as the prism angle gives 30, not 60. Double it at the end.

The idea to keep. Whenever δₘ = A, the prism formula reduces to μ = 2 cos A/2. Remember this shortcut, it turns the question into one line of trigonometry.

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