If the refractive index of the material of a prism is cot (A/2), where A is the angle of prism then the angle of minimum deviation will be

Solution

Physics sir · 4 steps

Write cot as cos over sin, and the prism formula hands you a sine you can match directly.

1. Prism formula. At minimum deviation δₘ, the refractive index of a prism with angle A is given by the relation below.

   μ = sin((A+δₘ)/2)/sin(A/2) = cot(A/2) = cos(A/2)/sin(A/2)

2. Match the numerators. The denominators are the same, so sin((A+δₘ)/2) = cos(A/2) = sin(π/2 - A/2).
3. Solve for deviation. So (A+δₘ)/2 = π/2 - A/2. Multiply by 2 to get A + δₘ = π - A.
4. So. δₘ = π - 2A, which is option (a).

The idea to keep. When μ is given as a trig function of A, put it into μ = sin(A+δₘ)/2 / sin A/2 and use cos θ = sin(π/2-θ) to compare the angles.

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