For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.
Options

Question

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

G1 Physics · Accepted Answer

Let the prism angle be A. Given, δ(min) = A. At minimum deviation, δ(min) = 2i-A. Therefore, A = 2i-A, so i = A. For a prism at minimum deviation, n = sin[(A+δ(min))/2]/ sin(A/2). Since δ(min) = A, n = sinA/sin(A/2) = 2cos(A/2). Also, incidence must satisfy i < 90°. Because i = A, A < 90°. Therefore, A/2 < 45°, so cos(A/2) > 1/√2. Hence, n = 2cos(A/2) > √2. Also, since cos(A/2) < 1 for a non-zero prism angle, n < 2. Therefore, √2 < n < 2. Correct option: D.