A light ray passes through a prism of apex angle A . If the angle of minimum deviation is observed to be exactly twice the apex angle, the refractive index of the material of the prism is :

Step-by-step solution

The refractive index of a prism is given by the formula: = ( A+ _m 2 ) ( A 2 ) Given that the angle of minimum deviation _m = 2A , we substitute this into the formula: = ( A+2A 2 ) ( A 2 ) = ( 3A 2 ) ( A 2 ) Using the triple angle identity (3x) = 3 x - 4 ^3 x with x = A 2 : = 3 ( A 2 ) - 4 ^3 ( A 2 ) ( A 2 ) = 3 - 4 ^2 ( A 2 ) Using the half-angle formula 2 ^2 ( A 2 ) = 1 - A , we get: = 3 - 2(1 - A) = 1 + 2 A Answer: 1 + 2 A