For a certain prism, the angle of minimum deviation is equal to the refracting angle of the prism. If the refractive index of the material of the prism is 2 , the refracting angle of the prism (in degrees) is ______.

Step-by-step solution

The refractive index of a prism is given by: = ( A+ _m 2 ) ( A 2 ) Given that the angle of minimum deviation _m = A : = ( A+A 2 ) ( A 2 ) = A ( A 2 ) Using the double angle identity A = 2 ( A 2 ) ( A 2 ) : = 2 ( A 2 ) ( A 2 ) ( A 2 ) = 2 ( A 2 ) Given = 2 : 2 = 2 ( A 2 ) ( A 2 ) = 1 2 A 2 = 45^ A = 90^ Answer: 90