A prism of refracting angle A produces an angle of minimum deviation equal to 180^ - 2A . If a light ray from inside the prism attempts to exit into the surrounding air, the critical angle for total internal reflection at the prism-air interface will be

Step-by-step solution

The refractive index of the prism is given by: = ( A + _m 2 ) ( A 2 ) Substitute _m = 180^ - 2A into the formula: = ( A + 180^ - 2A 2 ) ( A 2 ) = (90^ - A 2 ) ( A 2 ) Since (90^ - ) = , we have: = ( A 2 ) ( A 2 ) = ( A 2 ) The critical angle _c for total internal reflection is given by _c = 1 . _c = 1 ( A 2 ) = ( A 2 ) Therefore, _c = ⁻¹ ( ( A 2 ) ) . Answer: ⁻¹ ( ( A 2 ) )