A light ray is incident on one face of a prism of refracting angle 60^ . The refractive index of the material of the prism is 7 3 . If the ray undergoes grazing emergence at the second face, the angle of incidence is:

Step-by-step solution

At the second face, for grazing emergence, the angle of refraction is 90^ . Thus, the angle of incidence at the second face is the critical angle c . c = 1 = 3 7 c = 1 - ^2 c = 1 - 3 7 = 2 7 For a prism, r₁ + r₂ = A . Here r₂ = c and A = 60^ . r₁ = 60^ - c Applying Snell's law at the first face: i = r₁ = (60^ - c) i = ( 60^ c - 60^ c) i = 7 3 ( 3 2 2 7 - 1 2 3 7 ) i = 7 3 ( 3 7 - 3 2 7 ) = 7 3 ( 3 2 7 ) = 1 2 Therefore, i = 30^ . Answer: 30^