A light ray is incident at an angle i on one face of a prism of refracting angle A . The ray emerges grazing the second face. Which of the following is the correct algebraic expression for the refractive index of the prism material?

Step-by-step solution

Let r₁ be the angle of refraction at the first face and c be the angle of incidence at the second face. For grazing emergence, the angle of incidence at the second face is the critical angle c , so c = 1 and c = ^2 - 1 . For a prism, r₁ + c = A r₁ = A - c . Applying Snell's law at the first face: i = r₁ i = (A - c) i = ( A c - A c) Substituting the expressions for c and c : i = ( A ^2 - 1 - A 1 ) i = A ^2 - 1 - A Rearranging to solve for : i + A = A ^2 - 1 ^2 - 1 = i + A A Squaring both sides: ^2 - 1 = ( i + A A )^