A monochromatic ray of light is incident normally on a thin prism of refracting angle A . The ray is deviated through an angle (1 15)^ in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of (6 3)^ with the incident ray. The refractive index of the prism is

Step-by-step solution

A monochromatic ray incident normally on a thin prism of refracting angle A follows two distinct paths. Transmission path: The ray enters undeviated through the first face ( i₁ = 0 , r₁ = 0 ), then emerges from the second face with deviation ₁ = ( - 1)A = 1.15^ . Internal reflection path: After reflection at the second face, the ray emerges from the first face. Using the small-angle approximation, the deviation is ₂ = 2 A = 6.3^ . Solving the system: ( - 1)A = 1.15 2 A = 6.3 Substituting A = 1.15/( - 1) into the se