Question

A ray of light is incident at grazing angle of incidence on one face of a prism of refracting angle A and refractive index μ . Show that angle of emergence i₂ is

\(sin^{-1}[(μ^2 - 1)^{1/2} sinA-cosA]\)

Answer 1

Fig. shows incident ray PQ grazing face AB of prism ABC. The angle of incidence i₁ at point Q is 90° . Let r₁ be the angle of refraction inside prism. Let i_C be the critical angle of incidence from prism to air. Obviously r₁ = i_C . Also

Let i₂ be angle of imergence at point R from face AC of prism. Applying Snell’s law at R