A right-angled prism (refracting angle A = 90^ ) is completely immersed in a transparent liquid of refractive index 2 . A light ray hits one face of the prism at an angle of incidence of 45^ and emerges grazing the second face. The refractive index of the prism glass is:

Step-by-step solution

Let the refractive index of the prism be _g and that of the liquid be _L = 2 . At the first face, applying Snell's law: _L i = _g r₁ At the second face, the ray grazes the surface, so the angle of refraction is 90^ and the angle of incidence is the critical angle c for the glass-liquid interface: _g c = _L 90^ c = _L _g For a prism, r₁ + c = A . Given A = 90^ , we have r₁ = 90^ - c . Therefore, r₁ = (90^ - c) = c = 1 - ^2 c = 1 - ( _L _g )^2 . Substituting this into the first Snell's law equation: _L i = _g 1 - _L^