A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to each other. If r and r' are angles of reflection and refraction respectively, then the angle of incidence i is equal to [ ,C = critical angle ]

Step-by-step solution

Let the refractive index of the denser medium be ₁ and that of the rarer medium be ₂ . The critical angle C is given by C = ₂ ₁ . According to the law of reflection, the angle of incidence i is equal to the angle of reflection r , so i = r . It is given that the reflected and refracted rays are perpendicular to each other. From the geometry of the interface, the sum of the angle of reflection r and the angle of refraction r' is 90^ . r + r' = 90^ Since r = i , we have i + r' = 90^ , which gives r' = 90^ - i . Apply