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 1 ' are the angle of reflect

Question

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 1 ​ ' are the angle of reflection and refraction respectively and ' C ' is the critical angle, then the angle of incidence is

TestHub · Accepted Answer

Since reflected and refracted rays are perpendicular to each other, ​ r + r 1 ​ = 9 0 ∘ ∴ r 1 ​ = 9 0 ∘ − r ​ Refractive index of the denser medium ​ μ = sin r sin r 1 ​ ​ = sin r sin ( 9 0 ∘ − r ) ​ = sin r cos r ​ = cot r Also, μ = sin C 1 ​ ∴ sin C 1 ​ = cot r or sin C = tan r = tan i ∴ i = tan − 1 ( sin C ) ​

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