question_answer

Let the refractive index of a denser medium with respect to a rarer medium be \[{{n}_{12}}\]and its c critical angle be \[{{\theta }_{C}}.\]At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A given by  [JEE Online 08-04-2017]

A) \[{{\tan }^{-1}}(\sin {{\theta }_{C}})\]

B) \[\frac{1}{{{\tan }^{-1}}(\sin {{\theta }_{C}})}\]

C) \[{{\cos }^{-1}}(\sin {{\theta }_{C}})\]

D) \[\frac{1}{{{\cos }^{-1}}(\sin {{\theta }_{C}})}\]

Correct Answer: A

Solution :

[a]