A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i .$ The reflected and refracted rays make an angle of $90 °$ with each other. The angle of reflection and refraction are respectively $r$ and $r^{'} .$ The critical angle is given by,

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r + r ' + 90 ° = 180 ° ⇒ r ' = 90 - r = 90 - i n 1 sin i = n 2 sin r ' = n 2 sin ( 90 - i ) n 1 sin i = n 2 cos i ⇒ tan i = n 2 n 1 Now sin C = n 2 n 1 = tan i ⇒ C = sin - 1 ( tan i ) = sin - 1 ( tan r )

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