Question

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 : 

(1) sin^-1(cot r)

(2) tan^-1(sin i)

(3) sin^-1(tan r')

(4) sin^-1(tan r)

Answer 1

Correct option is (4) sin^-1(tan r)
r + r’ + 90° = 180°

⇒ r’ = 90 – r = 90 – i

n₁ sin i = n₂ sin r’ = n₂ sin (90 – i)