Q: A ray of light from a denser medium strikes a rarer medium at an angle of incidence i (see figure). The reflected and refracted rays make an angle of 90^{o} with each other. The angles of reflection and refraction are r and r’. The critical angle is

(A) sin^{–1} (tan r)

(B) sin^{–1} (cot i)

(C) sin^{–1} (tan r’)

(D) tan^{–1} (sin i)

Ans: (A)

Sol: r + r’ = 90°

Applying snell’s Law

$\large \mu_1 sini = \mu_2 sinr’$

$\large \mu_1 sini = \mu_2 sin(90-r) $

$\large \mu_1 sini = \mu_2 cosr $

$\large \frac{\mu_2}{\mu_1} = \frac{sini}{cosr} $

$\large \frac{\mu_2}{\mu_1} = tanr $ , (since i = r)

Critical Angle , $\large sinC = \frac{\mu_2}{\mu_1} $

$\large sinC = tanr $

$\large C = sin^{-1}(tanr) $