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 90o 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) $