Question

A ray of light is incident at an angle $i$ from denser to rarer medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively $r \& r^{\prime}$ then the critical angle will be:

• A. $\sin ^{-1}(\sin r)$
• B. $\sin ^{-1}\left(\tan r^{\prime}\right)$
• C. $\sin ^{-1}(\tan i)$
• D. $\sin ^{-1}(\sin i)$

Answer 1

Answer: (C)

${ }^{ D } \mu_{ R }=\frac{\sin i }{\sin r '} $
$\Rightarrow ^{ R } \mu_{ D }=\frac{\sin r '}{\sin i }$
$\frac{1}{\sin c }=\frac{\sin r '}{\sin i }$
$\sin C =\frac{\sin i }{\sin (90- r )}=\frac{\sin i }{\cos r }(\angle i =\angle r )$
$\therefore \sin C =\tan i$
$C =\sin ^{-1}(\tan i )$