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 & the angle of refraction are respectively $r$ and $r'$, then the critical angle will be

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

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} $
$\Rightarrow \sin C =\frac{\sin i}{\sin (90-r)}=\frac{\sin i}{\cos r}$
$=\frac{\sin i}{\cos i} \text { (as } \angle i=\angle r ) $
$\Rightarrow \sin C =\tan i$
$\Rightarrow C=\sin ^{-1}(\tan i) $