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 $r^{\prime }$, 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. ${\tan }^{-1}(\sin i)$

Answer 1

Answer: (C)

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