Question

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i .$ The reflected and refracted rays make an angle of $\pi / 2$ with each other. If the angles of reflection and refraction are $r$ and $r^{\prime},$ then the critical angle will be

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

Answer 1

Answer: (C)

$\sin \theta_{c}=\frac{\mu_{R}}{\mu_{D}}$. Also, Snell's law gives,
$\mu_{D} . \sin i=\mu_{R} \sin r^{\prime}$
$\Rightarrow \sin \theta_{c}=\frac{\sin i}{\sin r^{\prime}}=\frac{\sin i}{\sin (90-r)}$
As $i=x, \sin \theta_{c}=\frac{\sin i}{\cos r}=\frac{\sin i}{\cos i}= tan i $
$\theta_{c}=\sin ^{-1}(\tan i)$