Question

Light from a denser medium $1$ passes to a rarer medium $2 .$ When the angle of incidence is $\theta$ the partially reflected and refracted rays are mutually perpendicular. The critical angle will be

• A. $\sin ^{-1}(\cot \theta)$
• B. $\sin ^{-1}(\tan \theta)$
• C. $\sin ^{-1}(\cos \theta)$
• D. $\sin ^{-1}(\sec \theta)$

Answer 1

Answer: (B)

$\mu_{1} \sin \theta=\mu_{2} \times \sin \left(90^{\circ}-\theta\right)$
$\Rightarrow \frac{\mu_{1}}{\mu_{2}}=\tan \theta$
For $\theta_{c}$
$\Rightarrow \mu_{1} \times \sin \theta_{C}=\mu_{2} \times \sin \left(90^{\circ}\right)$
$\sin \theta_{C}=\frac{\mu_{1}}{\mu_{2}}=\tan \theta$
$\Rightarrow \theta_{C}=\sin ^{-1}(\tan \theta)$