Question

Let $P Q R$ is a right angled prism with other angles as $60^{\circ}$ and $30^{\circ} . P Q$ has a thin layer of liquid and light falls normally on the face $P R$ as shown in figure. If the refractive index of prism is $1.5$, then for total internal reflection, maximum refractive index of liquid will be

• A. 1.2
• B. 1.3
• C. 1.4
• D. 1.5

Answer 1

Answer: (B)

For total internal reflection, at $PQ$
$\theta < C$
From geometry of figure,
$\theta =60$ i.e., $60 > C$
$=\sin 60 > \sin C$
$=\frac{\sqrt{3}}{2} > \frac{\mu_{\text {liquid }}}{\mu_{\text {prism }}}$
$=\mu_{\text {liquid }}<\frac{\sqrt{3}}{2} \times \mu_{\text {prism }}$
$=\mu_{\text {liquid }}<\frac{\sqrt{3}}{2} \times 1.5$
$=\mu_{\text {liquid }}<1.3$