Question

Let $PQR$ is a right angled prism with other angles as $60^{\circ }$ and $30^{\circ }.PQ$ has a thin layer of liquid and light falls normally on the face $PR$ 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., $60>C$
$=\sin 60>\sin C$
$=\frac{\sqrt{3}}{2}>\frac{{\mu }_{\text{liquid }}}{{\mu }_{\text{prism }}}$
$={\mu }_{\text{liquid }}<\frac{\sqrt{3}}{2}\times {\mu }_{\text{prism }}$
$={\mu }_{\text{liquid }}<\frac{\sqrt{3}}{2}\times 1.5$
$={\mu }_{\text{liquid }}<1.3$