Question

PQR is a right angled prism with other angles as ${60}^{\circ }$ and ${30}^{\circ }$. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is

• A. 1.4
• B. 1.3
• C. 1.2
• D. 1.6

Answer 1

The correct option is B 1.3

For TIR at $PQ,\theta >C$

From geometry of figure $\theta =60i.e.60>C\Rightarrow sin\left(60\right)>sin\left(C\right)$
$\Rightarrow \frac{\sqrt{3}}{2}>\frac{{\mu }_{Liquid}}{{\mu }_{Prism}}\Rightarrow {\mu }_{Liquid}<\frac{\sqrt{3}}{2}\times {\mu }_{Prism}\Rightarrow {\mu }_{Liquid}<\frac{\sqrt{3}}{2}\times 1.5\Rightarrow {\mu }_{Liquid}<1.3$