Question

$ACB$ is right-angled prism with other angles as ${60}^{\circ }$ and ${30}^{\circ }$. Refractive index of the prism is $1.5$. $AB$ has thin layer of liquid on it as shown. Light falls normally on the face $AC$. For total internal reflections, maximum refractive index of the 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 $\theta =60$ i.e. $60>C$

$\Rightarrow \sin 60>\sin C$

$\Rightarrow \frac{\sqrt{3}}{2}>\frac{{\mu }_{Liquid}}{{\mu }_{Prism}}\Rightarrow {\mu }_{Liquid}<\frac{\sqrt{3}}{2}\times {\mu }_{Prism}$

$\Rightarrow {\mu }_{Liquid}<\frac{\sqrt{3}}{2}\times 1.5\Rightarrow {\mu }_{Liquid}<1.3$.