Question

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index $\mu$ is placed on the face AC of the prism. The prism is made of glass of refractive index 3/2. The limit of $\mu$ for which total internal reflection takes place on face AC is :

• A. $\mu <\frac{3\sqrt{3}}{4}$
• B. $\mu >\sqrt{\frac{5}{2}}$
• C. $\mu >\sqrt{2}$
• D. $\mu <\sqrt{3}$

Answer 1

The correct option is A $\mu <\frac{3\sqrt{3}}{4}$

Critical angle for glass-liquid :
${}_a{\mu }_{g}sinC{=}_a{\mu }_{i}sin{90}^o$
$\Rightarrow \frac{3}{2}sinC=\mu \times 1$
$\Rightarrow sinC=\frac{2\mu }{3}$
For Total Internal reflection on AC,
We must have ${60}^o\ge C$
$\Rightarrow sin{60}^o\ge sinC$
$\Rightarrow \frac{\sqrt{3}}{2}\ge \frac{2\mu }{3}$
Thus, we get $\mu \le \frac{3\sqrt{3}}{4}$