Question

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

• A. $n>\frac{3\sqrt{3}}{2}$
• B. $n>\sqrt{3}$
• C. $n<\frac{3\sqrt{3}}{4}$
• D. $n<\frac{3\sqrt{3}}{8}$

Answer 1

The correct option is C $n<\frac{3\sqrt{3}}{4}$

Answer is C.

Please refer the below diagram.

Using Snell's Law:
$\frac{3/2}{n}=\frac{1}{\sin 60}$.
Therefore, $n=sin60\times \frac{3}{2}=\frac{\sqrt{3}}{2}\times \frac{3}{2}=\frac{3\sqrt{3}}{4}$.Hence, the limit of n is lesser than $\frac{3\sqrt{3}}{4}$