Question

For an angle of incidence of ${45}^0$ at the top surface of a glass slab as shown in the figure, What is the maximum refractive index of glass for total internal reflection to take place? [For water $\mu =\frac{4}{3}$]

• A. $\frac{4}{3\sqrt{2}}$
• B. $\frac{4\sqrt{2}}{3}$
• C. $\frac{3}{4\sqrt{2}}$
• D. $\frac{3\sqrt{2}}{4}$

Answer 1

The correct option is B $\frac{4\sqrt{2}}{3}$

Conditions for TIR
1. Light should be travelling from a denser to a rarer medium.
2. Angle of incidence should be greater than the critical angle.

By applying Snell's law
$n_{1}Sini=n_{2}Sinr$
$nSin{45}^0=\frac{4}{3}\times Sin{90}^0$
$n\times \frac{1}{\sqrt{2}}=\frac{4}{3}\times 1$
$n=\frac{4\sqrt{2}}{3}$