Question

A point source $S$ is placed at the bottom of different layers as shown in Fig. the refractive index of bottommost layer is ${\mu }_0.$ The refractive index of any other upper layer is

$\mu (n)={\mu }_0-\frac{{\mu }_0}{4\pi -18}$ where $n=1,2,\dots$

A ray of light starts form the source $S$ as shown. Total internal reflection takes place at the upper surface of a layer having $n$ equal to

• A. 3
• B. 5
• C. 4
• D. 6

Answer 1

Answer: (C)

When $n=1$,
$\mu (1)={\mu }_0-\frac{{\mu }_0}{4\times 1-18}$
$\Rightarrow \mu (1)>{\mu }_0$
When $n=2$,
$\mu (2)={\mu }_0-\frac{{\mu }_0}{4\times 2-18}$
$\Rightarrow \mu (2)>{\mu }_0$
When $n=4$
$\mu (4)={\mu }_0-\frac{{\mu }_0}{4\times 4-18}$
$\Rightarrow \mu (4)>{\mu }_0$
When $n=5$
$\mu (5)={\mu }_0-\frac{{\mu }_0}{5\times 4-18}$
$\Rightarrow \mu (5)<{\mu }_0$
Clearly, the total internal reflection shall take place at the top of a layer having $n=4$.