Question

A point source $S$ is placed at the bottom of different layers as shown in Fig. The refractive index of the bottom-most layer is ${\mu }_0$. The refractive index of any other upper layer is $\mu \left(n\right)={\mu }_0-\frac{{\mu }_0}{4n-18}$, where $n=1,2,....$
A ray of light starts from 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

The correct option is C $4$

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