Question

A monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta ={30}^o$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m\Delta n$, where $n_m$ is the refractive index of the $m^{th}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1{)}^{th}$ and $m^{th}$ slabs from the right side of the stack. What is the value of $m$?

Answer 1

Given, $\theta ={30}^0$

$n_m=n-m\Delta n$

$\Delta n=0.1$

$n=1.6$

Using Snell's Law,

$nsin\theta =n_m\sin {\theta }_r,where{\theta }_r={90}^0$

$1.6sin{30}^0=[1.6-m(0.1\left)\right]sin{90}^0$

$1.6\times \frac{1}{2}=[1.6-0.1m]\times 1$

$1.6-0.1m=0.8$

$0.1m=0.8$

$m=8$