Question

A ray of light travelling in a medium of refractive index 2, is incident onto the flat surface of a slab, the angle of incidence is ${37}^o$. The refractive index of the material of the slab varies with depth ($x$) from the top surface, $\mu \left(X\right)=a-bx$, where $a=2,b=1m^{-1}$ and $x$ is in $m$. The maximum depth reached by the way is:

• A. $8/5m$
• B. $6/5m$
• C. $3/5m$
• D. $4/5m$
• E. $3/2m$

Answer 1

The correct option is D $4/5m$

When the ray travels from top to bottom of the slab,the refractive index of slab decreases $\left(\mu \right(x)=a-bx)$ and the ray will refract at 90° at critical angle.

By Snell's law, $2\times \sin 37°=\mu \left(x\right)\times \sin 90°$

$\mu \left(x\right)=2\times \frac{3}{5}=\frac{6}{5}$

$a-bx=\frac{6}{5}$

$2-x=\frac{6}{5}$

$x=\frac{4}{5}m$