Question

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is $\mu -m△\mu$. Here $\mu$ and $△\mu$ denote the RI of $0^{th}$ layer and the difference in RI between any two consecutive layers, respectively. The integer m = 0, 1, 2, 3..... denotes the numbers of the successive layers. A ray of light from the $0^{th}$ layer enters the $1^{st}$ layer at an angle of incidence of ${30}^o$. After undergoing the $m^{th}$ refraction, the ray emerges parallel to the interface. If $\mu =1.5$ and $△\mu =0.015$, the value of m is

• A. 20
• B. 30
• C. 40
• D. 50

Answer 1

The correct option is D 50

Given : $\mu =1.5$ $\Delta \mu =0.015$ $i={30}^o$

Let the ray emerges parallel to the interface $(r={90}^o)$ after traveling through the $m^{th}$ layer.

Using Snell's law, $\mu \sin i=(\mu -m\Delta \mu )\sin r$

$\therefore$ $1.5\times 0.5=(1.5-m\times 0.015)\times 1$ $(\because \sin {30}^o=0.5$ and $\sin {90}^o=1)$

$⟹$ $m=\frac{1.5-0.75}{0.015}=50$