Question

A ray of light travelling in a medium of refractive index $\mu$ is incident at an angle $i$ on a composite transparent plate consisting of three layers of refractive indices ${\mu }_1$, ${\mu }_2$ and ${\mu }_3$. The ray emerges from the composite plate into a medium of refractive index ${\mu }_4$ at angle $x$. Then

• A. $\sin x=\sin i$
• B. $\sin x=\frac{\mu }{{\mu }_4}\sin i$
• C. $\sin x=\frac{{\mu }_4}{\mu }\sin i$
• D. $\sin x={\mu }_4\sin i$

Answer 1

The correct option is B

$\sin x=\frac{\mu }{{\mu }_4}\sin i$

We know that $\mu \sin \theta =$ constant for a given pair of media.

So,
$\mu \sin i={\mu }_1\sin r_1={\mu }_2\sin r_2={\mu }_3\sin r_3={\mu }_4\sin x$
Thus,
$\mu \sin i={\mu }_4\sin x$
$\Rightarrow \sin x=\frac{\mu }{{\mu }_4}\sin i$

Why this question? Tips: When a number of media are arranged such that light passes through them in series, then for any pair of media $\mu \sin \theta =$ constant.