Question

A light ray passes through three different mediums as shown in the ray diagram.


If $i_1<i_3$, then choose the correct option.

• A. ${\mu }_1>{\mu }_2>{\mu }_3$
• B. ${\mu }_3<{\mu }_1<{\mu }_2$
• C. ${\mu }_1<{\mu }_2<{\mu }_3$
• D. ${\mu }_3>{\mu }_2<{\mu }_1$

Answer 1

The correct option is B ${\mu }_3<{\mu }_1<{\mu }_2$


Snell's law says that

${\mu }_1\sin i={\mu }_2\sin r$

$\therefore i>r\Rightarrow {\mu }_1<{\mu }_2$

So, at interface $\text{A}$:
$i_1>i_2\Rightarrow {\mu }_1<{\mu }_2.........\left(1\right)$

At interface $\text{B}$:
$i_3>i_2\Rightarrow {\mu }_2>{\mu }_3.........\left(2\right)$

But, $i_1<i_3$ (Given)
$\Rightarrow {\mu }_1>{\mu }_3........\left(3\right)$

From eqs. (1), (2) and (3),
${\mu }_3<{\mu }_1<{\mu }_2$

Hence, option $\left(b\right)$ is correct.