JEE PYQ: Wave Optics Question 33
Question 33 - 2019 (09 Jan Shift 1)
Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $\mu$. A student finds that, irrespective of what the incident angle $i$ (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $\mu$ is:
(1) $\sqrt{\frac{5}{3}}$
(2) $\frac{3}{\sqrt{5}}$
(3) $\frac{5}{\sqrt{3}}$
(4) $\frac{4}{3}$
Show Answer
Answer: (2)
Solution
According to Brewster’s law, refractive index of material ($\mu$) is equal to tangent of polarising angle.
$\therefore \tan i_p = \mu = \frac{1.5}{\mu}$
$\frac{1}{\mu} = \frac{1.5}{\sqrt{\mu^2 + (1.5)^2}}$ $(\because \sin i_c < \sin i_p)$
$\therefore \sin i_p = \frac{1.5}{\sqrt{\mu^2 + (1.5)^2}}$
$\sqrt{\mu^2 + (1.5)^2} < 1.5 \times \mu$
$\Rightarrow \mu^2 + (1.5)^2 < (\mu \times 1.5)^2$
$\Rightarrow \mu < \frac{3}{\sqrt{5}}$ i.e. minimum value of $\mu$ should be $\frac{3}{\sqrt{5}}$.
BETA
