Question

Consider a tank made of glass(reiractive 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 :

• A. $\frac{3}{\sqrt{5}}$
• B. $\frac{5}{\sqrt{3}}$
• C. $\sqrt{\frac{5}{3}}$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$C<i_b$
here $i_b$ is "brewester angle" and c is critical angle
${\sin }_c<\sin i_b$ since $\tan i_b={\mu }_{0_{rel}}=\frac{1.5}{\mu }$
$\frac{1}{\mu }<\frac{1.5}{\sqrt{{\mu }^2+{\left(1.5\right)}^2}}\therefore \sin i_b=\frac{1.5}{\sqrt{{\mu }^2+{\left(1.5\right)}^2}}$
$\sqrt{{\mu }^2\times {\left(1.5\right)}^2}<1.5\times \mu$
${\mu }^2+{\left(1.5\right)}^2<{\left(\mu \times 1.5\right)}^2$
$\mu <\frac{3}{\sqrt{5}}$
$\text{slab}\mu =1.5$