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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 :

(1) $3\over\sqrt5$ 

(2) $5\over\sqrt3$

(3) $\sqrt{5\over3}$ 

(4) $4\over3$

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Ans: (1) $3\over\sqrt5$

Sol: 

$C < i_b$

here $i_b$ is "brewester angle" and $c$ is critical angle

$\sin c < \sin i_b$

since $\tan i_b=\mu_{0_{rel}}={1.5\over\mu}$

${1\over\mu}<{1.5\over\sqrt{\mu^2+(1.5)^2}}$

$\therefore\sin i_b={1.5\over\sqrt{\mu^2+(1.5)^2}}$

$\sqrt{\mu^2\times(1.5)^2}<1.5\times\mu$

$\mu^2\times(1.5)^2<(\mu\times1.5)^2$

$\mu<{3\over\sqrt5}$

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