Question 156: Waves Optics

Question

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 :

Accepted Answer

When light is incident on the liquid at 90
o
, then from ssnells  law,
1.sin90
o
= $$\mu $$sin$$	heta $$
$$ \Rightarrow $$   sin$$	heta $$ = $${1 \over \mu }$$ . . . . . . (1)
Between liquid and glass,
$$\mu $$sin$$	heta $$ = 1.5 sin r
$$ \Rightarrow $$   $$\mu $$sin$$	heta $$ = 1.5 sin (90
o
$$-$$ $$	heta $$)
$$ \Rightarrow $$   $$\mu $$ tan$$	heta $$ = 1.5
$$ \Rightarrow $$   tan$$	heta $$ = $${{1.5} \over \mu }$$
$$ 	herefore $$   sin$$	heta $$ = $${{1.5} \over {\sqrt {{\mu ^2} + {{\left( {1.5} ight)}^2}} }}$$ . . . . . . (2)
$$ 	herefore $$    From (1) and (2) we get,
$${1 \over \mu }$$ = $${{1.5} \over {\sqrt {{\mu ^2} + {{\left( {1.5} ight)}^2}} }}$$
$$ \Rightarrow $$   $$\mu $$
2
+ (1.5)
2
= $$\mu $$
2
$$ 	imes $$ (1.5)
2
$$ \Rightarrow $$   $$\mu $$ = $${3 \over {\sqrt 5 }}$$

Answer

$$\sqrt {{5 \over 3}} $$

Answer

$${3 \over {\sqrt 5 }}$$

Answer

$${5 \over {\sqrt 3 }}$$

Answer

$${4 \over 3}$$

Waves Optics

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