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

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of the refracted beam with respect to the normal is . . . . . . . $(\tan ^{-1}(1.52)=57.7^{\circ}$, refractive indices of air and glass are $1.00$ and $1.52$, respectively) (in $^{\circ}$)

Unpolarised light is incident on the boundary between two dielectric media,whose dielectric constants are $2.8$ (medium $1$) and $6.8$ (medium $2$),respectively. To satisfy the condition that the reflected and refracted rays are perpendicular to each other,the angle of incidence should be $\tan ^{-1}\left(1+\frac{10}{\theta}\right)^{\frac{1}{2}}$. The value of $\theta$ is $.............$ (Given for dielectric media,$\mu_{r}=1$)

Light,whose electric field vectors are completely removed in the plane of incidence by using a good Polaroid,is incident on the surface of a prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

Explain the polarisation of light by reflection,state Brewster's law,and derive its formula.

$A$ solid glass sphere of refractive index $n=\sqrt{3}$ and radius $R$ contains a spherical air cavity of radius $\frac{R}{2}$,as shown in the figure. $A$ very thin glass layer is present at the point $O$ so that the air cavity (refractive index $n=1$) remains inside the glass sphere. An unpolarized,unidirectional and monochromatic light source $S$ emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point $O$ and is fully polarized,then the angle of incidence at the inner surface of the glass sphere is $\theta$. The value of $\sin \theta$ is