Two polarizers are placed such that the angle between their transmission axes is $60^o$. If unpolarised light of intensity $I_0$ is incident on the first polarizer,then the transmitted intensity from the second polarizer will be

Unpolarised light from air is incident on the surface of a transparent medium of refractive index $1.414$ such that the reflected light is completely polarised. Match the angles given in List-$I$ with the corresponding values given in List-$II$.

$A$. Angle of reflection	$(i)$ $2 \sin^{-1} \left(\sqrt{\frac{2}{3}}\right)$
$B$. Angle of refraction	$(ii)$ $\sin^{-1} \left(\sqrt{\frac{2}{3}}\right) - \sin^{-1} \left(\frac{1}{\sqrt{3}}\right)$
$C$. Angle between incident and completely polarised light	$(iii)$ $\sin^{-1} \left(\frac{1}{\sqrt{3}}\right)$
$D$. Angle of deviation of the incident ray	$(iv)$ $\cos^{-1} \left(\frac{1}{\sqrt{3}}\right)$

Two polaroids have their polarizing directions parallel so that the intensity of the transmitted light is maximum. The angle through which either polaroid must be turned so that the intensity of the transmitted light is dropped to one-half of the previous transmitted intensity is $.....^\circ$.

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. Polarised light can be used to study the helical surface of nucleic acids.
$B$. Optical axis is a direction and not any particular line in the crystal.

The figure shows a glass plate placed vertically on a horizontal table. $A$ beam of unpolarised light falls on its surface at the polarising angle of $57^\circ$ with the normal. The electric vector in the reflected light on screen $S$ will vibrate with respect to the plane of incidence in a:

The tourmaline crystal: