$A$ polaroid is placed at $45^{\circ}$ to an incoming linearly polarized light of intensity $I_0$. The intensity of light passing through the polaroid after polarization will be:

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of light which does not get transmitted is

Statement-$I$: On viewing the clear blue portion of the sky through a calcite crystal,the intensity of transmitted light varies as the crystal is rotated.
Statement-$II$: The light coming from the sky is polarized due to the scattering of sunlight by particles in the atmosphere. The scattering is largest for blue light.

$A$ source of light is placed in front of a screen. The intensity of light on the screen is $I.$ Two Polaroids $P_{1}$ and $P_{2}$ are placed between the source of light and the screen such that the intensity of light on the screen is $I/2.$ By what angle (in degrees) should $P_{2}$ be rotated so that the intensity of light on the screen becomes $3I/8?$

In an experiment,two polaroids are arranged such that the intensity of the polarised light emerged from the second polaroid is $37.5 \%$ of the intensity of the unpolarised light incident on the first polaroid. Then the angle between the axes of the two polaroids is (in $^{\circ}$)

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	$(iv)$ $\cos^{-1} \left(\frac{1}{\sqrt{3}}\right)$