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.

Explain polarisation by scattering.

$A$ beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45^{\circ}$ relative to that of $A$. The intensity of emergent light is:

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

An unpolarised light of intensity $I$ is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from the second polaroid is $\frac{I}{4}$. The angle between the pass axes of the polaroids is (in $^{\circ}$)

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle $30^{\circ}$ with each other. What fraction of incident unpolarised light is transmitted (in $\%$)? $(\cos 30^{\circ} = \sqrt{3} / 2)$