What is a polarizer and an analyser?

$A$ polaroid $(I)$ is placed in front of a monochromatic source. Another polaroid $(II)$ is placed in front of this polaroid $(I)$ and rotated until no light passes. $A$ third polaroid $(III)$ is now placed in between $(I)$ and $(II)$. In this case,will light emerge from $(II)$? Explain.

Two Nicol prisms are inclined at an angle of $60^o$ to each other. What percentage of the incident unpolarized light passes through the system?

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.

An unpolarized light passes through three polarizing sheets whose polarizing directions make an angle of $30^o$,$60^o$,and $30^o$ with the $y$-axis in the same sense. What fraction of the initial intensity is transmitted by the system?

Explain Malus's law and state its mathematical expression.