$A$ polarizer and an analyzer are placed such that the intensity of the transmitted light is maximum. If the analyzer is rotated by $60^{\circ}$,find the intensity of the transmitted light.

The figure shows four pairs of polarizing sheets,seen face-on. Each pair is mounted in the path of initially unpolarized light. The polarizing direction of each sheet (indicated by the dashed line) is referenced to either a horizontal $x$-axis or a vertical $y$-axis. Rank the pairs according to the fraction of the initial intensity that they pass,greatest first.

The tourmaline crystal:

Two polaroids $P_1$ and $P_2$ are placed with their axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. $A$ third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle $45^{\circ}$ with that of $P_1$. The intensity of transmitted light through $P_2$ is

An unpolarised beam of intensity $2 a^{2}$ passes through a thin polaroid. Assuming zero absorption in the polaroid,the intensity of emergent plane polarised light is

Two polaroids $A$ and $B$ are placed in such a way that the pass-axes of the polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A$ and $B$, bisecting the angle between them. If the intensity of unpolarised light is $I_0$, then the intensity of the transmitted light after passing through polaroid $B$ will be: