$A$ polariser is used to

When light of an unknown polarization is examined with a polaroid, it is found to exhibit maximum intensity $I_0$ along the $y$-axis and minimum intensity $\frac{2I_0}{3}$ along the $x$-axis. The intensity transmitted through a polaroid with pass axis at $45^{\circ}$ to the $y$-axis (in the $x$-$y$ plane) is:

An unpolarised light beam of intensity $2 I_{0}$ is passed through a polaroid $P$ and then through another polaroid $Q$ which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of $P$. The intensity of the emergent light is.

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

Two polaroid sheets are placed one over the other with their axes inclined to each other at $30^{\circ}$. The ratio of the intensity of the unpolarised incident light and the polarised emergent light is

Unpolarized light of intensity $I$ passes through an ideal polarizer $A$. Another identical polarizer $B$ is placed behind $A$. The intensity of light beyond $B$ is found to be $\frac{I}{2}$. Now,another identical polarizer $C$ is placed between $A$ and $B$. The intensity beyond $B$ is now found to be $\frac{I}{8}$. The angle between polarizer $A$ and $C$ is: ......$^{\circ}$