An unpolarized beam of intensity $2a^2$ passes through a thin polaroid. Assuming zero absorption in the polaroid,the intensity of emergent plane-polarized light is

Two nicols are crossed to each other. Now one of them is rotated through $60^{\circ}$. What percentage of incident light will pass through the system (in $\%$)?

$A$ polarized light of intensity $I_{0}$ is passed through another polarizer whose pass axis makes an angle of $60^{\circ}$ with the pass axis of the former. What is the intensity of emergent polarized light from the second polarizer?

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of the light beam emerging from the analyzer is measured as $100 \text{ Lumens}$. Now,if the analyzer is rotated around the horizontal axis (direction of light) by $30^{\circ}$ in the clockwise direction,the intensity of the emerging light will be .......... $\text{ Lumens}$.

As shown in the figure,three identical polaroids $P_1$,$P_2$,and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angles of $60^{\circ}$ and $90^{\circ}$ with respect to the axis of $P_1$. The source $S$ has an intensity of $256 \text{ W/m}^2$. The intensity of light at point $O$ is $........... \text{ W/m}^2$.

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: ......$^{\circ}$