Unpolarized light of intensity $32 \ W m^{-2}$ passes through three polarizers such that the transmission axes of the first and second polarizers make an angle of $30^\circ$ with each other,and the transmission axis of the last polarizer is crossed with that of the first. The intensity of the final emerging light will be.......$W m^{-2}$

Two polaroids are placed in the path of an unpolarised beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarisation axis makes an angle $\theta$ with the polarisation axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be:

When unpolarised light is passed through crossed polaroids, then light passing through the first polaroid:

An unpolarized light of intensity $I_0$ passes through a polarizer,then through a certain optically active solution,and finally through an analyzer. If the angle between the analyzer and the polarizer is $0^{\circ}$ and the intensity of light emerging from the analyzer is $\frac{3}{8} I_0$,the angle of rotation of the light by the solution with respect to the analyzer is . . . . . . degrees.

$A$ plane polarized light is incident normally on a tourmaline plate. Its $\vec{E}$ vectors make an angle of $60^{\circ}$ with the optic axis of the plate. Find the percentage difference between initial and final intensities. (in $\%$)

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 an angle of $60^{\circ}$ and $90^{\circ}$ with respect to the axis of $P_1$. The source has an intensity $I_0 = 256 \ W/m^2$. Find the intensity of light at point $O$. (in $W/m^2$)