Two polaroids $A$ and $B$ are placed perpendicularly in the path of a beam of unpolarized light. In between these two,a third polaroid $C$ is placed at an angle of $30^o$ with that of $A$. The percentage of intensity of incident unpolarized light that emerges from $B$ is ........$\%$.

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

The angle between a polarizer and an analyzer is $60^o$. If light with an amplitude $A$ is incident on the polarizer,what is the amplitude of the light emerging from the analyzer?

$A$ 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 $\%$)

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam.......$^o$

Three polaroid sheets are kept parallel to each other such that the first and the last are crossed. Unpolarised light of intensity $32 \ W m^{-2}$ falls normally on the first sheet and passes through all the polaroid sheets. If the intensity of the emerging light from the third sheet is $3 \ W m^{-2}$,then the angle between the axes of the first two polaroid sheets is: (in $^{\circ}$)