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?

Three identical polaroids $P_1, P_2$, and $P_3$ are placed one after another. The pass axes 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 has an intensity $I_0$. The intensity of light finally coming out 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.

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 ........$\%$.

$A$ 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 $\%$)

An unpolarized light beam of intensity $I_0$ is incident on a polarizer $A$ and then passed through a second polarizer $B$. If the principal plane of polarizer $B$ makes an angle of $45^\circ$ with respect to polarizer $A$,the intensity of the emerging light will be ........