An unpolarized light beam of intensity $I_0$ is passed through a first polaroid $A$ and then through a second polaroid $B$. If the principal plane of polaroid $B$ makes an angle of $45^{\circ}$ with that of $A$,find the intensity of the emerging light.

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 $\%$)?

$A$ $20 \ cm$ length of a certain solution causes right-handed rotation of $38^{\circ}$. $A$ $30 \ cm$ length of another solution causes left-handed rotation of $24^{\circ}$. The optical rotation caused by a $30 \ cm$ length of a mixture of the above solutions in the volume ratio $1:2$ is

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.......$W m^{-2}$

In the case of linearly polarized light,the magnitude of the electric field vector:

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 $^{\circ}$)