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 ........

An unpolarised light beam of intensity $2 I_{0}$ is passed through a polaroid $P$ and then through another polaroid $Q$ which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of $P$. The intensity of the emergent light is.

Unpolarized light falls on two polarizing sheets placed one after another. What should be the angle between the pass axes of the sheets so that the final transmitted light has one-fourth the intensity of the incident light?

$A$ light beam has an amplitude $A$,and the angle between the analyser and the polariser is $60^o$. What is the amplitude of the light reflected by the analyser?

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 $60^{\circ}$ and $90^{\circ}$ with respect to the axis of $P_1$. The source has an intensity $I_0$. What is the intensity of transmitted light through $P_3$? $\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$

$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see: