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.

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

$A$ polarized light of intensity $I_0$ is passed through another polarizer whose pass axis makes an angle of $60^o$ with the pass axis of the former. What is the intensity of emergent polarized light from the second polarizer?

The angle between the principal planes of two Nicol prisms is $60^o$. What percentage of the incident unpolarized light will be transmitted through this system?

Two polarisers $P_1$ and $P_2$ are placed such that the intensity of the transmitted light is zero. $A$ third polariser $P_3$ is inserted between $P_1$ and $P_2$. If the transmitted intensity of the light passing through all three polarisers is maximum,what is the angle between the polarisers $P_2$ and $P_3$?

Three polaroid sheets $P_{1}, P_{2}$ and $P_{3}$ are kept parallel to each other such that the angle between pass axes of $P_{1}$ and $P_{2}$ is $45^{\circ}$ and that between $P_{2}$ and $P_{3}$ is $45^{\circ}$. If an unpolarised beam of light of intensity $128 \ Wm^{-2}$ is incident on $P_{1}$,what is the intensity of light coming out of $P_{3}$?