An unpolarised light of intensity $I$ is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from the second polaroid is $\frac{I}{4}$. The angle between the pass axes of the polaroids is (in $^{\circ}$)

In a system of two crossed polarisers,it is found that the intensity of light from the second polariser is half of that from the first polariser. The angle between their pass axes is (in $^{\circ}$)

$A$ polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is $10 \%$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light,the angle by which the analyser needs to be rotated further to reduce the output intensity to zero is.....$^o$

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 $P_3$?

The figure shows four pairs of polarizing sheets,seen face-on. Each pair is mounted in the path of initially unpolarized light. The polarizing direction of each sheet (indicated by the dashed line) is referenced to either a horizontal $x$-axis or a vertical $y$-axis. Rank the pairs according to the fraction of the initial intensity that they pass,greatest first.

$A$ beam of plane polarised light of large cross-sectional area and uniform intensity of $3.3 \, W m^{-2}$ falls normally on a polariser (cross-sectional area $3 \times 10^{-4} \, m^2$) which rotates about its axis with an angular speed of $31.4 \, rad/s$. The energy of light passing through the polariser per revolution is close to ........ $\times 10^{-4} \, J$.