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 $^{\circ}$)

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 ........ $\times 10^{-4} \, J$.

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?

Two linear polarisers are placed coaxially. The transmission axis of the first polariser is at $30^{\circ}$ from the vertical,while the second one is at $60^{\circ}$ from the vertical,both in the clockwise sense. If an unpolarised beam of light of intensity $I_{0}=20 \,W/m^{2}$ is incident on this pair of polarisers,then the intensities $I_{1}$ and $I_{2}$ transmitted by the first and second polarisers respectively,will be close to:

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