$A$ source of light is placed in front of a screen. The intensity of light on the screen is $I.$ Two Polaroids $P_{1}$ and $P_{2}$ are placed between the source of light and the screen such that the intensity of light on the screen is $I/2.$ By what angle (in degrees) should $P_{2}$ be rotated so that the intensity of light on the screen becomes $3I/8?$

An unpolarised light of intensity $64 \text{ Wm}^{-2}$ passes through three polarizers successively such that the transmission axis of the last polarizer is crossed with the first. The intensity of the emerging light is $6 \text{ Wm}^{-2}$. The angle between the transmission axis of the first two polarizers is

The graph showing the dependence of intensity of transmitted light on the angle between polariser and analyser is ($I_0$ is intensity of plane polarised 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:

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 $^{\circ}$)

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.