The angle between a polarizer and an analyzer is $60^o$. If light with an amplitude $A$ is incident on the polarizer,what is the amplitude of the light emerging from the analyzer?

Statement-$I$: On viewing the clear blue portion of the sky through a calcite crystal,the intensity of transmitted light varies as the crystal is rotated.
Statement-$II$: The light coming from the sky is polarized due to the scattering of sunlight by particles in the atmosphere. The scattering is largest for blue light.

Two beams,$A$ and $B$,of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity),a rotation of the polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively,then $\frac{I_A}{I_B} = $

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.

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 polaroids have their polarizing directions parallel so that the intensity of the transmitted light is maximum. The angle through which either polaroid must be turned so that the intensity of the transmitted light is dropped to one-half of the previous transmitted intensity is $.....^\circ$.