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?

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.

$A$ polaroid is placed at $45^{\circ}$ to an incoming linearly polarized light of intensity $I_0$. The intensity of light passing through the polaroid after polarization will be:

Two polaroids $A$ and $B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now,another polaroid $C$ is placed between $A$ and $B$ bisecting the angle between them. If the intensity of unpolarised light is $I_0$,then the intensity of transmitted light after passing through polaroid $B$ will be:

When an unpolarized light of intensity $I_{0}$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

When a polaroid sheet is rotated between two crossed polaroids,then the transmitted light intensity will be maximum for a rotation of: (in $^{\circ}$)