When light of an unknown polarization is examined with a polaroid, it is found to exhibit maximum intensity $I_0$ along the $y$-axis and minimum intensity $\frac{2I_0}{3}$ along the $x$-axis. The intensity transmitted through a polaroid with pass axis at $45^{\circ}$ to the $y$-axis (in the $x$-$y$ plane) is:

Three polarising sheets are placed co-axially. The pass axes of polaroids $2$ and $3$ make angles of $30^{\circ}$ and $90^{\circ}$ respectively with the pass axis of polaroid $1$. If $I_0$ is the intensity of unpolarised light entering sheet $1$,what is the intensity of the light emerging from sheet $3$? $(\cos 30^{\circ}=\sqrt{3} / 2, \cos 90^{\circ}=0, \cos 60^{\circ}=1 / 2)$

Two polaroids $P_1$ and $P_2$ are placed with their axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. $A$ third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle $45^{\circ}$ with that of $P_1$. The intensity of transmitted light through $P_2$ is

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.

The angle between the principal planes of two Nicol prisms is $60^o$. What percentage of the incident unpolarized light will be transmitted through this system?

The figure shows a glass plate placed vertically on a horizontal table. $A$ beam of unpolarised light falls on its surface at the polarising angle of $57^\circ$ with the normal. The electric vector in the reflected light on screen $S$ will vibrate with respect to the plane of incidence in a: