$A$ plane polarized light is incident normally on a tourmaline plate. Its $\vec{E}$ vectors make an angle of $60^{\circ}$ with the optic axis of the plate. Find the percentage difference between initial and final intensities. (in $\%$)

An unpolarized light beam of intensity $I_0$ is incident on a polarizer $A$ and then passed through a second polarizer $B$. If the principal plane of polarizer $B$ makes an angle of $45^\circ$ with respect to polarizer $A$,the intensity of the emerging light will be ........

$A$ polaroid $(I)$ is placed in front of a monochromatic source. Another polaroid $(II)$ is placed in front of this polaroid $(I)$ and rotated until no light passes. $A$ third polaroid $(III)$ is now placed in between $(I)$ and $(II)$. In this case,will light emerge from $(II)$? Explain.

Unpolarised light of intensity $32 \, W m^{-2}$ passes through a combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of the first polaroid. If the intensity of the emerging light is $3 \, W m^{-2}$,then the angle between the pass axis of the first two polaroids is $............ \, ^{\circ}$.

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?

An unpolarised beam of intensity $2 a^{2}$ passes through a thin polaroid. Assuming zero absorption in the polaroid,the intensity of emergent plane polarised light is