$A$ beam of natural light falls on a system of $6$ polaroids,which are arranged in succession such that each polaroid is turned through $30^\circ$ with respect to the preceding one. The percentage of incident intensity that passes through the system will be....$\%$

$A$ polarized light of intensity $I_0$ is passed through another polarizer whose pass axis makes an angle of $60^o$ with the pass axis of the former. What is the intensity of emergent polarized light from the second polarizer?

Unpolarised light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam?

The intensity of incident unpolarized light on a polaroid is $I_1$ and the intensity of emergent polarized light from this polaroid is $I_2$. The relation between $I_1$ and $I_2$ is $.......$

$A$ point source $S$ emits unpolarized light uniformly in all directions. At two points $A$ and $B$,the ratio $r = I_A / I_B$ of the intensities of light is $2$. If a set of two polaroids having $45^{\circ}$ angle between their pass-axes is placed just before point $B$,then the new value of $r$ will be.

Two nicols are crossed to each other. Now one of them is rotated through $60^{\circ}$. What percentage of incident light will pass through the system (in $\%$)?