When unpolarized light of intensity $I_0$ is incident on a polarizer,what will be the intensity of the light that does not pass through it?

Two polarizers are placed such that the angle between their transmission axes is $60^o$. If unpolarised light of intensity $I_0$ is incident on the first polarizer,then the transmitted intensity from the second polarizer will be

In a system of two crossed polarisers,it is found that the intensity of light from the second polariser is half of that from the first polariser. The angle between their pass axes is (in $^{\circ}$)

Light passes successively through two polarimeter tubes,each of length $0.29 \ m$. The first tube contains a dextrorotatory solution of concentration $60 \ kg/m^3$ and specific rotation $0.01 \ rad \ m^2/kg$. The second tube contains a laevorotatory solution of concentration $30 \ kg/m^3$ and specific rotation $0.02 \ rad \ m^2/kg$. The net rotation produced is.......$^\circ$.

$A$ 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.

An optically active compound: