The transverse nature of light was confirmed by the phenomenon of

Unpolarized light of intensity $I$ is incident on a system of two polarizers,$A$ followed by $B$. The intensity of emergent light is $I/2$. If a third polarizer $C$ is placed between $A$ and $B$,the intensity of emergent light is reduced to $I/3$. The angle between the polarizers $A$ and $C$ is $\theta$. Then:

$A$ 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 Nicol prisms are inclined at an angle of $60^o$ to each other. What percentage of the incident unpolarized light passes through the system?

Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids $2$ and $3$ make $30^{\circ}$ and $90^{\circ}$ with the pass axis of polaroid sheet $1$. If $I_0$ is the intensity of the incident unpolarised light entering sheet $1$,the intensity of the emergent light through sheet $3$ is

$A$ $300 \, mm$ long tube contains $60 \, cm^3$ of a concentrated sugar solution. When placed in a polarimeter,it produces an optical rotation of $10^\circ$. If the specific rotation of sugar is $60^\circ$,calculate the amount of sugar in grams present in the tube.