Two polaroids are oriented with their planes perpendicular to incident light and their transmission axes making an angle of $30^{\circ}$ with each other. What fraction of the incident unpolarised light is transmitted? (Express as a percentage)

Statement-$1$: The blue part of the sky is clearly visible through a calcite crystal. The intensity of the transmitted light changes as the crystal is rotated.
Statement-$2$: Light from the sky is due to the scattering of sunlight by particles in the atmosphere.

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of the light beam emerging from the analyzer is measured as $100 \text{ Lumens}$. Now,if the analyzer is rotated around the horizontal axis (direction of light) by $30^{\circ}$ in the clockwise direction,the intensity of the emerging light will be .......... $\text{ Lumens}$.

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 ........

$A$ $300 \, mm$ 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.

The phenomenon of polarization shows that light has ......... nature.