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

An unpolarized light of intensity $I_0$ passes through a polarizer, then through a certain optically active solution, and finally through an analyzer. If the angle between the analyzer and the polarizer is $0^{\circ}$ and the intensity of light emerging from the analyzer is $\frac{3}{8} I_0$, the angle of rotation of the light by the solution with respect to the analyzer is . . . . . . degrees.

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle $30^{\circ}$ with each other. What fraction of incident unpolarised light is transmitted (in $\%$)? $(\cos 30^{\circ} = \sqrt{3} / 2)$

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.

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 $\%$)?

An unpolarized light beam of intensity $I_0$ is passed through a first polaroid $A$ and then through a second polaroid $B$. If the principal plane of polaroid $B$ makes an angle of $45^{\circ}$ with that of $A$,find the intensity of the emerging light.