When a plane-polarised light is passed through an analyser and the analyser is rotated through $90^{\circ}$,the intensity of the emerging light

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:

Two polaroids $A$ and $B$ are placed perpendicularly in the path of a beam of unpolarized light. In between these two,a third polaroid $C$ is placed at an angle of $30^o$ with that of $A$. The percentage of intensity of incident unpolarized light that emerges from $B$ is ........$\%$.

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.

Unpolarized light of intensity $I$ is scattered from point $A$. What is the intensity of light perceived by the given observer?

When light is incident on a doubly refracting crystal,two refracted rays-ordinary ray ($O$-ray) and extraordinary ray ($E$-ray) are produced. Then: