Two polaroids are kept crossed to each other. Now one of them is rotated through an angle $45^{\circ}$. The percentage of incident light now transmitted through the system is ......$\%$

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

Consider the following statements $A$ and $B$. Identify the correct choice in the given answers.
$A$. The refractive index of the extra-ordinary ray depends on the angle of incidence in double refraction.
$B$. The vibrations of light waves acquire one-sidedness for both ordinary and extraordinary rays in double refraction.

Two polaroids $A$ and $B$ are placed in such a way that the pass-axes of the polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A$ and $B$, bisecting the angle between them. If the intensity of unpolarised light is $I_0$, then the intensity of the transmitted light after passing through polaroid $B$ will be:

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

$A$ polaroid is placed at $45^{\circ}$ to an incoming linearly polarized light of intensity $I_0$. The intensity of light passing through the polaroid after polarization will be: