For light of intensity $I_0$,a polaroid is placed at an angle of $45^\circ$. What will be the intensity of the light passing through the polaroid after polarization?

$A$ beam of unpolarized light passes through a tourmaline crystal $A$ and then it passes through a second tourmaline crystal $B$ oriented so that its principal plane is parallel to that of $A$. The intensity of emergent light is $I_0$. Now $B$ is rotated by $45^{\circ}$ about the ray. The emergent light will have intensity $(\cos 45^{\circ} = \frac{1}{\sqrt{2}})$.

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.

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.

Polarised glass is used in sunglasses because

$A$ beam of light of intensity $I_0$ falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through $60^{\circ}$ with respect to the preceding one. The fraction of the incident light intensity that passes through the system is $\left(\cos 60^{\circ} = 1/2\right)$.