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.

In the visible region of the spectrum,the rotation of the plane of polarization is given by $\theta = a + \frac{b}{\lambda^2}$. The optical rotation produced by a particular material is found to be $30^\circ$ per mm at $\lambda = 5000 \ \mathring{A}$ and $50^\circ$ per mm at $\lambda = 4000 \ \mathring{A}$. The value of constant $a$ will be:

Three linear polarisers are placed coaxially. The transmission axis of the first polariser is at $30^{\circ}$,the second one is at $60^{\circ}$,and the third at $90^{\circ}$ to the vertical,all in the clockwise sense. Each polariser additionally absorbs $10 \%$ of the light. If a vertically polarised beam of light of intensity $I=100 \, W/m^2$ is incident on this assembly of polarisers,then the final intensity of the transmitted light will be close to ................ $W/m^2$.

$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

The tourmaline crystal: