Two polaroids are oriented with their planes perpendicular to incident light and their transmission axes making an angle of $30^{\circ}$ with each other. What fraction of the incident unpolarised light is transmitted? (Express as a percentage)

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:

Longitudinal waves cannot

If a polaroid is kept in the path of uniformly unpolarised light,the ratio of the intensity of the transmitted light to the intensity of the light when the polaroid was not kept in its path is:

The intensity of incident unpolarized light on a polaroid is $I_1$ and the intensity of emergent polarized light from this polaroid is $I_2$. The relation between $I_1$ and $I_2$ is $.......$

$A$ plane polarized light is incident on a polarizer with its pass axis making an angle $\theta$ with the $x-$axis,as shown in the figure. At four different values of $\theta$,namely $\theta = 8^o, 38^o, 188^o$ and $218^o$,the observed intensities are the same. What is the angle between the direction of polarization and the $x-$axis in degrees?