Unpolarized light falls on two polarizing sheets placed one after another. What should be the angle between the pass axes of the sheets so that the final transmitted light has one-fourth the intensity of the incident light?

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:

When unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of light that does not pass through is:

$A$ polarized light of intensity $I_{0}$ is passed through another polarizer whose pass axis makes an angle of $60^{\circ}$ with the pass axis of the former. What is the intensity of emergent polarized light from the second polarizer?

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:

Two polaroids are placed in the path of an unpolarised beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarisation axis makes an angle $\theta$ with the polarisation axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be: