Two polarisers $P_1$ and $P_2$ are placed such that the intensity of the transmitted light is zero. $A$ third polariser $P_3$ is inserted between $P_1$ and $P_2$. If the transmitted intensity of the light passing through all three polarisers is maximum,what is the angle between the polarisers $P_2$ and $P_3$?

Explain polarisation by scattering.

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 light of an unknown polarization is examined with a polaroid, it is found to exhibit maximum intensity $I_0$ along the $y$-axis and minimum intensity $\frac{2I_0}{3}$ along the $x$-axis. The intensity transmitted through a polaroid with pass axis at $45^{\circ}$ to the $y$-axis (in the $x$-$y$ plane) is:

Four polaroids are placed such that the optic axis of each is inclined at an angle of $30^{\circ}$ with the optic axis of the preceding one. If unpolarised light of intensity $I_0$ falls on the first polaroid,the intensity of light transmitted from the fourth polaroid is $[\cos 30^{\circ} = \sqrt{3} / 2]$.

Two beams,$A$ and $B$,of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity),a rotation of the polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively,then $\frac{I_A}{I_B} = $