$A$ polarizer and an analyzer are placed such that the intensity of the transmitted light is maximum. If the analyzer is rotated by $60^{\circ}$,find the intensity of the transmitted 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:

In the case of linearly polarized light,the magnitude of the electric field vector:

Unpolarized light of intensity $32 \ W m^{-2}$ passes through three polarizers such that the transmission axes of the first and second polarizers make an angle of $30^\circ$ with each other,and the transmission axis of the last polarizer is crossed with that of the first. The intensity of the final emerging light will be.......$W m^{-2}$

$A$ beam of plane polarised light of large cross-sectional area and uniform intensity of $3.3 \, W m^{-2}$ falls normally on a polariser (cross-sectional area $3 \times 10^{-4} \, m^2$) which rotates about its axis with an angular speed of $31.4 \, rad/s$. The energy of light passing through the polariser per revolution is close to ........ $\times 10^{-4} \, J$.

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam.......$^o$