Problem 5.194

A Kerr cell is positioned between two crossed Nicol prisms so that the direction of electric field $\mathbf{E}$ in the capacitor forms an angle of $45^{\circ}$ with the principal directions of the prisms. The capacitor has the length $l=10 \mathrm{~cm}$ and is filled up with nitrobenzene. Light of wavelength $\lambda=0.50 \mu \mathrm{m}$ passes through the system. Taking into account that in this case the Kerr constant is equal to $B$ $=2.2 \cdot 10^{-10} \mathrm{~cm} / \mathrm{V}^{2},$ find: (a) the minimum strength of electric field $E$ in the capacitor at which the intensity of light that passes through this system is independent of rotation of the rear prism; (b) how many times per second light will be interrupted when a sinusoidal voltage of frequency $v=10 \mathrm{MHz}$ and strength amplitude $E_{m}=50 \mathrm{kV} / \mathrm{cm}$ is applied to the capacitor.

Note. The Kerr constant is the coefficient $\bar{B}$ in the equation $n_{e}-$ $-n_{0}=B \lambda E^{2}$