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 \(n_{e}-\) \(-n_{0}=B \lambda E^{2}\)