Question #43740

Unpolarized light is incident from a transparent solid medium of dielectric constant $K_1 = 2$ onto the flat surface of a liquid. Initially, in the absence of any external electric field, the reflected light is found to be completely plane-polarized when the angle of incidence is $\theta_0 = 60^\circ$. A uniform electric field $E = 2 \times 10^4 \text{ V/m}$ is then applied throughout the liquid. Due to the Kerr effect, the liquid remains optically isotropic but its dielectric constant shifts according to the relation $K_2(E) = K_{20} + \alpha E^2$, where $K_{20}$ is the zero-field dielectric constant and $\alpha = 5 \times 10^{-9} \text{ m}^2/\text{V}^2$. Assuming the magnetic permeability of both media is equal to $\mu_0$, what is the new angle of incidence $\theta_1$ at which the reflected light is completely plane-polarized?