Question #43122

A plane electromagnetic wave of angular frequency $\omega$ is incident from vacuum onto the flat surface of a uniaxial anisotropic crystal. The boundary is the $x$-$y$ plane ($z=0$), and the crystal occupies the region $z > 0$. The plane of incidence is the $x$-$z$ plane, and the angle of incidence is $\theta_i = 60^\circ$. The optic axis of the crystal lies along the $x$-axis. The ordinary and extraordinary refractive indices of the crystal are $n_o = \sqrt{3}$ and $n_e = 2$, respectively. If the incident wave is linearly polarized such that it excites only the extraordinary wave in the crystal, what is the angle of refraction $\theta_r$ of the ray (the direction of energy flow) with respect to the $z$-axis inside the crystal?