Correlative principal indices of refraction of an anisotropic crystal

The principal indices of refraction are normally assumed to be independent quantities of an anisotropic crystal. Note that the energy of an electromagnetic wave is a function of the refractive index of the medium, and consider the energy conservation in a reversible transition from an ordinary to an extraordinary wave by a total internal reflection in a right-angle prism composed of the anisotropic crystal. It is found that the principal indices of refraction are correlative properties, which is confirmed by the experimental results of material dispersion.