The first factor being zero defines a " sphere "; this is the solution for " ordinary rays ", in which the effective refractive index is exactly " n o " regardless of the direction of "'k " '.
12.
In brief, conditions at the two terminii of a path generally cause dissimilar polarization shifts, dissimilar splits into ordinary rays and extraordinary or " Pedersen rays " which are erratic and impossibly identical or similar due to variations in ionization density, shifting zenith angles, effects of the earth's magnetic DIPOLE contours, antenna radiation patterns, ground conditions and other variables.
13.
The different angles of refraction for the two polarization components are shown in the figure at the top of the page, with the optic axis along the surface ( and perpendicular to the plane of incidence ), so that the angle of refraction is different for the " p " polarization ( the " ordinary ray " in this case, having its polarization perpendicular to the optic axis ) and the " s " polarization ( the " extraordinary ray " with a polarization component along the optic axis ).
