The velocity at which a monochromatic plane wave front propagates along its normal direction is called the phase velocity of the wave. The speed at which light wave energy travels is called ray velocity. The direction in which the light travels as observed by the human eye is the direction in which the light travels.

For non-magnetic single crystal, the phase velocity of planar light wave is perpendicular to the direction of electric displacement D and magnetic field intensity H, while the energy propagation direction of light wave is perpendicular to H and electric field intensity E. The dielectric constant of anisotropic optical media is a second-order tensor. D and E are generally not parallel, so the direction of the phase velocity v and the linear velocity v_r are generally not consistent. The included Angle α between them is called the discrete angle, which is a function of the direction of the phase velocity (or ray velocity) and the direction of D (or E) (as shown in the figure below). The phase velocity and the linear velocity are generally not equal, and the relation between them is v=v_rcosα.

The ratio of the speed at which light travels in a vacuum (c) to its phase velocity v in a given direction in an anisotropic optical medium is called the refractive index for that direction. Similarly, the ratio of c to the speed of the ray in a certain direction n_r=c/v_r is called the refractive index of the ray in that direction.

WISOPTIC wave-plates