Monochromatic ray, of plane polarized light, upon entering an anisotropic mineral is split into two rays, the FAST and SLOW rays, which vibrate at right angles to each other.
Due to differences in velocity the slow ray lags behind the fast ray, and the distance represented by this lagging after both rays have exited the crystal is the retardation - D.
The magnitude of the retardation is dependant on the thickness (d) of the mineral and the differences in the velocity of the slow (Vs) and fast (Vf) rays.
The time it takes the slow ray to pass through the mineral is given by:
during this same interval of time the fast ray has already passed through the mineral and has travelled an additional distance = retardation.
substituting 1 in 2, yields
The relationship (ns - nf) is called birefringence, given Greek symbol lower case d (delta), represents the difference in the indices of refraction for the slow and fast rays.
In anisotropic minerals one path, along the optic axis, exhibits zero birefringence, others show maximum birefringence, but most show an intermediate value.
The maximum birefringence is characteristic for each mineral.
Birefringence may also vary depending on the wavelength of the incident light.