Double Refraction

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Double refraction (or "birefringence") refers to the splitting up of unpolarized light into two unpolarized rays.
Due to chemical bonding of atoms inside anisotropic minerals, these two rays will travel at different speeds and thus will refact at different angles.

One ray will vibrate in the direction perpendicular to the optic axis and will obey Snell's law (one can calculate it's angle of refraction), this ray is name the ordinary ray (usually indicated with ω). The other will vibrate in the direction on the optic axis and does not obey Snell's law (i.e. the angle of refraction will vary). That ray is name the extra-ordinary ray (indicated by ε).

The maximum RI difference between these two rays is names "double refraction" and is often indicated by "Δ" (greek letter delta). This maximum birefringence is largest when light enter the gemstone at an angle perpendicular to the optic axis.

Gemstones belonging to the cubic crystal system have only one RI and therefor do not show birefringence, all other gemstones do.
Uniaxial stones (those crystallizing in the trigonal, hexagonal and hexagonal systems) will show two readings and have one optic axis.
Biaxial gemstones (Orthorhombic, monoclinic and triclinic systems) have twp directions in which the incident light will react as it were isotropic and therefor have two optic axes.