The principal refractive indices are the three distinct refractive indices, conventionally written n_α, n_β, and n_γ, measured along the three principal optical axes of a biaxial crystal. In biaxial gem species such as tanzanite, topaz, peridot, andalusite, and tourmaline of orthorhombic or lower symmetry, light vibrates at different velocities along three mutually perpendicular directions, producing three measurable refractive index values rather than the one or two that characterise isotropic and uniaxial gems. The gemmologist measures these values on a refractometer and uses them, together with the differences between them, as a primary species identification tool.

Why three indices, not one or two

The number of distinct refractive indices a gem produces follows directly from the symmetry of its crystal structure. Cubic-system gems such as diamond, spinel, and garnet are isotropic; light travels at the same velocity in every direction and the gem produces a single refractive index. Tetragonal, hexagonal, and trigonal gems are uniaxial; light vibrating perpendicular to the optic axis travels at one velocity, light vibrating parallel travels at another, and the gem produces two refractive indices, conventionally n_o and n_e. Orthorhombic, monoclinic, and triclinic gems are biaxial; light vibrating along three mutually perpendicular directions travels at three distinct velocities, producing three indices.

The names n_α, n_β, and n_γ are conventional, with n_α the lowest, n_γ the highest, and n_β intermediate. The vibration directions along which these indices are measured are called the X, Y, and Z optic directions and lie at right angles to each other; in orthorhombic gems they coincide with the crystallographic axes, in monoclinic and triclinic gems they do not.

Measuring the principal indices

The standard tool for measuring refractive indices on faceted gems is the gemmological refractometer, a hemicylinder of high-index glass coupled to a polariser and a calibrated scale. The gem's table facet is placed in optical contact with the hemicylinder using a drop of high-index liquid, light is introduced from below, and the boundary between bright and dark on the scale gives the refractive index of the light vibrating in the direction parallel to the polariser. By rotating the polariser through ninety degrees, the gemmologist captures the second vibration direction at the same orientation of the gem.

For a biaxial gem, the technique requires rotating the gem itself in addition to rotating the polariser, because the three principal indices are not all visible at any single orientation of the table to the hemicylinder. The standard procedure is to take readings at six rotational positions of the gem, ninety degrees apart, recording the maximum and minimum reading at each position; the lowest reading across all positions is n_α, the highest is n_γ, and the intermediate reading at the appropriate orientation is n_β.

In practice, n_β is the hardest of the three to identify confidently, and many working gemmologists report only n_α and n_γ, the maximum and minimum readings, together with the calculated birefringence. For routine identification this is usually sufficient.

Birefringence and optic sign

The birefringence of a biaxial gem is the difference between the highest and lowest principal indices, n_γ minus n_α. The value is diagnostic for species; tanzanite, peridot, and topaz, for example, have characteristic birefringence ranges that distinguish them from each other and from other gems of similar appearance. Birefringence values for biaxial gems are tabulated in the standard gemmological reference works.

The optic sign of a biaxial gem, positive or negative, depends on the position of n_β relative to the midpoint between n_α and n_γ. If n_β is closer to n_α, the gem is biaxial positive; if closer to n_γ, it is biaxial negative. The determination is made on a polariscope rather than a refractometer and is a useful confirmatory test in cases of identification ambiguity.

The role of pleochroism

Biaxial gems are also pleochroic, often strongly so. The light vibrating along each of the three optic directions interacts differently with the colour-causing chromophores in the gem and produces three distinct body colours visible through a calcite dichroscope. Tanzanite is the canonical example, showing blue, violet, and brown-red pleochroism along the three optic directions; iolite shows blue, blue-violet, and yellow; andalusite shows green, red, and yellow.

The pleochroic colours are not directly the principal refractive indices, but they share the same optical-direction framework, and the cutter who orients a biaxial gem to maximise face-up colour is implicitly choosing which of the three optic directions to align with the table. The relationship between the principal indices and the pleochroism is one of the reasons cut orientation matters so much in biaxial coloured stones.

Diagnostic use in species identification

For an unknown faceted gem, the combination of refractive indices, birefringence, optic sign, pleochroism, specific gravity, and spectroscopy will resolve the species in nearly all cases. The principal refractive indices are the first measurement most working gemmologists take after weight and dimensions, because the refractometer is fast, non-destructive, and produces a value that immediately narrows the candidate species list to a manageable number.

For biaxial species specifically, a full set of three principal indices is more diagnostic than a partial set, because the position of n_β distinguishes between species that share similar n_α and n_γ values. In demanding cases, such as separating tanzanite from synthetic forsterite or distinguishing chrysoberyl from sinhalite, taking the full three readings is worth the additional time on the refractometer.

In the trade

Working gemmologists in the laboratory and at the bench rely on principal refractive indices as a routine identification tool. The refractometer is the single most-used piece of testing equipment in any working gem laboratory, and the principal indices are the values that take the most diagnostic weight in routine identification. The technique is taught in the first weeks of any formal gemmological training and remains, despite the introduction of advanced spectroscopic methods, the foundation of basic gem identification.

Further reading

• GIA — gemstone reference and refractive index tables
• GIA Gems and Gemology — gemmological identification articles
• International Gem Society — refractive index reference