Positive Birefringence — Optic Sign in Uniaxial Crystals
Positive Birefringence — Optic Sign in Uniaxial Crystals
When the extraordinary ray travels more slowly than the ordinary, and what the diagnostic implies
Positive birefringence is the optic-sign condition in which the extraordinary ray within an anisotropic crystal travels more slowly than the ordinary ray, producing a positive optic sign on standard polarised-light measurement. The property is one of two possible signs in uniaxial crystals (the other being negative birefringence) and is one of three possible signs in biaxial crystals (positive, negative, or neutral). Optic sign is a diagnostic feature in gemmological identification and is recorded as part of the standard refractive-index workup on a refractometer.
Optical principle
Anisotropic crystals split incident light into two rays travelling at different velocities through the crystal, the ordinary (o) ray and the extraordinary (e) ray. The two rays correspond to two refractive indices, conventionally written as ω (omega) for the ordinary and ε (epsilon) for the extraordinary in uniaxial crystals. Where ε is greater than ω, the extraordinary ray travels more slowly than the ordinary, and the crystal is positive uniaxial. Where ω is greater than ε, the extraordinary ray travels faster than the ordinary, and the crystal is negative uniaxial.
The relationship is reported on a refractometer by reading both indices and noting the larger value. A polariscope with conoscopic accessory provides an alternative measurement using the interference figure of the crystal viewed along the optic axis, with the orientation of the isogyre cross indicating the sign.
Examples among gem species
Positive uniaxial gem species include quartz (ω = 1.544, ε = 1.553), zircon, ice, and brucite. Negative uniaxial species include corundum (ω = 1.768, ε = 1.760), beryl, tourmaline, and apatite. The optic sign is determined by the underlying crystal structure and is constant for a given species, making it a reliable diagnostic feature when other identification routes (refractive index, specific gravity, absorption spectrum) leave ambiguity.
The biaxial case is more complex: biaxial crystals have three refractive indices (α, β, γ) and the optic sign is determined by the relationship of β to (α + γ)/2. Biaxial-positive species include topaz, danburite, and chrysoberyl; biaxial-negative species include peridot, kyanite, and most amphibole-group gem materials. The biaxial determination requires the polariscope and the conoscopic optic figure rather than the refractometer alone.
Practical use in identification
Optic sign is one of the standard data points recorded during gemmological identification, alongside refractive index, birefringence (the numerical difference between the highest and lowest indices), specific gravity, and absorption spectrum. The combination of these data points is typically sufficient to identify common gem species without recourse to laboratory-grade instrumentation. For lookalike pairs, optic sign is sometimes the deciding diagnostic — for example, the distinction between certain colourless quartz and topaz specimens rests in part on the contrasting positive (quartz) and positive (topaz, but biaxial) signs read on the polariscope.
Relationship to birefringence magnitude
Optic sign is independent of the magnitude of birefringence. A crystal can be strongly birefringent and either positive or negative; another crystal can be weakly birefringent and again either positive or negative. The numerical birefringence and the optic sign are reported as separate quantities on a complete identification. Strongly birefringent positive uniaxial species (e.g., zircon at 0.039) and strongly birefringent negative uniaxial species (e.g., calcite at 0.172) are both diagnostically distinctive on the basis of birefringence magnitude alone, with optic sign providing supporting confirmation.
In the trade
For working gemmologists, positive birefringence determination is part of the routine identification workup conducted on bench instruments. The data point is recorded in laboratory notes and identification reports, and is one of the diagnostic features that supports confident species attribution. The standard reference texts including Hurlbut and Klein's Manual of Mineral Science, Nassau's Gemstone Enhancement, and the GIA Gem Reference Guide document optic sign for the principal gem species.