Ordinary Ray — The Snell-Obeying Component in Uniaxial Birefringence
Ordinary Ray — The Snell-Obeying Component in Uniaxial Birefringence
The ray that travels at constant velocity in a uniaxial crystal, defining the n-omega refractive index
The ordinary ray is one of the two rays produced when a beam of unpolarised light enters a uniaxial anisotropic crystal. It is the ray that obeys Snell's law of refraction in the conventional sense, vibrates perpendicular to the principal section of the crystal, and travels at a velocity independent of the direction of propagation through the medium. It is contrasted with the extraordinary ray, which does not obey Snell's law in the simple form, vibrates in the principal section, and travels at a velocity that varies with direction. Together the two rays generate the phenomenon of double refraction, or birefringence, that is fundamental to optical mineralogy and to the gemmologist's refractometer.
Optics
In a uniaxial crystal — one with a single optic axis — light propagating in any direction other than along the optic axis splits into two linearly polarised components. The ordinary ray, often denoted n-omega or n-o, has a refractive index that is constant for all directions of propagation. The extraordinary ray, denoted n-epsilon or n-e, has a refractive index that varies between a maximum and minimum value depending on direction. Along the optic axis, the two refractive indices coincide and no splitting occurs.
The maximum difference between n-omega and n-epsilon is the birefringence, a diagnostic property used routinely in gem identification. In sapphire (uniaxial negative corundum), n-omega is approximately 1.768 and n-epsilon is approximately 1.760, giving a birefringence of about 0.008. In tourmaline (uniaxial negative), the indices are typically around 1.620 and 1.640 with birefringence of 0.018 to 0.020. In zircon (uniaxial positive), birefringence reaches 0.039 to 0.059.
Sign convention
A uniaxial crystal is described as positive when n-epsilon is greater than n-omega and negative when n-omega is greater than n-epsilon. The convention matters in gem identification because optic sign distinguishes species with overlapping refractive indices. Tourmaline and beryl are both uniaxial negative; zircon is uniaxial positive.
On the refractometer
On a standard contact refractometer, the gemmologist sees the two refractive indices as separate shadow-edges that change position as the polarising filter is rotated. The lower index (n-omega in uniaxial negative species, n-epsilon in uniaxial positive) holds steady as the polariser turns through 180 degrees in the appropriate orientation; the other shadow-edge moves between extremes. This pattern, recorded for several stone orientations, yields the species identification and the optic sign together.
Practical significance
For the cutter, knowledge of the ordinary and extraordinary rays informs orientation decisions in dichroic species. A tourmaline cut with its c-axis perpendicular to the table maximises the saturated colour seen along the optic axis, where only the extraordinary ray contributes; a stone cut with the c-axis in the plane of the table will show the ordinary-ray colour from many viewing positions. The gemmological literature on pleochroism is in effect a literature on which colour the ordinary ray carries and which the extraordinary ray carries.
See also optic axis, extraordinary ray, birefringence, pleochroism.