Axis & Sign

Optic Axis - Uniaxial / Biaxial

Not every direction in a doubly refracting stone is a direction of double refraction Directions of single refraction in an anisotropic stone are known as the optic axis direction.

• Depending on the crystal system to which it belongs, every anisotropic stone has one or two directions of single refraction i.e. directions along which light is not polarised.
• Light that is transmitted along a path parallel to the optic axis will have only a single refractive index.
• Crystal belonging to the Tetragonal, Hexagonal and Trigonal system has only one optic axis, parallel to the crystallographic "C" axis direction, and is known as uniaxial gemstones.
• Crystals belonging to the Orthorhombic, Monoclinic and Triclinic systems, have two directions of single refraction i.e. two optic axis and hence these crystals are termed biaxial gemstones. The angle between the optic axes varies from species to species. There is no simple relationship between optic axis directions and crystallographic axes.

Optic Sign - Positive / Negative

The optic sign is calculated on the refractometer by noting whether

• the ordinary ray or the extra-ordinary ray (in uniaxial) moves faster or slower, or
• alpha or gamma (in biaxial) moves beyond the half way mark of the total birefringence.
• For accurate determination, the stone should be rotated in all directions on any particular facet, and sets of readings observed.
• Uniaxial positive (U+): varying ray (extraordinary) has a higher R.I. than the fixed ray (ordinary).
• Uniaxial negative (U−): varying ray has a lower R.I. than the fixed ray.
• Biaxial positive (B+): beta R.I. reading is closer to alpha reading. The higher shadow edge moves beyond the half way position between maximum and minimum.
• Biaxial negative (B−): beta R.I. reading is closer to gamma reading. The lower shadow edge moves past the halfway position.

Examples:

The examples given in the box are over simplified to give an idea as to the calculation for positive and negative signs. In the case of corundum, ω = 1.759 , ε = 1.767. Increasing substitution of Al³⁺ by Cr³⁺ increases both ω (upto 1.763) and ε (upto 1.772). Similarly the readings would vary with respect to the elemental percentages in a species.