guide to thin section microscopy - Mineralogical Society of America

Guide to Thin Section Microscopy
Optical properties: basic principles
Anisotropic materials
Light propagation in optically anisotropic materials is direction-dependent. All non-cubic
crystalline substances (Fig. 3-1) are optically anisotropic. Light entering an anisotropic
crystal is "split" into two light waves that vibrate orthogonal to each other (with exceptions
applying to specific directions in the crystal). The two light waves propagate through the
crystal with different velocities. This phenomenon is called double refraction (Fig. 4-5).
Figure 4-5. Double refraction in a calcite rhombohedron (Huygenian construction)
Raith, Raase & Reinhardt – February 2012
Crystals of hexagonal, trigonal and tetragonal symmetry
The 3-D models for ray velocities (expressed as v or 1/n) in crystals of hexagonal, trigonal
and tetragonal symmetry are therefore double surfaces (Fig. 4-6 A). They illustrate that one of
the two light waves (O-wave) propagates like light in an isotropic substance, with the same
velocity in all directions, while the other wave (E-wave) changes its velocity dependent on
the direction in the crystal. The E-wave has either the highest or lowest value (v e ) in the
direction normal to the crystallographic c-axis. Any rotation away from this direction,
towards the c-axis, will shift v e towards the v o value (decreasing if v e > v o , or increasing if v e
< v o ). In an orientation parallel c, v e has reached the same value as v o . Thus, in this particular
direction, the condition of optical isotropy is realised. This specific direction is referred to as
the optic axis. Minerals belonging to the group of hexagonal, trigonal and tetragonal
symmetry are optically uniaxial. The vibration directions of the waves are fixed within the
crystal: the E-wave vibrates within the plane defined by the ray direction and the c-axis; the
O-wave vibrates orthogonal to the E-wave.
Mineralogists prefer the single-surface indicatrix model for explaining optical phenomena
over the double-surface model of light propagation. The construction principle is illustrated in
Fig. 4-6 B: considering the centre of a crystal as the origin, the refractive indices of two light
waves belonging to one wave normal and vibrating orthogonal to each other are marked off in
proportional distances from the origin. Thus, a "refraction cross" is created which shows the
short and long axes of an ellipse. A construction of the ellipses for all possible wave-normal
directions in crystal space results in an ellipsoid which is the indicatrix.
The optical indicatrix of the crystal systems discussed here is an ellipsoid of revolution. It has
either a prolate form (n e > n o ; optically uniaxial positive) or an oblate form (n e < n o ; optically
uniaxial negative) (Fig. 4-6 C,D). The rotation axis (= optical axis) is identical to the c-axis.
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