2.2.5 Interference colours
As you have seen, in between extinction positions light is transmitted through crossed polars (Figure 31e), but in an anisotropic mineral the two light rays would travel at different speeds in each permitted vibration direction. The second, crossed polariser effectively combines the two rays, but as they have travelled at different speeds through the mineral, they arrive out of step, to an extent (called the optical path difference) that depends on the difference in refraction (the birefringence) and the thickness of the mineral (Figure 32). Consequently, the transmitted light is no longer the mixture of colours that makes white light, but is a single interference colour as a result of interference effects between the two waves when recombined. The theory associated with production of interference colours need not concern you here, but the consequences are important.
The interference colour observed depends on the optical path difference and hence both the thickness of the mineral and the birefringence of the crystal in its particular orientation. A whole range of these interference colours can be seen when viewing a shallow wedge of quartz between crossed polars. Effectively, because the thickness of the wedge changes gradually while the birefringence remains the same throughout, the sequence of colours is a consequence of the transmitted rays becoming more and more out of step. The result is a 'spectrum' of interference colours called Newton's scale of colours - depicted on the Michel-Levy chart in Figure 33.
If the thickness of minerals to be observed were held constant, then the interference colours of the transmitted light would depend only on the difference in the refractive indices (the birefringence) for the light path in a given crystal. To see the more distinct interference colours shown in the left side of the chart (Figure 33), produced at the thin end of the wedge, the waves must not be too far out of step, so the mineral path must be short. In practice, slices of rock ground down to a thickness of just 30 µm ensure the transparency of most minerals, yet are sufficiently thick for distinct interference colours to be visible. By using this standard thickness of rock slices prepared for optical microscopy, uniformity is maintained, so that all observations of optical features are consistent from mineral to mineral and rock slice to rock slice.
The colour scale of the Michel-Levy chart can be divided into sections, called orders, separated by pinkish-purple bands (Figure 33). The more distinct colours at the thin end of the wedge are called low-order colours, and the lighter, less distinct colours at the thicker end are called high-order colours. For a slice of constant thickness, higher-order colours are produced by a mineral exhibiting higher birefringence. Calcite, with its high degree of anisotropy, is such a mineral.
When looking at interference colours, it is important to be aware of possible ambiguity in using the Michel-Levy chart. Some colours - particularly yellows and greens - appear in several places (i.e. in different orders) on the chart. Sometimes it can be difficult to establish the order of a particular interference colour. In general, higher-order colours appear much more washed out and pastel-like than lower-order colours, which are brighter and more vivid (Figure 33).
The refractive indices of an anisotropic mineral are related to its crystallographic axes and so its birefringence will vary according to its crystallographic orientation. This is an important point. If a single crystal of a mineral were taken and sliced in many different orientations, the interference colour would be different for each section - even for sections of the same thickness. In a rock that contains crystals of the same mineral in many different orientations, there will be differences in refractive index, hence birefringence, so that many different interference colours will be observed. However, the extent to which refractive indices can vary, and therefore the range of birefringence, is limited for any given mineral. In practice, it is the greatest difference in refractive index (i.e. the largest birefringence) and the maximum interference colour that can be identified, that is taken as characteristic (and can be diagnostic) of a particular mineral.
However, for some anisotropic minerals, slices can be cut in such a way that the refractive indices of the two plane-polarised rays are the same. This applies to minerals of the tetragonal, hexagonal and trigonal systems, when looking down their long (z) axes. Such a slice is often referred to as a basal section.
How would such a mineral, sliced perpendicular to its long axis, appear between crossed polars?
It would be in darkness throughout when rotated, just like an isotropic mineral.
What would be the range of interference colours visible for such a mineral present as grains in random orientations?
They would range from a maximum interference colour down through a range of intervening colours on the Michel-Levy chart to black.