Kaleidoscope Calcite

Calcite – calcium carbonate, CaCO3 – is a very common mineral. Different colours are due to impurities; without impurities and well crystallized, it is colourless transparent. Crystals occur in a wide variety of habits (of trigonal rhombohedral symmetry), and exhibit perfect cleavage on three directions. Cropped pieces of clear calcite are called Iceland spar from their original source, but the specimens found today in mineral stores originate from many places around the world.

Calcite is (uniaxially) birefringent (doubly refracting). Birefringence is observed in many materials; the difference of indices of refraction for the ordinary and extraordinary rays in calcite is about 40 times larger than that in ice. The ordinary ray where the polarisation is orthogonal to the symmetry axis of the crystal, follows Snell's law of refraction, while the extraordinary one with the other polarisation obeys a more complicated law. This is seen in the following pictures:

calcite, birefringence calcite, iceland spar
Birefringence of calcite: ordinary and extraordinary rays are clearly separated.
Click on any picture for magnification

Colours of different origin

 

Thin gaps

Due to the perfect cleavage property, cracks form easily in the process of cropping or due to other mechanical stress. The thin cracks show the colours well known as Newton rings or colours of thin films. This case of two-beam interference has been treated already and several examples have been given; it is not the topic of this section. The picture to the left shows a magnified detail.

Dispersive refraction

In general, the refractive index depends on the wavelength of light. This holds also for the normal and the anomalous index of refraction of birefringent substances. Light entering through one side may leave the crystal after one or more internal reflections through a plane at a different orientation. In this process, the different colours are separated in much the same way as by a simple prism, and their ordering is the well known one of the spectrum as described first by Newton, namely red, orange, yellow, green, cyan, blue, and violet (using the modern names cyan and blue instead of blue and indigo).

The pictures below show spectral colours appearing when the crystal was spotlighted with an incandescent lamp. The left image shows one more or less complete spectrum and an incomplete one (which, at a slightly different viewing angle would be seen completely). This is due to birefringence: one spectrum from the ordinary and another one from the extraordinary ray. But it is even more involved: after internal reflection, each ray may again split into two, ordinary and extraordinary corresponding to the new direction of propagation. Holding the crystal close to the eye I could see up to four spectra for a given light path, but I did not succeed to produce a convincing photograph.


Colours produced by dispersive refraction

Birefringent lamellae

In an Iceland spar specimen from Brazil, I found colours which obviously are not due to the two causes discussed above, see the following pictures. Turning the crystal, sometimes it looks completely colourless, and then again it is vividly coloured in geometric shapes with straight borders, colours resembling those of soap bubbles.


The left picture has been taken with spotlight illumination, the right one with diffuse light from the overcast sky.

Birefringence of the crystal alone can not be the cause of these colours, as there are other specimens which do not show the faintest trace of them. Wikipedia informs that twinning is common with calcite, and that there are four twinning laws. Lamellar twinning can be induced by pressure (shear strain), presumably of tectonic origin (A.R. Woolley, A.C. Bishop, W.R. Hamilton: The Hamlyn Guide to Minerals, Rocks, and Fossils, ISBN 0600 34398 7).

The crystals showing these colours obviously contain such twinning lamellae.

The next four pictures below are made from a crystal piece containing only one major lamella. Under most circumstances it is nearly invisible, but under certain viewing angles (left image) it can be seen as a faintly coloured plane – it is very thin, less than 10 μm, measured under the microscope – while under slightly changed conditions the plane itself is invisible, but its mirror image in the bottom surface can be seen (right image).


Left: A twinning lamella as seen under diffuse light (faint pink and green colours). Right: The mirror image (bluish) of the lamella in the bottom plane.

Left: Through the front surface, the twinning lamella (faintly red and green) and its mirror image in the bottom face (yellowish) are visible; through the top surface, one sees the mirror image of the plane in the back face (direct sunlight). Right: Here the mirror image of the plane is doubled because of birefringence.

Often, due to the fact that the intensities of reflected and refracted rays depend on polarisation, one of the two rays (ordinary or extraordinary) is considerably stronger than the other one, and therefore the doubling of an image as seen in the last picture above, is not always perceived. More often, when the crystal's orientation is changed, one notes that the sight flips when the other ray takes over.

This is also relevant for the explanation of the phenomenon: in any situation where one of the rays strongly outweighs the other, one does not need a polarisation filter to have polarised light.

In the twinning lamellae, the optical axis has an other direction than in the surrounding crystal. Thus, each of the two rays will split again into "new" ordinary and extraordinary rays when entering the lamella. If the incoming and the outgoing rays are polarised as discussed above, the situation is similar to a birefringent layer between polarisers, as has been discussed elsewhere.

This now also explains why under some viewing conditions one does not see any effect: this happens, if the incoming (with respect to the twinning lamella) or outgoing ray is not sufficiently polarised on its path through the crystal.

As the twinning lamellae are weakly reflecting, the number of possible light paths which lead to "prismatic" spectral colours is increased. Interference and prismatic colours may mix to produce brilliant kaleidoscope-like views.


Spotlight illumination: Left: interference colours, right: predominantly prismatic spectral colours.

All the pictures have been taken without a pol-filter; the colours are seen with the unaided eye.


The doubling of images by Iceland spar is well observable only at short distances; it is seen best when the crystal touches the object. Looking through a crystal, distant objects are not seen clearly in most cases, and a shift by two or three millimeters is not perceivable. If, however, there are twinning lamellae, the situation is different. Lamps are best suited as well visible objects.


A lamp as seen through a calcite specimen with a twinning lamella.

The direction of rays entering and leaving and leaving a faultless crystal through opposite faces does not change, even though ordinary and extraordinary rays have slightly different directions in the birefringent medium. But when they meet a twinning lamella, each of the two rays is split again, and each of the resulting four is split once more when leaving the lamella. The exact result depends on details of the geometry; but in general, after leaving the crystal, there are outgoing rays which are not in the same direction as the ingoing one.


View through a calcareous spar specimen with several twinning lamellae with different orientations. The angular distance of the side images changes if the crystal is tilted.

In his treatise on colours (Farbenlehre), Goethe (1749–1832) discusses also the colours due to polarisation and birefringence. On calcite he writes:

"Ein besonderes Stück aber dieses Minerals besitze ich, welches ganz vorzügliche Eigenschaften hat. Legt man nämlich das Auge unmittelbar auf den Doppelspat und entfernt sich von dem Grundbilde, so treten gleich [...] zwei Seitenbilder rechts und links hervor, welche, nach verschiedener Richtung des Auges und des durchsichtigen Rhomben, bald einfach [...] bald doppelt [...] erscheinen. [...]"
"I possess a peculiar specimen of this mineral with very remarkable properties. Holding the spar close to the eye, when one steps back from the object, immediately two side-images appear to the left and the right, which, depending on the orientation of the clear rhombohedron, appear sometimes singly, sometimes doubly [...]"

From the detailed description it is obvious that at Goethe's time the colour phenomena described here were already known.




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