Investigating Optical Properties of Calcite

Optical quality Iceland spar calcite with box carved by Leif Karlsen.
Rhomb 65x45x35 mm
Photo: E. Skalwold

The Optics of Calcite

Historically a Mineral of
Profound Importance
under construction
For a historical perspective on Icelandic Spar calcite and its impact on science, please see the delightful paper written by Dr. Leo Kristjansson on "Iceland Spar: The Helgustadir Calcite Locality and its Influence on the Development of Science" (pdf file, 559 KB reproduced with permission of the author). A more recent and vastly updated paper in Icelandic will be available soon in English.

The stats: Trigonal crystal system / Uniaxial negative / Refractive Index: ω= 1.658, ε=1.486 (sodium light) birefringence = 0.172. What does all that mean? Well, when light enters the calcite crystal it slows down and at some angles in which it strikes the surface (angle of incidence), it breaks into two light rays named ω and ε. Right after the interface of the air and crystal surface, the two rays bend at different angles and travel at different speeds through the calcite. They also become what is known as plane polarized. When they leave the crystal they become parallel. You don't have to know all that - it just explains why you see double through the crystal. So if a speck of dirt or dot of tar is on one side of the crystal, you will see two dots looking from the other side - or if you place the crystal over words on a paper, you will see them doubled.

Those two refractive indices listed above represent the slowing of the two rays of light travelling through the crystal. The greater the difference between them, the more the doubling will be observed at particular orientations. (note: while the birefringence is greatest perpendicular to the optic axis, the two rays which are travelling at different speeds are not bending so there is no doubling observed -see figure 1 below - the unaided eye does not discern the two rays.). A crystal of quartz has a much lower difference or birefringence than calcite. A peice of quartz and a piece of calcite of exactly the same size and orientation will have a much different spread of images - the quartz will hardly be noticable unless it is a very, very thick peice while the calcite of the same size will show noticable doubling.

An aside for the those interested in gems:

Considered a collector gemstone because of its low hardness, calcite is not suitable for wear except with extreme care. However, a faceted optical quality calcite can be quite beautiful. Pockets of Iceland spar were found in the late 1960s in New York State which yielded rhombohedral crystals over 60 cm across.

Master faceter Arthur Grant cut some of these which later became part of the gem collection of the Smithsonian Institution in Washington, D.C. as well as several other major museums. In the Winter 1984 issue of Gems & Gemology, Hurlbut and Francis describe the optics resulting from the twinning commonly found in these stones. A fantastic kaleidoscope of colors occurs as the light is broken up into progressively more pairs of rays as it crosses the twinning planes within the stones (Robinson, G.W. and Chamberlain, S.C., 2007).

Calcite 1,017 ct
St. Joe Minerals mine
Balmat, St. Lawerence County, New York
Photo courtesy of G. Robinson.

Optical quality calcite

Calcite has three directions of perfect cleavage which reflect its three-fold symmetry. Each cleavage direction is inclined at the same angle to the c-axis; none are perpendicular or parallel to the c-axis (in calcite this is also the optic axis direction). When a crystal is broken, it tends to break on these directions forming a rhombohedron or "rhomb" - the crystal habit employed by Karlsen in his theory of the Viking Sunstone. These could be found in Iceland on the surface scree.

Calcite Crystals and Cleavage Rhombs
Photo courtesy of Dr. Mickey Gunter.
Gunter, M.E. (2003) "A lucky break for polarization:
The optical properties of calcite."
In extraLapis, Calcite, 4, 40-45, East Hampton, CT.

Figure 1

$Refraction in Calcite Rhomb.$
Refraction in Calcite Rhomb
Image courtesy of Dr. Mickey Gunter.
Dyar, M.D. and Gunter, M.E. (2007) Mineralogy and Optical Mineralogy.
Mineralogical Society of America, Chantilly, Virginia, 708 pp.

Figure 2

Figure 1 shows calcite crystals and cleavage rhombs demonstrating the visual effects of light propagating through them.

The top left crystal is the basal form and is shaped like a hexagon. Light behaves as the ordinary ray ω and travels along the c-axis straight out of the screen at you. The light remains unpolarized, does not break into two rays and therefore you don't see a double image.

In the long prism form on the right, the c-axis is parallel to your screen and light is passing through the crystal perpendicular to the c-axis - that is straight out of your screen at you again. Even though the light travels along two seperate vibration directions in this orientation, the classic double refraction does not occur. In reality the light entering the crystal becomes two rays traveling at different speeds. The single image below the crystal becomes two which are aligned one on top of the other - appearing as a single image.

Because of its perfect cleavage, calcite is most often found as a rhombohedron. Light entering the crystal perpendicular to the face of the crystal ("normal") is neither parallel nor perpendicular to the optic axis as described in the crystals above. In the rhomb doubling occurs; that is, two images are produced as described below.

The middle crystal shows a rhomb (rhombehedron) which has had the edges cut off on the left and right. The text on the paper underneath appears double when viewed through the rhomb. What you are observing is double refraction in which light entering the crystal is slowed and split into two mutually perpendicular plane polarized rays moving at different speeds: the ordinary ray (o-ray or ω) and the extraordinary ray (e-ray or ε).

The intact rhomb below it shows the same effect, although this time 2 sheets of polarizing filter are placed on top of the rhomb with their transmission directions indicated by the white arrows. Notice that the images of the line underneath is seen doubled between the sheets, but singular through the sheets. The left sheet reveals the image generated by the e-ray; the right sheet reveals the image generated by the o-ray.

This effect can also be observed by inking a dot on a peice of paper and placing a calcite rhomb over it. One will observe two dots from above. If the rhomb is rotated while kept flat on the paper, the dot produced by the e-ray will rotate around the stationary dot transmitted by the o-ray. The thicker the rhomb, the more spread out the images of the dots will appear.

Figure 2 details the passage of the rays through a calcite rhomb. The rhomb is shown in various orientations with the vibration direction of each ray indicated by cross-bars mutually perpendicular to each other on the respective rays. In the middle side view, the o-ray vibration indicators are perpendicular to your screen and the e-ray indicators are parallel to your screen. "WN" indicates "wave normal."

For in-depth information on optical properties of calcite as well as other minerals, see "Mineralogy and Optical Mineralogy" written by Melinda Darby Dyar and Mickey E. Gunter

Also see extraLapis English No. 4, "Calcite, the Mineral with the Most Forms," 2003, East Hampton, CT. USA.

Leif K. Karlsen's approach:

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