Two for one, birefringence or double refraction

Last updated on September 16, 2023

Two for One: Exploring Birefringence or Double Refraction

When observing a rhombus-shaped calcite crystal, one may notice a fascinating phenomenon: the object beneath the crystal appears as a double image. This intriguing effect is known as birefringence or double refraction. Calcite, a crystalline form of calcium carbonate, exhibits this unique optical property due to its anisotropic nature and the arrangement of its carbonate ions in parallel sheets.

The lattice structure of calcite consists of positively charged calcium ions and negatively charged carbonate ions. As light enters the crystal, it splits into two polarized components. The electric vectors of the radiation interact differently with the induced dipoles of the carbonate oxygen, resulting in the formation of two distinct rays: the ordinary (O) ray and the extraordinary (E) ray.

The O ray behaves similarly to light passing through glass or water, following Snell's law of refraction. On the other hand, the E ray exhibits extraordinary behavior by refracting at a different angle compared to the O ray. What makes this phenomenon even more intriguing is that the extent of refraction, determined by the refractive index, is direction dependent and cannot be predicted by Snell's Law alone.

To visualize the double image produced by calcite, one can observe it from a top-down perspective. As the crystal is rotated, one image remains nearly stationary while the other moves around it. By using a plane polarizing camera filter and rotating it, one can isolate and observe each polarized image separately.

While all non-cubic symmetry crystals exhibit birefringence to some degree, it is often imperceptibly small. However, certain substances, such as ice with its hexagonal symmetry, display enough birefringence to be noticeable. By carefully rotating a polarizing filter, one can observe doubly imaged sundogs caused by the birefringence of ice crystals.

In addition to the visual effects produced by birefringent materials, they also exhibit another interesting property: interference. When O and E rays pass through thin sheets of birefringent materials, they travel different optical path lengths, leading to the formation of colored bands. This phenomenon is often observed when looking through airplane windows, adding a touch of beauty to the aerial view.

To summarize the key points about birefringence or double refraction:

• Calcite, a crystalline form of calcium carbonate, is birefringent due to the arrangement of its carbonate ions in parallel sheets.
• Birefringence causes light entering the crystal to split into two polarized components: the ordinary (O) ray and the extraordinary (E) ray.
• The O ray behaves according to Snell's law of refraction, while the E ray refracts at a different angle.
• The extent of refraction for the E ray is direction dependent and cannot be predicted by Snell's Law alone.
• Observing a rhombus-shaped calcite crystal from a top-down perspective reveals a double image, with one image remaining stationary and the other moving around it as the crystal is rotated.
• By using a polarizing filter and rotating it, one can isolate and observe each polarized image separately.
• Non-cubic symmetry crystals, such as ice with its hexagonal symmetry, can also exhibit noticeable birefringence.
• Birefringent materials can produce interference patterns, resulting in the formation of colored bands when O and E rays pass through thin sheets.
• These colored bands are often observed when looking through airplane windows, adding a visual spectacle to the aerial view.

In conclusion, birefringence or double refraction is a fascinating optical phenomenon exhibited by certain crystals like calcite. Understanding the behavior of light within these materials adds to our appreciation of the intricate properties of the natural world. Whether observing double images or experiencing the vibrant colors created by interference, birefringence continues to captivate scientists and enthusiasts alike.

Two for One. Double image produced by a crystal of Iceland spar, calcite. Images by Les Cowley.

Look straight down on a rhombus shaped calcite crystal (mineral specimen stores often have them) and an object beneath it is seen double. Rotate the crystal. One image stays nearly stationary and the other (the one farthest from the top blunt corner) moves around it. Calcite is 'birefringent' or 'double refracting'.

Calcite is a crystalline form of calcium carbonate, CaCO3, and the crystal is a lattice of positively charged calcium and negatively charged carbonate ions. The very large optical effects shown by calcite arise because the flat carbonate ions are arranged in parallel sheets. Light travelling perpendicular or parallel to them has very different electronic interactions. The crystal is anisotropic and its optical properties are direction dependent.

Light entering the crystal splits into two polarised components because the differently oriented electric vectors of the radiation interact differently with the induced dipoles of the carbonate oxygen.

One ray, called the ordinary or O ray, behaves in the familiar way of light passing through glass or water (as predicted by Snell's law of refraction). The second - the extraordinary or E ray - is indeed extraordinary, it is refracted through a different angle to the O ray. Worse, Snell's Law does not predict the refraction because its extent, given by the refractive index, is direction dependent.

At right, the upper unpolarised view shows the double image. In the lower views a plane polarising camera filter is rotated to reveal one or other of the polarised images.

All non-cubic symmetry crystals (calcite is trigonal, common salt is cubic as also is diamond) are birefringent but often only to an unnoticeably small degree. Ice (hexagonal symmetry) is birefringent enough that a carefully rotated polarising filter shows the presence of doubly imaged sundogs (see Richard Fleet's images).

The O and E rays passing through thin sheets of birefringent materials have different optical path lengths. The rays interfere giving the coloured bands that are often seen when looking through airplane windows.

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Reference Atmospheric Optics

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