Objective: Our objective is to explain what exactly makes singly or doubly refractive gems and how these properties relate to symmetry.
Light behaves in mysterious ways-it will slow down, bend, even split, depending on the material through which it travels. But what is really responsible for how light behaves as it moves through different media?
In order to answer this question, we chose to examine the special case of light travelling through crystals. Crystal has very specific properties that make it an ideal researching material. Light passing through the gem and bouncing around within the internal structure gives the crystal the familiar "fire" that we commonly associate with precious gems. We had a hunch that there was something about the crystal structure that determines how light behaves as it enters the gem itself.
We first discovered that there are different ways that light behaves as it enters crystals. Light bends differently as it enters various crystals, and accordingly, each crystal has a refractive index, which measures how light bends when it enters the crystal from the air. Upon learning about this aspect of the reaction between crystal and light, we later found out that not only does light bend differently as it enters different crystals, but the light ray can actually be altered depending on the crystal's internal atomic structure. This accounts for a crystal having single or double refraction.
A crystal can either have single or double refraction. For single refraction, the light is simply bent in one direction, while for double refraction, the light is split into two rays travelling at different velocities. But we really wanted to know WHY this happened. We soon learned that one of the most important factors determining single or double refraction was the internal symmetry of the crystal's atomic structure and which crystal system the gem belonged to.
In order to find answers to our questions, we consulted many professors, including our own Marty Fejer, and others from the earth sciences and geology departments at Stanford, and upon receiving information from them, and synthesizing our findings with our own research from books including Gems and Gem Materials and Handbook of Gem Identification, we finally found a definite answer to our question.
It turns out that the properties of single and double refraction are directly linked to the symmetry of a crystal's atomic arrangement. We found out that gems that are cubic or amorphous are always singly refractive. This is due to the fact that in single refractive materials, "the atomic density and therefore the electron density is [symmetrical] in all directions.-Gary Ernst." Cubic solids refract light in all directions at the same velocity. The cubes are very symmetrical, and have 3 equal and perpendicular axes.
However, the situation changes with less symmetrical crystal systems. For instance, in hexagonal or tetragonal solids, some of which have only two-fold, three-fold, or six-fold rotation axes, double refraction occurs because there are at least "two different directions of atomic structure and electron density." -Gary Ernst. Similarly, a crystal with triple refraction has three different directions of atomic structure and electron density. The other crystal groups that are doubly refractive include orthorhombic, monoclinic, and triclinic, all of which have specific internal symmetries and axes that dictate how light bends as it enters the crystal.
Therefore, after all of our findings, we know more about what specifically accounts for single and double refraction. You might wonder why single and double refraction is significant anyway. If we could extend our research farther, we might want to investigate how important the single or double refraction plays a role in gemcutting. When we were researching gemcuttting, we found that the refractive index was the central tool used by lapidaries, gemcutters, to determine the angle of the facets on a cut gemstone. Now that we know what accounts for the single and double refraction, and how it is linked with symmetry and the gem's refractive index, we might want to investigate to what extent gemcutters take single and double refraction into account when cutting gems. This could give us more information on how gemcutters are able to produce that brilliant fire in beautifully cut gemstones.