Optical Effects in Gems: Gemstone Refraction Index
Table of Opticks c1728, Cyclopaedia of Arts and Sciences
Color, Dispersion & Reflectiveness
The visual appeal and characteristics of a gemstone are determined by several factors that include: brilliance (sparkle), color, fire (light dispersion), and luster (surface reflectiveness). A stone's brilliance, fire, and to a lesser extent luster, are influenced by the type of cut (faceting) that is employed.
The faceting of a gemstone will affect how light will behave as it passes through the outside surface into the interior of the gem. Light can either be reflected off of the stone's exterior surface affecting its luster; or the light can pass through the exterior surface of the stone and be refracted, scattered, and dispersed as the light bounces off of interior surfaces then exiting the stone. As a light beam passes through a gem it is bent or "refracted" before it exits the crystal. The light beam is also broken into its component parts (dispersion) causing the effect known as "fire."
The dispersion effect creates a rainbow of color, widening the beam of light to the point where the observer can see the full visible spectrum of the light-beam broken into its component parts; from red (long wave) to violet (short wave). As the stone is moved, the refraction and reflection points of the facets change, showing the stone's scintillation or "play of color."
The "critical angle" at which a light beam intersects with a given series of facets is the angle at which total "internal reflection" is achieved. Light traveling through the crown and interior of the stone will eventually intersect the outer surface of the stone's pavilion facets (from the inside). If the light intersects within the "critical angle" the facet will act like a mirror, and the light will exit, or "return" through the stone's crown. If the light intersects outside of the critical angle of incidence it will be internally reflected and lost.
The "critical angle" calculation is used to determine how facets should be placed in relation to each-other in order to control the path of light within a gemstone. In a properly faceted gemstone, the light should be reflected internally off the pavilion facets, and pass back through the crown facets ("light return") to achieve maximum brilliance, sparkle and scintillation (below). On the other hand, the light path shoud not escape through the pavilion.
When light passes from one density or type of material (air) into another (the gemstone), it is bent or "refracted." The amount, or degree, that the beam of light is bent will be determined by the density difference between the air and the gem. The measurement used to quantify the amount that a light beam is bent in a given material is known as its "refractive index" (R.I.).
There are two factors when calculating a gem's refractive index: "angle of incident" and "refractive angle." The "incident angle" is the angle of the approaching light as it intersects with the stone's exterior surface. The "refractive angle" is the altered angle of the light as it passes through the stone's interior. The Refractive Index is the ratio of difference between these two angles. Each material has its own unique density and Refractive Index.
The color of a gemstone, and the frequency (color) of the light traveling through it, can also effect its refractive index. As the light's frequency changes, so does its angle of refraction. Higher light frequencies travel through the stone more slowly, while lower frequencies travel faster, causing a spreading effect known as dispersion. As each frequency is reflected it is dispersed throughout the stone's interior at varying speeds and directions. As the scattering and dispersion of light within the stone is increased, so to is the amount of "fire" that is returned to the viewer.
The amount, and "coefficient" of dispersion is determined by a stone's refractive index, quantifying its average optical dispersion (NF-NC) and dispersive power (ND). NF refers to the refractive index of light with a wavelength equal to 486.1 nm (F Fraunhofer line), and NC refers to the refractive index of light with a wavelength equal to 656.3 nm (C Fraunhofer line), ND refers to the refractive index at 589.3 nm (D Fraunhofer line).
Mathematical formula for reconciling the critical angle to N: critical angle = sin-1(1 / n)
The optical characteristics of a given transparent material is categorized as being either anisotropic or isotropic. In an isotropic material, the refractive index is uniform regardless of the light ray's angle of incidence, meaning that the material exhibits no "birefringence," and is "singly refractive." Isotropic crystals that belong to very symmetrical crystal systems (ie. cubic or hexagonal) are singly refractive, and isotropic gems include: Cubic Zirconia, Diamond, Garnet, Opal and Spinel.
Certain anisotropic crystals exhibit a phenomenon known as "double refraction," where the incident light is split into two separate rays, each with different refractive indices and velocities, and their refractive indices will typically vary between two extreme values. The mineral calcite (above, left) has two different refractive indices (birefringence) of 1.490 and 1.660 exhibiting strong double refraction.
Crystals belonging to asymmetrical crystal systems (ie. monoclinic, triclinic) tend to have a higher occurrence of double refraction . Gemstones that are "doubly refractive" can exhibit pleochroism, dichroism or trichroism, all of which can alter the apparent color of the gemstone through pseudochromatic coloration.
Reflection vs Refraction
In order to understand why a gem is faceted or cut en cabochon, it is important to understand how light will behave once it passes into a gemstone or is reflected off its surface. The table below shows several different types of optical effects that are the result of light being refracted (1. spectral dispersion, 2. double refraction) and/or reflected (3. light scattering) from the gemstone.
1. Pseudochromatic Coloration: Caused from optics effects created by spectral dispersion:
2. Double Refraction: Caused by incident light being split into two separate rays:
3. Pseudochromatic Coloration: Caused from optics effects created by light scattering:
Refractive Index of Common Gemstones
Refractive Index of Metals
- Copper: 1.100
- Gold: 0.470
- Nickel: 1.080
- Platinum: 2.330
- Silver: 0.180
- Titanium: 2.160
Bibliography on Gemstone Refraction Index
1. Paul R. Shaffer, Herbert S. Zim, Raymond Perlman, Rocks, Gems and Minerals . Martin's Press
2. Stanford University, Refraction in Gems . www.stanford.edu
3. Wuerzburg Uniaxial Minerals . www.geographie.uni-wuerzburg.de
4. Stephen A. Nelson Introduction to Uniaxial Minerals . www.tulane.edu
5. Judith Crowe, The Jeweler's Directory of Gemstones . DK Publishing.
6. Cally Hall, Gemstones . Simon & Schuster.
7. Antoinette L . Matlins, Antonio C. Bonanno, Gem Identification Made Easy . Gemstone Press
8. R. V. Dietrich, Brian J. Skinner, Gems, Granites, and Gravels . Cambridge University Press