Optics in Gemology
Optical properties of gems are incredibly important in gemstone differentiation and identification. Because the optical properties of a crystal are sensitive to minute changes in composition and strain within the crystalline structure, they are a great way to differentiate one species or variety of a gemstone from another.
The basis of crystal optics is the premise that light travels in the form of waves, like ripples on a pond. The distance between successive crests or troughs of such a wave is known as the wavelength, and the amplitude of the wave is the height of the wave above the median (middle position between crest and trough). In familiar terms, different colors are different wavelengths and the amplitude is the intensity of the light. Light vibrates at right angles to its direction of motion, and the vibration takes place in all directions perpendicular to the light path.
When light passes from one medium, such as air, into another, such as water, the light is actually slowed down. In addition, the light path is bent. The deviation is always referred to a line perpendicular to the interface between the two media, which is known as the normal to the interface. The light is always bent toward the normal in the medium in which the light travels slower.
The ratio between the velocity of light in the two media is called the index of refraction or refractive index. The first medium is usually taken to be air, in which the light velocity is considered unity (1). The refractive index then becomes 1/v, where v is the velocity of light in the denser medium. Refractive index (usually abbreviated n) is also frequently described in terms of the angle to the normal made by the incoming light beam, or incident ray, and that made by the refracted beam (traveling within the denser medium). Index of refraction in these terms equals the sine of the angle of incidence divided by the sine of the angle of refraction.
It is possible for light traveling from a given medium into a less dense medium, as, for example from a crystal into air, to strike the interface at such an angle that the light is totally reflected at the interface, back into the denser medium. The incidence angle at which this takes place is known as the critical angle. This angle has great significance in terms of gem cutting. If the angles at which the gemstones are cut are incorrectly matched to the refractive index of the material, light entering the stone may “leak out” the bottom, causing a loss of brilliance. If the angles are correct at the bottom of the stone, light is totally reflected internally and returns to the eye of the viewer, creating brilliance that is most pleasing and is, in fact, the whole reason for cutting facets on gemstones.
The optical properties of gemstones and minerals are determined by the crystallographic symmetry of these materials. For example, isometric crystals have crystal structures that are highly symmetrical in all directions. The result of this symmetry is that light traveling in an isometric crystal travels at the same speed in any direction and is not slowed down measurably in any one direction within the material. This is also true of glass, which is actually amorphous and has no crystal structure. Such a material is termed isotropic and is characterized by a single refractive index, abbreviated in Arem’s Color Encyclopedia of Gemstones as N.
In all other crystals, those that are not isometric, light is separated into two components. These two rays are polarized, that is, they each vibrate in a single plane rather than in all directions perpendicular to the direction of travel of the light. The two rays arising in such crystals are known as the ordinary ray and the extraordinary ray. All crystals other than isometric ones cause this splitting of incident light and are termed anisotropic.
The existence of polarized light can be demonstrated by means of a special prism known after its inventor as a Nicol prism. This prism contains specially cut pieces of the mineral calcite that are oriented in such a way as to allow only light polarized in a single plane to pass through. If two Nicol prisms are lined up and turned with their polarization directions at right angles to each other, no light may pass through at all. Similarly, a Nicol prism, or comparable device, can be used to test for the polarization directions of light that has traveled through a crystal specimen or gemstone. This is the basic function of devices such as the polariscope and polarizing microscope. The polarizing microscope is not generally used with gemstones, but instead with tiny mineral grains. Gemologists prefer to work with larger polarizing devices, usually 1-3 inch diameter discs of polaroid plastic, mounted in a device called a polariscope.
In tetragonal and hexagonal crystals there is a unique crystal axis, which is either longer or shorter than the other two axes in the crystal. Light traveling in a direction parallel to this axis vibrates in the plane of the other two axes. Since the other two axes are equivalent, this vibration is uniform and resembles the light vibration in an isotropic crystal. If a pair of Nicol prisms is placed in line with light traveling in this direction in such a crystal and the prisms are rotated so that the polarization directions are crossed (perpendicular), no light will be seen emerging from the crystal. As a result of the presence of this unique optical direction in tetragonal and hexagonal crystals, substances crystallizing in these crystal systems are termed uniaxial.
All other crystals contain two directions in which light vibrates uniformly perpendicular to the direction of travel. Consequently, crystals in the orthorhombic, monoclinic, and triclinic systems are termed biaxial. The complete description of the behavior of light in such crystals is very complex and beyond the scope of Arem’s Color Encyclopedia of Gemstones. The interested reader is referred to standard works on optical crystallography indicated in the bibliography on page 237 of Arem’s Color Encyclopedia of Gemstones.
The ray in uniaxial crystals that travels along the optic axis and vibrates equally in a plane at right angles to this direction, is the ordinary ray. The other ray, which vibrates in a plane that includes the unique crystal axis direction, is the extraordinary ray. The refractive indices for these rays (directions) are the basic optical parameters for a uniaxial mineral, and are listed in Arem’s Color Encyclopedia of Gemstones as o and e. If the o ray has a velocity in the crystal greater than the e ray, the crystal is termed positive (+); the crystal is considered negative (-) if they e ray has a greater velocity. The birefringence in a uniaxial crystal is the difference between the refractive indices for o and e.
In biaxial crystals there are three different crystallographic axes as well as two unique directions within the crystal that resemble the unique optic axis in a uniaxial crystal. The refractive indices of a biaxial crystal are designated by the Greek letters α (alpha), β (beta), and γ (gamma). The lowest index, alpha, is referred to a direction in the crystal known as X, and is associated with the fastest light speed within the crystal. Beta, the intermediate index, corresponds to the Y crystallographic direction, and represents an intermediate ray velocity. Gamma is the highest refractive index and corresponds to the Z crystallographic direction. Gamma is associated with the lowest ray velocity.
The birefringence in a biaxial crystal is the difference between the alpha and gamma index. The acute angle between the two optic axes within the crystal is designated 2V and is a useful parameter to the mineralogist. It turns out that if the beta index is exactly halfway between alpha and gamma, the 2V angle is exactly 90 degrees. Finally, if beta is closer in value to gamma than to alpha, the crystal is considered optically negative. If the value of beta is closer to that of alpha, the crystal is termed optically positive.
Both refractive indices and birefringence are useful parameters in characterizing and identifying crystals, and both change with composition, the presence of impurities, and may vary even within a single crystal.
It should always be remembered that the refractive index is basically a measure of relative light velocity. Every wavelength of light travels through a given medium (other than air) at a different velocity and, consequently, every wavelength has its own refractive index. The difference in refractive index with variation in wavelength is known as dispersion.
Dispersion is what makes a diamond sparkle with colors. The difference in refractive index for red versus blue light in a diamond is quite large, which accounts for the sparkle. As light travels through a cut gemstone, the various wavelengths (colors) diverge, and when the light finally emerges from the stone the various color portions of the spectrum have been completely separated.
Dispersion is reported as a dimensionless number, meaning the number has no unit of measure, but there is some degree of choice in selecting the wavelengths to use as reference points. By convention, the dispersion of a gemstone is taken as the difference in refractive index as measured using the Fraunhofer B and G lines. These are spectral lines observed in the spectrum of the sun, respectively at 6870 and 4308 Å (Ångstrom units: one Ångstrom is equal to one ten-billionth of a meter. This unit of length is used to describe light wavelengths).
In some cases, no dispersion information exists for a mineral or gemstone in the gemological literature; however, the mineralogical literature may have data for the refractive index measured at certain different wavelengths (not including the B and G wavelengths). In such cases it is possible to calculate the dispersion using a special type of graph paper known as a Hartman Dispersion Net. This is a logarithmic-type paper on which one can plot refractive indices at specific wavelengths covering the entire useful range. Such plots are linear and can be extrapolated to the positions of the B and G lines. The B-G dispersion is then simply picked off the graph. Approximately 20 gemstone dispersions never before reported and based on calculations such as are included in Arem’s Color Encyclopedia of Gemstones.
In some cases, as with opaque or translucent materials, the gemologist using only a refractometer cannot measure accurate refractive indices; rather the instrument gives only a vague line representing a mean index for the material. Since this number is useful in that it indicates what can be expected in routine work, it has sometimes been included in the text of Arem’s Color Encyclopedia of Gemstones. Also, the refractometer effectively measures all indices of refraction (that is, for all light wavelengths) simultaneously; more accurate measurements can be made if only a single wavelength is selected. This is universally taken to be the spectral (yellow) line known as D, which is characteristic of the emission spectrum of sodium.
Light may be absorbed differently as it passes through a crystal in different directions. Sometimes the differences are only in degree of absorption or intensity. In other cases, however, different wavelength portions of the transmitted light are absorbed in different directions, resulting in colors. This phenomenon is termed pleochroism. In the case of uniaxial materials, there are only two distinct optical directions and the phenomenon is termed dichroism. Other materials may be trichroic, meaning they have three distinct optical directions. Pleochroic colors are sometimes very distinct and strong, making them useful for gem identification. The pleochroic colors reported for various gems are presented in Arem’s Color Encyclopedia of Gemstones in the order X/Y/Z, separated by slashes.
Since isotropic materials, including glasses, do not affect the velocity or properties of light passing through them in different directions, isotropic materials never display pleochroism. Occasionally, however, an isotropic material may display anomalous colors in polarized light. These effects are generally attributed to strain, although there is abundant evidence that a more likely cause is the ordered arrangement of atoms on specific crystallographic sites.