Table of contents:
- Wavelengths of Light
- Refractive Index
- Critical Angle
- Isotropic Crystals
- Anisotropic Crystals
- Polarized Light
- Uniaxial Crystals
- Biaxial Crystals
- Birefringence in Uniaxial Crystals
- Birefringence in Biaxial Crystals
- Refractive Indices for Opaque or Translucent Materials
- Using a Single Wavelength to Measure Refractive Indices
- Anomalous Colors
Wavelengths of Light
Light travels in the form of waves, like ripples on a pond. This forms the basis of crystal and gemstone optics.
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).
To put this in familiar terms, different wavelengths are different colors, and the amplitude is the light’s intensity. 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, it actually slows down. In addition, the light path bends. The deviation always refers to a line perpendicular to the interface between the two media, known as the normal to the interface. The light always bends toward the normal in the medium in which the light travels slower.
The index of refraction or refractive index equals the ratio between the velocity of light in the two media. The first medium, usually air, sets the unity light velocity (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). In these terms, the refractive index equals the sine of the angle of incidence divided by the sine of the angle of refraction.
Light traveling from a given medium into a less dense medium — for example, from a crystal into air — may 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 for gem cutting. If a faceter cuts a gemstone at angles matched incorrectly to its refractive index, light entering the stone may “leak out” the bottom. This causes a loss of brilliance. However, if the angles are correct at the bottom of the stone, light is totally reflected internally and returns to the eye of the viewer. This creates a most pleasing brilliance. In fact, gem cutters facet stones precisely to create this wonderful return of light.
The crystallographic symmetries of gemstones determine their optical properties. For example, isometric crystals have crystal structures highly symmetrical in all directions. As a result of this symmetry, light traveling in any direction within an isometric crystal travels at the same speed. Within the material, no single direction measurably slows down light. (This is also true of amorphous materials, such as glass, which have no crystal structure). Such materials are called isotropic and are characterized by a single refractive index, abbreviated as N.
In all other non-isometric crystals, light separates into two components — two polarized rays known as the ordinary ray and the extraordinary ray. All non-isometric crystals cause this splitting of incident light and are called anisotropic.
Each polarized ray vibrates in a single plane rather than in all directions perpendicular to the direction of travel of the light.
Named after its inventor, William Nicol, a Nicol prism can demonstrate the presence of polarized light. It contains specially cut pieces of calcite oriented to allow only light polarized in a single plane to pass through. If you line up two Nicol prisms and turn their polarization directions at right angles to each other, no light may pass through at all.
Similarly, gemologists can use a comparable device, such as a polariscope or polarizing microscope, to test for the polarization directions of light that has traveled through a crystal specimen or gemstone. Typically, mineralogists use polarizing microscopes to examine tiny mineral grains, not gemstones. Gemologists prefer to work with larger polarizing devices, usually 1-3 inch diameter discs of polaroid plastic, mounted in a polariscope.
Anisotropic crystals in the tetragonal and hexagonal system have 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 special direction in tetragonal or hexagonal crystals, and if 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, gemstones crystallizing in these crystal systems are called uniaxial.
Anisotropic crystals in all other systems contain two directions in which light vibrates uniformly perpendicular to the direction of travel. Consequently, crystals in the orthorhombic, monoclinic, and triclinic systems are called biaxial. The complete description of the behavior of light in such crystals is very complex.
Birefringence in Uniaxial Crystals
In uniaxial crystals, the ray 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) — designated as o (ordinary) and e (extraordinary) — are the basic optical parameters for a uniaxial gemstone.
If the o ray has a velocity in the crystal greater than the e ray, the crystal is termed positive (+). If the e ray has a greater velocity, the crystal is termed negative (-).
The birefringence in a uniaxial crystal equals the difference between the refractive indices for o and e.
Birefringence in Biaxial Crystals
Biaxial crystals have three different crystallographic axes. They also have two unique directions within the crystal that resemble the unique optic axis in a uniaxial crystal. The Greek letters α (alpha), β (beta), and γ (gamma) designate the refractive indices of a biaxial crystal.
Alpha, the lowest index, refers to a direction in the crystal known as X 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, the highest refractive index, corresponds to the Z crystallographic direction and has the slowest ray velocity.
The birefringence in a biaxial crystal equals the difference between the alpha and gamma index.
Mineralogists find the acute angle between the two optic axes within the crystal, designated 2V, a useful parameter. It turns out that if the beta index is exactly halfway between alpha and gamma, the 2V angle is exactly 90°.
Finally, if the value of beta is closer to gamma than alpha, the crystal is termed 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. Both change with composition and the presence of impurities, and they may even vary within a single crystal.
Always remember 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. Consequently, every wavelength has its own refractive index. The difference in refractive index with variation in wavelength is known as dispersion.
Dispersion makes gemstones sparkle with colors. In diamonds, for example, the difference in refractive index between red and blue light is quite large. This accounts for their sparkle. As light travels through a cut gemstone, the various wavelengths (colors) diverge. When the light finally emerges from the stone, the various color portions of the spectrum have completely separated.
Scientists report dispersion as a dimensionless number, meaning it has no unit of measure. However, some degree of choice exists in selecting the wavelengths used as reference points. Typically, gemologists take a gemstone’s dispersion as the difference in refractive index between the Fraunhofer B and G lines. Fraunhofer lines are spectral lines observed in the spectrum of the sun, at 6870 and 4308 Å, respectively.
An ångstrom (Å) equals one ten-billionth of a meter, and scientists use it to measure light wavelengths. They also use the nanometer (nm), one billionth of a meter, or 10 Å.
In some cases, no dispersion information exists for a 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, gemologists can calculate the dispersion using a special type of graph paper known as a Hartmann Dispersion Net. On this logarithmic-type paper, one can plot refractive indices at specific wavelengths covering the entire useful range. Gemologists can extrapolate such linear plots to the positions of the B and G lines.
Refractive Indices for Opaque or Translucent Materials
In some cases, as with opaque or translucent materials, a refractometer alone can’t measure refractive indices accurately. Instead, the instrument gives only a vague line representing a mean index for the material. Nevertheless, this number still indicates what gemologists may expect to find in a routine examination.
Using a Single Wavelength to Measure Refractive Indices
A refractometer effectively measures all indices of refraction (all light wavelengths) simultaneously. Gemologists could make more accurate measurements by selecting only a single wavelength. Universally, they choose the spectral (yellow) line known as D, which characterizes the emission spectrum of sodium.
A crystal may absorb light differently as it passes through in different directions. Sometimes, the differences are only in degree of absorption or intensity. In other cases, however, the absorption in different directions of different wavelength portions of the transmitted light results in colors. This phenomenon is termed pleochroism.
In the case of uniaxial materials, since they have only two distinct optical directions, gemologists call the phenomenon dichroism. Other non-isotropic materials have three distinct optical directions, so they may show trichroism.
Pleochroic colors sometimes appear very distinctly and strongly. This can make them useful for gem identification.
Since isotropic gemstones don’t affect the velocity or properties of light passing through them differently according to its direction of travel, these materials never display pleochroism. Occasionally, however, an isotropic material may display anomalous colors in polarized light. In general, these effects are attributed to crystal strain, although abundant evidence indicates that the ordered arrangement of atoms on specific crystallographic sites is a likelier cause.