The optical properties of crystals are intimately related to their crystal structures. This article examines the precise relationship between optic character and sign and crystal structure.
Optic character/sign with the jeweler's refractometer
The jeweler's refractometer is a powerful tool, but a fundamental understanding of the optical properties of crystals is needed to use it to its maximum potential.
Most gemologists are aware that, given a wellpolished flat facet, the refractometer can determine the refractive index (RI) of a gem, and also the full birefringence of a doubly refractive gem. However many gemologists do not understand that the following can also be calculated on any single facet of a gem so long as the facet being tested gives clear readings:
 Optic character: Single refraction (SR), double refraction (DR), and further for DR gems, uniaxial (U) or biaxial (B) optic character.
 Optic sign: (+, –, or neutral).
In order to determine optic character and sign, a few tricks must be learned. This article is an attempt to teach the tricks that unlock the power of the jeweler's refractometer.
What is refractive index (RI)?
Refractive index is a measure of the optical density of a material. In a vacuum (and air is close enough to represent a vacuum), light travels at approximately 300,000 km/second. When it enters a more optically dense material, it slows down (and if the entry angle is oblique, it is also bent or 'refracted' towards the normal). Refractive index represents a ratio between the speed of light in a vacuum vs. the speed of light in another material. In other words, it explains how much light slows down in other more optically dense materials. Spinel has an RI of about 1.72. This means light travels 1.72 times slower in spinel than in a vacuum (or air).
Fraunhofer lines
If one points a spectroscope at the sky, a series of dark absorption lines will be seen. These were first discovered by the English chemist, William Hyde Wollaston in 1802, but as is often the case, the original discoverer doesn't get credit. The German scientist, Joseph von Fraunhofer, independently rediscovered them and are now named after Fraunhofer. These absorption lines are caused by the gases surrounding the Sun and Earth, and represent reference points in the visible spectrum.
What is dispersion?
Dispersion is defined as a variation of RI with wavelength. It so happens that RI is dependent on the wavelength of light used to measure it. Different wavelengths will be slowed (and refracted) by different amounts, and thus have different refractive indices. Thus if we are to measure RI in a material, we need to have a standard wavelength of light against which to measure it. The standard wavelength for measuring RI is using the Fraunhofer D line (589 nm), which is produced by sodium. All refractive measurements are thus noted as n_{D}, meaning that the RI was measured using light of a wavelength of 589 nm.
Dispersion manifests itself in faceted gems as a splitting of white light into its spectral colors when it travels through nonparallel surfaces. We call this "fire."
In gemology, dispersion is measured by measuring the RI of a substance using light of the Fraunhofer B line (red; 687 nm) and then with the Fraunhofer G line (violet; 431 nm). The differences in RI is the dispersion of the substance, and is also known as the BG interval. The BG interval in diamond is 0.044.
Regarding the refractometer, what is important is to understand that in order for RI's to be compared with one another, they must be measured using light of the same wavelength. Yellow light corresponding to the Fraunhofer D line (589 nm) was chosen as the standard. Because yellow is the narrowest color in the solar spectrum, so long as your light source is yellow, your RI should be close to that measured with a pure sodium Fraunhofer D source.
How does the refractometer work?
The jeweler's refractometer utilizes the concept of total internal reflection to reveal the RI of a gem placed into optical contact with the prism/hemicylinder. The refractometer displays the point at which total internal reflection occurs as a shadow edge against a calibrated scale. This is the point where the RI reading is taken.
 To create an optical contact, a contact liquid with an RI between the RI of the prism/hemicylinder and the gem being tested must be used. The highest RI of any liquid that is reasonably safe to use in a nonlab environment is 1.81. Thus this is the de facto limit to RI measurements using the jeweler's refractometer. Should nontoxic liquids of higher RI be developed, this would push the high RI limit past the current 1.81 limit.
RI curves vs. actual lab practice
In the material that follows, refractive indices will be plotted out graphically as the stone is rotated through 180° on the refractometer hemicylinder/prism. In actual practice, RI readings of DR gems should be taken as follows:
 Using the refractometer eyepiece polaroid plate, isolate the lower of the two curves. Then rotate the gem bit by bit, readjusting the polaroid plate to maintain isolation of the lower RI curve, while noting its minimum and maximum readings. These are then noted down.
 Repeat the process for the high RI curve
 The end result is something like this: Low curve = 1.762 to 1.770; High curve = 1.770 to 1.770
From these readings, we can see that the low RI curve goes from 1.762 to 1.770, while the high RI curve is constant at 1.770. Using the pattern matching described below, the result would be DR U–.
Overview of the crystal systems and their symmetry and optical properties
Structure 
Structure type Crystal axes Angles 
Symmetry (of highest crystal class)  Optic character 
Refractive index (RI) 
Optic sign  Pleochroism 
Gem examples 
Amorphous 
No order
No axes 
No symmetry 
Isotropic
Singly refractive 
1 RI 
None  None 
Glass
Amber 
Cubic 
Isometric: 1 axis length
a_{1} = a_{2} = a_{3} 
13 planes
9 axes 
Isotropic
Singly refractive 
1 RI
n 
None  None 
Diamond 
Tetragonal 
Dimetric: 2 axis lengths
a_{1} = a_{2} ≠ c 
5 planes
5 axes 
Anisotropic
Doubly refractive 
2 RIs n_{ω} and n_{ε} 
+ = n_{ε} > n_{ω}
– = n_{ε} < n_{ω} 
May be dichroic  Zircon 
Hexagonal 
Dimetric: 2 axis lengths
a_{1} = a_{2} = a_{3} ≠ c 
7 planes
7 axes 
Anisotropic
Doubly refractive 
2 RIs n_{ω} and n_{ε}

+ = n_{ε} > n_{ω}
– = n_{ε} < n_{ω}

May be dichroic 
Beryl
Apatite 
Trigonal 
Dimetric: 2 axis lengths
a_{1} = a_{2} = a_{3} ≠ c 
3 planes
4 axes 
Anisotropic
Doubly refractive 
2 RIs
n_{ω} and n_{ε} 
+ = n_{ε} > n_{ω}
– = n_{ε} < n_{ω}

May be dichroic 
Corundum
Quartz 
Orthorhombic 
Trimetric: 3 axis lengths
a ≠ b ≠ c 
3 planes
3 axes 
Anisotropic
Doubly refractive 
3 RIs
n_{α}, n_{β}, n_{γ} 
+ = n_{β} closer to n_{α}
– = n_{β} closer to n_{γ} ± = n_{β} midway to n_{α} & n_{γ} 
May be trichroic 
Topaz
Zoisite 
Monoclinic 
Trimetric: 3 axis lengths
a ≠ b ≠ c 
1 axis
1 plane 
Anisotropic
Doubly refractive 
3 RIs
n_{α}, n_{β}, n_{γ} 
+ = n_{β} closer to n_{α}
– = n_{β} closer to n_{γ }± = n_{β} midway to n_{α} & n_{γ} 
May be trichroic 
Orthoclase
Spodumene 
Triclinic 
Trimetric: 3 axis lengths
a ≠ b ≠ c 
No planes
No axes 
Anisotropic
Doubly refractive 
3 RIs
n_{α}, n_{β}, n_{γ} 
+ = n_{β} closer to n_{α}
– = n_{β} closer to n_{γ }± = n_{β} midway to n_{α} & n_{γ} 
May be trichroic 
Axinite
Labradorite 
Optic character/curve variations: Uniaxial or biaxial?
 Two constant curves = Uniaxial
 Two variable curves = Biaxial
 One constant/one variable, which meet but do not cross = Uniaxial
 One constant/one variable which don't meet

Check the polaroid angle of the constant curve
 Biaxial = polaroid angle of constant curve = 90°
 Uniaxial = polaroid angle of constant curve ≠ 90°
Symbols
Uniaxial crystals
 nω = omega, the constant RI of a uniaxial crystal which is found when light vibrates in the plane of the a axes
 nε = epsilon, the RI of a uniaxial crystal when light vibrates parallel to c. This is found only when light travels perpendicular to c.
Biaxial crystals
 nα = alpha, the lowest RI of a biaxial crystal = light vibrating parallel to the X optical direction
 nβ = beta, the intermediate RI of a biaxial crystal = light vibrating parallel to the Y optical direction, or along one of the two optic axes
 nγ = gamma, the highest RI of a biaxial crystal = light vibrating parallel to the Z optical direction
Optic sign
Uniaxial stones
 High RI curve varies = (+)
 Low RI curve varies = (–)

Both curves constant: At 0° polaroid angle, only the oray is seen
 a. If low curve is seen = (+)
 b. If high curve is seen = (–)
Biaxial stones
 If nβ is closer to nα, the gem is (+)
 If nβ is closer to nγ, the gem is (–)
 If nβ is halfway between nα and nγ, the gem is (±)
Finding beta
 If two possible betas exist (neither curve crosses the midpoint), false beta will have a polaroid angle equal to 90°. True beta will have a polaroid angle unequal to 90°.
 In biaxial stones, beta is the highest RI of the low curve or the lowest RI of the high curve, where the curve passes a point midway between nα and nγ.
 In biaxial stones, beta is the point where the two curves meet or cross.
 In biaxial stones, if one reading is constant and the other varies, beta is the extreme intermediate point of the variable curve.
 If both curves vary and neither crosses the midpoint, false beta will have a polaroid angle equal to 90°. True beta will have a polaroid angle unequal to 90°.
Polaroid angle
 0° polaroid angle is when the transmission direction of the polaroid plate is parallel to the refractometer scale divisions.
 90° polaroid angle is when the transmission direction of the polaroid plate is perpendicular to the refractometer scale divisions.
Overview of the crystal systems and their optical properties
Optic Character Type  RI Pattern  Optic Sign Determination  Crystal Orientation  RI Curves 
Amorphous and Isometric 
Single RI in all directions  N/A  N/A  
Dimetric = Uniaxial  Two constant RIs 
At 0° polaroid angle, only oray is seen;

C axis perpendicular to facet tested  
One constant and one variable curve that meet but do not cross 

C axis is parallel to the facet tested. When c is parallel to the refractometer testing direction the curves come together (only a single RI is visible) 

One constant and one variable curve that do not meet or cross 

C axis is oblique to the facet tested. Polaroid angle of the constant curve ≠ 90° 

Trimetric = Biaxial  Constant low RI 

X axis is perpendicular to the facet tested  
Constant intermediate RI 

Y axis is perpendicular to the facet tested  
Constant high RI 

Z axis is perpendicular to the facet tested  
One constant and one variable curve that do not meet or cross 

Z direction perpendicular to the facet tested  
Two variable curves, neither crossing the midpoint 

Random section  
Two variable curves, one crossing the midpoint 

Random section 
Author's Notes
The above technique for determining the optic character and sign with the jeweler's refractometer was first developed by Dr. Cornelius Hurlbut:
 Hurlbut, C.S. (1984) The jeweler's refractometer as a mineralogical tool. American Mineralogist, Vol. 69, pp. 391–398.
The technique is also detailed in the second edition (but not the first) of his book, Gemology.

Hurlbut, C.S. and Kammerling, R. (1991) Gemology. New York, NY, Wiley, 2nd ed., 337 pp.
The technique has also been beautifully described as well by:
 Sturman, Darko (2005) Use of the polarizing filter on the refractometer. Journal of Gemmology, Vol. 29, No. 5/6, pp. 341–348.
I have reversed the polaroid angles of Hurlbut as I find it easier to remember relative to the refractometer scale divisions.
For more on crystal optics, see:

Hughes, R.W. (2014) Pleochroism in faceted gems: An introduction. Gems & Gemology, Vol. 50, No. 3, Fall, pp. 216–226.