Refractometer

The instrument

A refractometer reads the refractive index of one polished facet, usually the table, laid on a drop of contact liquid on a glass of higher index. Light inside the glass meets its flat top at an angle θ from the normal. Wherever the stone’s index is too low to take that light in, all of it reflects back to a scale. The scale is graduated in s = N sin θ, so each point on it is an index, and the boundary between light and dark, the shadow edge, falls at the stone’s own refractive index.

The critical angle here is the one in the glass, against the stone: sin θ_c = n/N. It is not the stone’s own critical angle against air, sin θ_c = 1/n, which the gemstone pages give (40.4° for amethyst, 22.2° for moissanite) and which decides how a cut stone returns light. A stone above the glass and the liquid, such as moissanite, has no critical angle in the glass at all, but still has its own.

Glass

N = 1.88, a dense lanthanum glass; the lead glass of older instruments is about 1.90

Contact liquid

1.81, the liquid most commonly used; it sets the highest index the instrument can read

Scale

1.30 at the top, lines every 0.01, longer every 0.05, on to 1.85; the liquid limits readings to 1.81. Readings are taken to the third decimal by eye. Real scales open up slightly towards the high end; the tool draws them evenly, as teaching drawings do

Light

yellow, at 589 nm (the sodium line at which gemstone indices are published), so each edge is a single sharp line

How the scale is lit

Each point on the scale is lit by the share of light that comes back from the glass’s top at its angle. Where the stone sits, light passes from the glass into the liquid film and then meets the stone; the two interfaces are added incoherently, each with its Fresnel reflectance, separately for light polarised across the plane of incidence (s) and in it (p), and the two averaged. Short of the critical angle most of the light passes into the stone and only a few per cent comes back, so the scale is dark. At the critical angle, sin θ_c = n/N, the reflection becomes total and the scale beyond it is bright: dark above the edge, bright below.

The Fresnel share climbs steeply in the last few thousandths before the edge (about 30% at 0.02 below an edge at 1.544, 55% at 0.005). Through the eyepiece the eye still sees a sharp line there, so the tool draws the partial share as it is seen: each wave’s share is cubed, which keeps a faint glow under the edge and compresses the rise into its last few thousandths. The screen brightness then follows a gentle curve with a small lift (0.1 + 0.9 × level^0.62), so the dark side reads as the dim olive that observers describe rather than black.

The stone covers 80% of the lit glass. The rest carries bare liquid, which returns a quarter of the light that enters it (the rest escapes through the drop’s curved surface) until the liquid’s own critical angle, where it reflects all of it. That makes the faint liquid line at 1.81, which shows in every reading and is the only edge left when a stone is over the limit. A little stray light, 1.2%, keeps the dark side from black.

Two edges

A doubly refractive stone splits light into two rays vibrating at right angles, each with its own index, and each gives its own edge: the gap between them is the birefringence. Between the two edges one ray is reflected totally and the other only partly, so the band between them is about half as bright.

Ruby, sapphire, emerald, amethyst and moissanite are uniaxial. As in the 3D Gemstone Simulator, the table is cut across the optic axis. The light that marks an edge then travels along the table, at right angles to the axis, whatever way the stone is turned: the ordinary ray (polarised across the plane of incidence) shows the ordinary index ω, the extraordinary ray the extraordinary index ε, and both edges stay put through a full turn, the full birefringence apart. The extraordinary ray’s reflection is computed for an axis normal to the surface. With the table cut another way one edge moves as the stone turns; the tool does not model that, so it has no rotation.

Over the limit

A stone whose index is above the contact liquid’s cannot be read. Light passes through the liquid into the stone at every angle up to the liquid’s own critical angle, 74.3° in a glass of 1.88; beyond that the glass reflects it all at the liquid. So the scale stays dark down to the liquid line. This is called over the limit (OTL). Diamond, moissanite and cubic zirconia all read this way, so a standard refractometer cannot tell them apart, and moissanite’s double refraction cannot be seen on it.

The stone on the glass

The side view is drawn from the cut’s own 3D model, the geometry we sell: the model turned table-down, its longer side to the viewer, every facet that faces the viewer filled with a flat shade (a key light from the upper left and a fill from below) and its edges drawn. For the Heart, whose notch hides some facets behind others, a facet is left out when a line from its centre towards the viewer meets another facet first. All stones are drawn at the same plan size. Coloured stones take the body colour of the simulator’s absorption for their gemstone.

Light comes in through the curved glass aimed at the centre of the table, so it does not bend there, at one ray for each 0.10 on the scale, from 1.30 to 1.80. Beyond the critical angle a ray reflects whole to the scale (solid). Short of it, most of the ray passes into the stone, bending away from the normal at sin φ = s/n, and only a little reflects (dashed). The critical ray of each edge is drawn in white with its angle from the normal; for a stone over the limit, it is the liquid’s. Changing the gemstone slides the edges and the critical rays from one index to the other.

The gemstones

The indices are the ones the 3D Gemstone Simulator uses, at 589 nm, checked against the sources below.

None of the seven gives a single edge on the scale: diamond and cubic zirconia are singly refractive but over the limit. A singly refractive stone within range, such as spinel, shows one edge.

What the tool leaves out

• Turning the stone, other optic orientations and biaxial stones, in which edges move.
• The polarising filter, which hides one edge at a time and tells the ordinary ray from the extraordinary.
• White light, in which the edge becomes a narrow coloured band, and liquids other than 1.81.
• The spot (distant vision) method for cabochons and other curved surfaces.
• Facet size, polish and the amount of liquid, which change how clearly an edge shows but not where.
• Real readings have a tolerance of about 0.005 on a well-polished facet; the tool draws each edge exactly at its published index.

Sources

We are not affiliated with any of these publishers or makers.

• C.S. Hurlbut Jr., “The jeweler’s refractometer as a mineralogical tool”, American Mineralogist 69, 391 to 398, 1984.
• C.S. Hurlbut Jr., “A cubic zirconia refractometer”, Gems & Gemology 17(2), 1981.
• Gem-A Instruments, Gem-A Refractometer instruction leaflet: scale, liquid, readings and the over the limit view.
• R.W. Hughes, “Crystal optics with the refractometer”, Lotus Gemology.
• The Gemology Project, “Refractometer” (also in the LibreTexts Gemology book, section 11.4).
• J.W. Anthony and others, Handbook of Mineralogy: diamond, corundum, beryl and quartz.
• K. Nassau, S.F. McClure, S. Elen and J.E. Shigley, “Synthetic moissanite: a new diamond substitute”, Gems & Gemology, Winter 1997.
• GIA gem encyclopedia: ruby, sapphire, emerald, amethyst and diamond.

The Refractometer shows what a standard gem refractometer shows when one of our seven gemstones lies table-down on its glass: the scale through the eyepiece, with its shadow edge or edges, and beside it the light meeting the stone. It is a teaching model of the instrument. It does not measure, identify or grade any real stone.