A cutter decides how bright a stone will be when choosing its angles. Pick a gem, move the pavilion and crown angles, and follow the light through a slice of the stone: where it comes back to the eye and where it leaks out.
Light returned at each pavilion angle
Same crown and table, pavilion angle from 30° to 56°. The dashed line is the critical angle; the shaded band is the published starting range for this gem (see the table below). Your setting is the dot.
Light inside a gem that meets a facet more steeply than the gem's critical angle cannot get out: it is reflected back inside. The higher the refractive index, the smaller this angle (diamond 24.4°, quartz about 40°). The pavilion is cut so that light from above meets it beyond that angle and is sent back up.
If the pavilion is flatter than the critical angle, light coming straight down passes through it. Looking into the stone you see through the middle, like a window, and the centre looks washed out. Low refractive index gems such as quartz and beryl window easily.
If the pavilion is too steep, light reflects off one side but meets the opposite side too directly and escapes through the bottom. The stone looks dark in the centre and the cutter has kept weight the eye does not see. Native cuts made for weight often look like this.
| Gem | Refractive index (mean) | Critical angle | Published starting pavilion angle |
|---|
In the chart the most light often comes back with the pavilion only just above the critical angle. Cutters still stay a few degrees above it: a real stone is tipped and moved, its facets are cut to slightly different angles, and a pavilion right at the critical angle opens a window as soon as the light or the stone moves. The published starting angles include that margin.
Cutters treat these as starting points, not rules: the design, the stone's colour and how deep it can be cut all change the choice. A stone's two refractive indices (most gems have two) are averaged here.
Most of a rough crystal ends up as dust. How much survives depends on the shape of the rough, the flaws that must be cut away and whether the stone is cut for beauty or for weight.
For a clean, facetable piece of coloured stone rough (International Gem Society). Evenly shaped rough yields more; rough with projections or flaws to remove yields less. Diamond is planned with scanners and has its own yields, not shown here.
Recutting: what the weight does
Recutting a deep, bulging stone to better angles makes it brighter but lighter. Enter the stone now and after; the weight comes from the same formula as JewelLoop's carat estimator.
The left picture is a slice through the middle of a round stone, the way Marcel Tolkowsky analysed the diamond in 1919. Light falls onto the stone from above, from directions up to 10° either side of vertical (the drawing shows only the straight-down rays); each ray is bent as it enters (Snell's law), reflected inside wherever it meets a facet beyond the critical angle, and partly reflected and partly let out where it does not (Fresnel equations). "Comes back through the top" adds up the light that leaves through the table and crown. A real stone has many more facets and is seen in three dimensions, so the figures compare angles with each other; they are not a brilliance grade for a real stone. Fire (dispersion), colour and the viewer's head are left out.