The working rule
critical angle = arcsin(1 ÷ RI)
Pavilion mains about 3° above the critical angle is the practical target — that margin is what keeps light in the stone. 2° is the floor; 5° is safe but digs a deeper pavilion than needed.
Cutting quartz or glass for practice (RI ≈ 1.54, critical ≈ 40.3°)? Set mains at 43° — a 41° main leaves almost no margin.
Synthetics & hard-to-find materials
Computed, not looked up — arcsin(1 ÷ RI), rounded to 0.1°. For birefringent materials the angle uses the lower RI; cut conservatively.
| Material | RI | Critical angle | Notes |
|---|---|---|---|
| YAG, undoped | 1.83 | 33.1° | The baseline garnet simulant. |
| Nd:YAG | 1.82–1.83 | 33.2° | Common laser-crystal pull material; sometimes sold as facet rough. |
| Cr:YAG (pink/red) | 1.83 | 33.1° | Chromium-doped; the classic pink YAG. |
| Nd:Ce:YAG (light pink) | 1.83 | 33.1° | High-fire pink YAG, a favorite for brilliant cuts. |
| GGG | 1.97–1.98 | 30.4° | Gadolinium gallium garnet — dense, heavy in hand. |
| CZ | 2.15–2.18 | 27.5° | Cubic zirconia — very forgiving pavilion angles. |
| Strontium titanate | 2.41 | 24.5° | Huge dispersion but soft (Mohs ≈ 5.5) — display stones only. |
| Synthetic rutile | 2.62–2.90 | 22.4° | Strongly birefringent; cut conservatively. |
| Moissanite | 2.65–2.69 | 22.2° | Silicon carbide; birefringent — cut conservatively. |
| Synthetic spinel | 1.73 | 35.4° | Close to natural spinel (RI 1.72). |
| Synthetic corundum | 1.76–1.77 | 34.5° | Flame-fusion and pulled sapphire/ruby. |
| Synthetic quartz | 1.54–1.55 | 40.2° | Hydrothermal; same optics as natural quartz. |
| Synthetic emerald | 1.57–1.58 | 39.4° | Hydrothermal; flux-grown runs slightly higher. |
Putting it to work
Beacon Round's 41° pavilion main: at RI 1.62 the critical angle is 38.1°, so 41° gives about 3° of margin — right on the working rule, at the bottom of the design's target range.
Radiance Round opens at 40°: in Nd:Ce:YAG (RI 1.83, critical 33.1°) that's roughly 7° of margin — very safe, with room to spare.
Angles are computed from refractive index, not measured per stone. When in doubt, cut the pavilion a degree steep — a slightly deep stone keeps its light, a shallow one leaks.