From The Gemology Project
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Total Internal Reflection in a Diamond.
Light reaching the facet at an angle larger than the critical angle will be reflected.

Brilliance is the degree of brightness resulting from the reflected light from the pavillion facets of a gemstone when viewed through the crown.
This is based on the laws of refraction and reflection.

When light enters a gemstone it will be (partly) refracted inside the stone. It will then hit a pavillion facet and will then either be refracted out of the stone, or reflected inside the stone depending at which angle the lightray approaches the facet.
Every stone has an angle at which the light ray will either be refracted or reflected. This angle is known as the critical angle and depends on the refractive index of the stone (the higher the refractive index, the lower the critical angle).

When a lightray approaches the facet in an angle that is larger than the critical angle, it will be completely reflected inside the stone. This property is very important in the fashioning of a gemstone to create brilliance or "life".
In a well proportioned Diamond all light that enters the Diamond from the crown, will be trapped inside the stone for a while and then be refracted out of the stone through the crown.
This behaviour is known as Total Internal Reflection (often abbreviated as TIR).
When the Diamond is poorly cut (with either a too shallow or too deep pavillion) light will leave through the pavillion. This causes the Diamond to either appear too light or too dark.


The critical angle can be calculated as the inverse sine of 1 divided by n (the refractive index) of a gemstone. For Diamond with n = 2.417, the calculation will be the inverse sine of 1/2.417 (where 1 is the refractive index of air).

<math>critical\ angle = \arcsin \left (\frac {1}{n}\right )\ \Rightarrow \ critical\ angle = \arcsin \left ( \frac {1}{2.417}\right )\ \approx\ 24^\circ.26'</math>