# Brilliance

## Basic

Fig.1: 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 off the pavillion facets and the reflection on crown facets of a gemstone when viewed through the crown. This is based on the laws of refraction and reflection.

When light hits the surface of a transparent optically denser medium (like a gemstone) it will be partially refracted inside the stone (other parts get reflected). The refracted ray will then hit a pavillion facet and will either be refracted out of the stone, or reflected inside the stone depending on which angle the light ray approaches the facet (Fig.1).

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 smaller the critical angle).

When a light ray approaches the pavillion facet in an angle that is larger than the critical angle, it will be completely reflected inside the stone. The opposite dictates that light which falls inside the critical angle will be refracted outside the stone. This property is very important in the fashioning of a gemstone to create brilliance or "life".

Explanation of Fig.1.: In this example a brilliant cut Diamond is used with a critical angle ("ca") of approx. 24°26' (24 degrees and 26 minutes). The path the light travels is as follows:

1. light reaches the crown of the stone and is refracted (bend) inside the stone and bends towards 2
2. the light ray reaches a pavillion facet at an angle larger than the critical angle (ca), so it will be reflected (bounced) towards 3
3. at point 3 the light ray again reaches the pavillion facet at an angle larger than the critical angle and will be reflected towards 4
4. here the light ray reaches the crown at an angle which is smaller than the ca, so it will be refracted out of the stone

Note: The critical angle is measured from an imaginary line named the normal (NO). This line is drawn at 90° to the surface of the facet at the point where the light reaches that facet.

In a well proportioned Diamond all light that enters the Diamond through 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) and it is the key ingredient in the design of a refractometer.
It should be noted that this unique phenomenom only occurs on the boundaries of an optically denser medium (gemstone) and an optically rarer medium (such as air), when the light travels inside the denser medium.

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.

Brilliance relies much on transparency, therefor stones with good transparency will show better brilliance when cut well.
As every gemstone has its own critical angle, the design of the cut needs to be adjusted for the stone at hand.
Of course in colored gemstones other factors such as colorzoning, pleochroism etc also play a role in the decision making of how the gemstone needs to be cut for best performance.

$critical\ angle = \arcsin \left (\frac {1}{n}\right )\ \Rightarrow \ critical\ angle = \arcsin \left ( \frac {1}{2.417}\right )\ \approx\ 24^\circ26'$