Where the light goes when a pavilion is cut shallow

A diamond has no colour and makes no light of its own. Everything a cut stone does, it does by taking light that was already in the room, sending it down inside itself, and giving it back to your eye. Where it gives it back — and how much of it comes back at all — is decided almost entirely by one number: the angle of the pavilion, the cone of facets below the girdle.

Why light stays inside a stone at all

Diamond has a refractive index of about 2.42. That is very high; water is 1.33 and ordinary glass around 1.5. One consequence of a high index is a low critical angle. Light travelling inside the stone and meeting the boundary with air at less than 24.4 degrees from the surface’s normal passes straight out. At more than 24.4 degrees, none of it passes out at all: it is reflected back inside, perfectly, with no loss. This is total internal reflection, and it is the whole mechanism of a brilliant cut.

So the pavilion is not a decorative shape. It is a pair of mirrors, and it only works as a mirror if the light arrives at it steeply enough. A ray entering through the table, crossing the stone, striking the first pavilion facet at 25 degrees, bouncing to the second pavilion facet, and leaving through the crown has made a journey that depends on the pavilion angle twice over. Change that angle by a degree and you change the arrival angle at both bounces.

The failure at the shallow end

Below about 40.2 degrees, the first bounce starts to arrive too shallow. Instead of reflecting, part of the light refracts and leaves through the back of the stone, into the setting, into the finger, and out of your life. What you see from above is a stone with a dull, glassy circle in the middle — the trade calls it a fish-eye or a window, because you can very nearly read print through it.

This is why a shallow stone can be simultaneously larger and cheaper. Weight in a round brilliant is mostly depth. Cut the pavilion shallow and you spread the same weight across a wider girdle: a stone that measures 6.9mm across and weighs one carat instead of the 6.5mm it ought to. It looks bigger in a photograph, it looks bigger on a hand held still, and the moment it moves the middle of it goes grey.

The failure at the steep end

Steep fails differently and less obviously. Past about 41.2 degrees the light makes its two bounces cleanly but comes back up too close to the axis, and much of it is then blocked by the head of the person looking at the stone. The result is a stone that is dark under the observer and bright at the edges — a nailhead. It is not leaking light; it is returning it into your own shadow.

The narrow band that works

Everything usable sits between roughly 40.4 and 41.0 degrees, and where inside that band you sit is a real choice rather than a compromise. We cut nearer 40.4 for pendants and drops, because a piece that swings is seen through a wide arc of angles and a shallower stone spreads its return across that arc. We cut nearer 41.0 for a trilogy centre, because a narrow, hard return is what makes a centre stone read as brighter than the two beside it.

The crown angle and the table are the second and third terms in the same equation. A large table lets a lot of light in and out through one flat surface, which is bright and characterless. A small table pushes more of the traffic through the crown mains, which is where dispersion happens — where white light is spread into colour on the way out. That is the difference between a stone that is bright and a stone that has fire, and it is a matter of taste rather than of grade.

The demonstration on the front page of this site is not an animation of a stone. It is the arithmetic above, run for every pixel: rays entering the crown, refracting at the surface, bouncing off the pavilion facets if they arrive steeply enough, and leaving if they do not. Drag the pavilion angle down to 38 degrees and you will watch the middle of the stone empty out.