Girls best friend?

I've always been interested in gems.

Particularly diamonds.

No, not in the 'pretty pretty shiny things, oh male being won't you buy me one?', more in the.. well, the physics of them.

There's a long history involved with diamond cutting, before the late middle ages, the natural octahedral shape of diamonds was the best you could get, and there was simply no way to improve upon it. Not due to it being a brilliant cut, far from it, but because diamond is the strongest naturally occurring substance of earth, and there was no way to shape it.

The first step in diamond cutting wasn't even cutting, per say. The jewelers would simply polish the gems to create even, flat faces. This first octahedral shape is now called the 'point cut' and isn't created for commercial use anymore, as it makes no use of the gems refractive index.

Refractive index is a term used to show how much light is refracted when it passes through a material, the more light refracted, the more light gets back to the eye and the 'shinier' the object appears. In order to make a diamond with good fire (dispersion of light), the angles had to be figured out!

The aim of the game in diamond cutting is try attempt to reflect ALL the light taken in back into the eye of the viewer. Lights hitting the gem through the entire 1080' of it's being must be attempted to be reflected back to the viewer, to make the gem appear brighter than apparently possible.

The first cut created to work towards this was the table cut, in which you take a standard point cut gem and saw the top off, creating a flat-top gem. The idea being the flat-top is on the top of the ring / bracelet and all internal light of the diamond is reflected back out of this facet. This idea holds true today and all commercial diamonds and gems will have the exit facet on top.

New cuts with more faces to the diamonds and gems were created over the years, spanning the single cut to the rose to the peruzzi. These pre-Tolkowsky cuts were created through trial and error originally, created for the 16th century idea of a symmetrical radiating pattern, allowing the light to travel within the gem and, for the most part, be reflected back till it all reached the exit facet.

This idea held true till around 1900 when the development of diamond saws and jewelry lathes enabled the more modern gem cuts to be born. Taken from Wikipedia:

Because every facet has the potential to change a light ray's plane of travel, every facet must be considered in any complete calculation of light paths. Just as a two-dimensional slice of a diamond provides incomplete information about the three-dimensional nature of light behavior inside a diamond, this two-dimensional slice also provides incomplete information about light behavior outside the diamond. A diamond's panorama is three-dimensional. Although diamonds are highly symmetrical, light can enter a diamond from many directions and many angles. This factor further highlights the need to reevaluate Tolkowsky's results, and to recalculate the effects of a diamond's proportions on its appearance aspects. ...

Another important point to consider is that Tolkowsky did not follow the path of a ray that was reflected more than twice in the diamond. However, we now know that a diamond's appearance is composed of many light paths that reflect considerably more than two times within that diamond. Once again, we can see that Tolkowsky's predictions are helpful in explaining optimal diamond performance, but they are incomplete by today's technological standards.

Not a definitive solution and the problem of creating the optimum proportions for losing no light still exists. In the 1970's a complete mathematical model was developed for gem design, which has since been the subject of computer modelling. As such, within our lifetimes we may discover the ideal cut of a diamond with higher purity of light retention than the round brilliant cut used today!