Critical Angles for Gemstones

[chrono]

I recall someone on PS asking about the critical angles for coloured gemstones (similar to critical angles for ideal cut colourless diamonds) and I replied that it will vary for each gem variety. While the answer is probably too generic for the poster, this PDF address that question a little, in addition to providing other factors that lapidaries have to contend with to bring out the best of any gemstone.
http://www.cigem.ca/pdf/sandrine.pdf

 

[kenny]

Cool article, I plan to read.

Thanx for posting.

 

[Treenbean]

Thanks Chrono
That is a really great paper. Explains a lot.

 

[Michael_E]

Critical angles are only important for very specific areas of a gem and usually don't play all that significant a part in deciding how a stone will be cut. The reason is that it's more important where the light is coming from and where it's going to than where it's "leaking out" of a stone. After all if it didn't leak out in your direction, you'd never see it. The really odd thing about these kinds of papers is that they simplify how light bounces throughout a stone dramatically and give the wrong impression about how critical angle affect things in reality. For instance those diagrams showing light bouncing in 2D are really only true for one small area in a gem. In every other area the angles of the facets are in a compound direction from the direction that the light is travelling.

Sounds confusing, but it's a little easier to grasp with a picture showing how light bounces in 3D. I've attached an image showing light entering a round brilliant zircon at 16°. One ray enters along the centerline of the stone and "leaks" out the pavilion since it is under the critical angle of this material. The other ray hits a pavilion facet at compound angle, bounces across the stone and exits through the crown next to the girdle. Looking at it in this way and you can see that there is more going on than the 2D diagrams show, (unless you're looking at a design with long flat facets, like an emerald cut). If you look far enough into this, it becomes apparent that you can actually cut the pavilion of a gem below the critical angle as long as the crown of that gem is designed to accommodate those low pavilion angles. You still get tilt windows, just in different places and angles than you do with a more traditional crown.