Hello John,

> Regarding your comments about girdle thickness affecting
> brilliance I don’t agree with them, in order to get the best
> brilliance we are looking to achieve total internal
> reflection. The calculation for total internal reflection
> does not include any reference to the girdle. Reference to any
> good gemmological text will show the principle and formula for
> total internal reflection.

There is little chance that any faceter would want to achieve
total internal reflection in a gemstone because the resulting
stone is unsettable and unattractive. Any more than 4 facets on
the stone will compromise total internal reflection. Anything
other than a knife edge girdle will compromise total internal
reflection. Such a stone is also known as a corner block.
Holographers and others who play with lasers have commissioned
these from me cut from various high RI material.

I would hope that most gemstone enthusiasts would strive to cut
the most attractive gem possible. Bending and scattering of the
light returned from the pavilion by the crown facets is an
example of compromising total internal reflection. It is called
chromatic dispersion because the light is dispersed leaving only
little coloured bits of the rays being returned to the eye.
Artistic cutting would exploit such phenomena. The same goes for
scintillation, the little facets that provide the twinkle either
leak or return the rays providing that effect again at the cost
of perfect reflection

Optical physics and mathematics are vital to a cutter, but not
so much for getting things right but much more important, such
knowledge is for preventing getting things wrong. I agree as far
as physics is concerned a perfect 90 degree girdle has little or
no effect on the amount of light being reflected through the
crown. The size, shape and polish of the girdle however have a
huge impact on the attractiveness of the finished stone.

Cutting a girdle to a precise percentage of anything may get you
points from a judge but a commercial setter will not be
impressed. For a stone to be easily and safely set the girdle
width has to be within fairly small limits. A stone with a
girdle width outside of these limits will not only look wrong,
it will compromise setting. Both small and large stones with
percentage cut girdles would qualify.

If a girdle were to be cut at anything other than precisely 90
degrees then it most certainly would have an influence on the
amount of internal reflection. I have never heard a reasonable
argument as to why girdles should be cut at 90 degrees and
usually cut mine at 80-85. The improvement in looks and
performance may be measurably infinitesimal but it all adds up.