I read with great interest your discussion of brilliance vs
dispersion concerning the Hearts on 'Fire Diamond. I would be
interested in whether you have any references about this.
Not specifically regarding the hearts on fire cut, but the basic
principles are mostly the same regardless of the exact facet
As far as I can tell from my reading brilliance might be
higher for colored stones with low crown angles, but dispersion
requires a high crown. I haven't seen any discussions of crown
angle vs dispersion and brilliance. Thanks for all your great
Here’s how it works. (gemology 101… )
The pavilion of a diamond or other stone, to be brilliant
functions in essence as a reflector, much like a "corner cube"
reflector. The idea is that light must bound twice, first
incoming light hits the pavilion surface (which it must do within
an angle that results in it’s total reflection back into the
stone, rather than it’s refraction totally out of the stone). It
now is travelling roughly horizontally in the pavilion, until it
reaches the other side, where it again must totally reflect, in
order to now be going back out the crown of the stone. If the
pavilion angle of the stone is too shallow, light is unable to
properly make the first reflection, and leaks directly out the
pavilion. In such stones, you literally can see what’s
underneath the stone. If the pavilion angle is too steep, the
light makes the first reflection, but ends up going too close to
perpendicular to the second surface, and is lost there. The key
to pavilion angles is that they must not only maximize total
internal reflection for light entering perpendicular to the
table, but hopefully also include as wide a cone of entry angles
for the light as possible, while still letting the light totally
reflect. For colored stones with lower refractive indexes, this
can by difficult, but with diamond, you can get a fairly
substantial angular range for entrant light. The result, when
this is maximized, is the best brilliance in a stone… However,
the most efficient place for light to enter the stone for
brilliance is the table. Crown facets scatter the light more,
and loose some of it. So the larger the table, the higher total
reflectivity can be.
Crown angles are more complex, and are concerned with more than
just dispersion. Dispersion or fire, the breaking up of white
light into it’s spcetral colors, occurs when light enters or
exits the stone at an angle. The closer to the stones “critical
angle” this happens, the greater this seperation into colors, but
at least on entry to the stone, increased angle of entry is also
coupled with some surface reflectance of the light back away from
the stone instead of into it as desired. The idea is to find an
angle at which the best balance of the amount of light entering
to be refracted into colors as well as an angle that’s high
enough so the degree of that refraction is suffiencent to cause
attractive color seperation in the first place. Then, it’s also
important that there is enough of the crown facets available to
perform this refractive task. If the table is small, a large
crown facet area will result in a large degree of dispersion and
fire visible (just think of the old mine cut diamonds you’ve
seen. Tiny tables, but a heck of a lot of fire.) The size of
the table must be balanced with the area allowed the crown
facets, to both maximize brilliance with a large enough table,
and maximize dispersion with a small enough table. Finding the
best balance here is somewhat subjective, in terms of how you
define the most beautiful stone.
Also, the crown facets do more than just cause dispersion.
There is also the property of scintillation, or that sense of
sparkle and movement that you get when you move the stone or your
eye relative to the stone. If a stone has a large table, then
moving the stone around, changing the angle of view, presents
little difference in the appearance of the stone. It stays
bright, but your image of it doesn’t change all that much. With
more crown facet area, that refraction of entering and exiting
light, and the distortion of the image of the interior of the
stone that this causes, makes the diamond seem much more lively
Couple this with the effect of facet design… A large table
means that crown facets will be individually smaller, so
individual refelctions and flashes of light will be smaller.
With a large table, you get an image of lots of confusing small
sparkles surrounding a relatively dead center, while with smaller
tables, the whole stone’s appearance is of more evenly sized
sparkles of light covering the whole area of the stone.
In general, the goal of the cutter, if cutting for beauty, is to
maximize all of these properties. But Brilliance itself, the
total amount of light reflected by the stone, is in conflict with
the functions of the crown angles. Therefor, calculating exact
maximum beauty is a bit more than doing just the math. You have
to decide what that maximum beauty actually is, first. They eye
knows it easily enough. But getting there isn’t always as clear
a set of choices.
As I mentioned, the early history of the era of "ideal cutting"
had several proponants of slightly differing cuts. One good
reference for these variants is Eric Bruton’s “Diamonds”. Some
of the variants discussed there aRe:
Tolkowsky, 1919: 53% table, 34.5 degree crown, and 40.75 degree pavilion
Johnson & Rosch, 1926: 56.1% table, 41.1 degree crown, 38.6 degree pavilion
Eppler, 1940: 56% table, 33.2 degree crown, 40.8 degree pavilion
Scan. D.N., 1970: 57.5% table,34.2 degree crown, 40.75 degree pavilion.
(note that Bruton lists angles as degrees and minutes, which I
sorta estimated above to decimal points. The decimal I’ve given
above is probably not precise, but is close enough for
discussion. I’m not gonna bother to calculate em exactly for ya
The above are only the most notable of the historic variants.
Several other researchers have also published variants, and
computer simulations have added their own twists of much of this.
Factors such as the notion that the viewers head will block some
light from reaching the stone, for example, had one author
modifying figures slightly. And some of the new cuts since WW2
have also attempted to address the visual appeal of the shape and
the facet placement as well as just optical calculations.
Anyway. 'nuff for now. If you want additional discussion on
it, Bruton is a good place to start your reading…
Hope this helps.