Faceting limits

By Bruce
L. Harding
Holden, Massachusetts, USA
Copyright GIA 





Figures 1
(click image for big view) 
Figures 1 through 8 show a grid which represents all
combinations of pavilion slopes from 35° to 45° and
bezel slopes from 0° to 60°. Pavilion slopes greater
then 45° are not considered in this initial discussion but
will be described in future articles as they apply to certain
facets.
It is easier to define that which
is bad about a gem than that which is good, so the object of
this study is to delete areas of the grid which represent poor
designs. Dark shading will be used for the worst conditions,
medium shading for those which are less severe, and light shading
for minor faults. "Best" designs will then lie in
the areas of lightest shading. 


If the pavilion slope is less
than the critical angle, no reflections can be seen through
the table when looking into it perpendicularly; furthermore,
reflections through the table cannot be seen from more then
one side of the pavilion in other positions.
This "dead" center condition
is very undesirable so pavilion slopes less than the critical
angle are shaded dark on the grid, as shown for peridot in Figure
1. 



Figure 2 
Rays which are reflected to the
viewer`s eye must come from directions which missed his head.
Figure 2 shows that at a viewing distance of one foot,
as when examining a stone prior to purchase, the angle (or divergence)
between incident and reflected directions of the same ray must
be at least 10°; otherwise the viewer will see reflections
of himself. 



Figures
3a 

Figures
3b
(click image for big view) 
Figure 3A shows a ray entering and leaving the table, being
reflected off both sides of the pavilion. For each pavilion
slope P the internal divergence D (=180°4P) is constant
regardless of the ray angles. The corresponding external divergence
is larger and varies according to the refractive index of
the material and the ray angles; it is minimum when it is
symmetrical as shown in Figure 3A.
For this minimum external divergence
to be 10°, the pavilion slope is about 1.5° more or
less than 45°. Slopes between these values produce less
divergence, so that they are shaded dark in Figure 3B.




Figures
4a 

Figures
4b
(click image for big view) 
Figure 4A shows a ray entering the table perpendicularly,
which returns to the bezel at an angle BD to the bezel normal.
By refraction, the corresponding external angle must be B±10°
to provide the required minimum divergence of 10°.
Figure 4B shows plots of
the two bezel slopes which satisfy this condition for each pavilion
slope. Slope combinations between these plots produce divergence
less than 10deg;. Because a large portion of returned light
passes this way, this area is shaded dark. 

Rays which enter the bezel and
leave via the table follow paths identical to those described
above, except in the opposite direction; accordingly, the shaded
area of Figure 4B applies to these rays also. 
