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Faceting limits

By Bruce L. Harding
Holden, Massachusetts, USA
Copyright GIA
 
Appendix table of contents

The following nomenclature and formulas were used in this analysis:

R = refractive index
C = critical angle (sinC =1/R)
D = internal divergence
D' = external divergence
P = pavilion slope
B = bezel slope
= internal ray angle
= external ray angle
T = table width
W = girdle width

Table-to-table rays blocked (Figure 3):
sin D/2 = RsinD/2 ... where: D = 4(45°-P), D' = 10°

Table-to-bezel rays blocked, and vice versa (Figure 4):
sin (B-) = Rsin (B-D) ... where: = 10°

Bezel-to-bezel rays blocked (Figure 5):
sin (B-) = Rsin (B-D/2) ... where: = 5°

Internal reflection from bezel (Figure 6):
Bmax = +C (Figure 7A) Bmin = -C (not illustrated)

Maximum pavilion ray angle (max = 180°-C-3P):
Bmax = 180°-3P Bmin = 180°-2C-3P

Mean bezel-to-bezel ray ( = D/2 = 90°-2P):
Bmax = 90°+C-2P Bmin = too low to matter

Minimum internal ray angle (min = C-P):
Bmax = 2C-P Bmin = too low to matter

"Live center" seen by both eyes (Figure 8):
sin = Rsin (C-P) ... where: = 6°

Maximum table size (Figure 9):
(T/W)max = tanC (tanP + tanB) / (tanC tanB +1)

Minimum table size (Figure 10):
(T/W)min = tan (tanP + tanB) / (tan tanB +1) ... where: sinB = R sin(B-)

Derivations of formulas will be provided upon request from the author:
Bruce Harding, 33 Anthony Drive,
Holden, Mass. 01520 (now 110 Maple Street, E. Brookfield, Mass. 01515)

 

 
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