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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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