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
Tabletotable rays blocked (Figure 3):
sin D/2 = RsinD/2 ... where: D = 4(45°P), D' = ±10°
Tabletobezel rays blocked, and vice versa (Figure 4):
sin (B)
= Rsin (BD) ... where:
= ±10°
Bezeltobezel rays blocked (Figure 5):
sin (B)
= Rsin (BD/2) ... where:
= ±5°
Internal reflection from bezel (Figure 6):
Bmax = +C
(Figure 7A) Bmin = C
(not illustrated)
Maximum pavilion ray angle (max
= 180°C3P):
Bmax = 180°3P Bmin = 180°2C3P
Mean bezeltobezel ray (
= D/2 = 90°2P):
Bmax = 90°+C2P Bmin = too low to matter
Minimum internal ray angle (min
= CP):
Bmax = 2CP Bmin = too low to matter
"Live center" seen by both eyes (Figure 8):
sin
= Rsin (CP) ... 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)
