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Faceting limits

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

Bezel-to-Bezel Rays table of contents
Figure 5a
(click image for big view)
          Figure 5A shows a symmetrical ray entering one bezel and leaving via the other; its internal angles to the bezel normals are B-D/2. By refraction, the corresponding external angles must be B±5° to provide the required minimum divergence of 10°.
     Figure 5B shows plots of the two bezel slopes which satisfy this condition for each pavilion slope. Slope combinations between these plots produce divergence less than 10°. Because the major portion of returned light passes this way, this area is also shaded dark.
The Basic Faceting Chart table of contents
Figure 5b
(click image for big view)
        Figure 5B is the basic «faceting chart» which indicates the well-known critical angle limitation and the areas which violate the 10° minimum divergence imposed by the viewer`s head. These separate the chart into three unshaded areas which are labeled Zones A, B and C for simple reference.
     Most recommended designs lie in Zone A; those for refractive indexes from 1.6 to 1.7, however, lie in Zone B. This explains the odd discontinuity in faceting data which must have puzzled inquisitive faceters. It is curious that experimenters found their way into Zone B for these stones only. There are no commonly recommended designs in Zone C; however, it applies to the exceptional emerald which inspired this study.
     Note that the shading is intensified when one shaded area overlaps another; this indicates the worse situation of two bad conditions at the same design points.
     Additional criteria will now be added to this basic faceting chart.
Internal Reflections From the Bezel table of contents
Figure 6a
          Figure 6A shows an internal ray approaching the bezel at an angle to the gem axis. If its angle B- to the bezel normal is more than the critical angle C, it will be reflected back into the stone. The probability is that such rays will ultimately be lost through the pavilion (see future sequel), so such reflections are to be avoided as much as possible.
     The maximum angle of a ray reflected from the pavilion is 180°-C-3P; if this ray is reflected as shown in Figure 6A, then all rays reflected from the pavilion are reflected back by the bezel. Designs which cause this intolerable condition are indicated by the dark area in the upper right of Figure 6B.
      According to Figure 5A, a symmetrical bezel-to-bezel ray approaches the bezel at an angle B-D/2 to the bezel normal. If this angle is greater than the critical angle C, then all bezel-to-bezel rays are reflected because they cannot enter the first bezel at an angle which prevents such reflection from the second bezel. Designs which cause this bad condition are indicated by a medium-shaded diagonal area in Figure 6B.
Figure 6b
(click image for big view)
          Some rays will be reflected back by the bezel unless the minimum internal angle (= C-P) is not reflected. Designs corresponding to this limited back-reflection are indicated by the light-shaded diagonal area of Figure 6B; the area below this corresponds to designs with no internal reflections from the bezel, except for the following unusual situation.
     With very low bezel and pavilion slopes, it is possible to have max greater than B such that -B is greater than C. This causes reflections of some rays and is shown by a light shaded diagonal at the lower left for refractive indexes greater than 1.7.
© Octonus Software & MSU Gemological Center.