If the geometry of the pavilion facets is such that light strikes them at an angle below the critical angle, it is refracted and leaks out of the pavilion, rather than being reflected and returned to the viewer through the crown of the gemstone. A very simple gemstone model can be employed with a ray tracer as a model to illustrate how light is leaked from the pavilion when its facet angles are too shallow or too steep. When incident light propagating through quartz strikes a pavilion facet at an angle below 40.49 degrees, it refracts and exits the stone through the pavilion, rather than being reflected and returned to the crown. Incident light striking a facet at an angle equal to the quartz's critical angle travels along the surface of the facet and is lost at the culet in this model. When incident light propagating through quartz strikes pavilion facets at an angle above 40.49 degrees, it is internally reflected and strikes another facet.
Reflection is a symmetrical phenomena, that is, the incident and reflected angles are equal.
The result when internally reflected light strikes the next facet in its path depends on its angle of incidence relative to that facet. If that angle is greater than the critical angle, the light is reflected once again. But if that angle is below the critical angle, the light gets refracted by the next facet and exits the stone through it. For angles exceeding 47 degrees, incident light is reflected when it strikes the first pavilion facet. However with pavilion angles above 47 degrees the geometry changes such that the reflected light strikes the second pavilion facet with an angle of incidence below the critical angle, becoming refracted and lost.