The Crown
In a diamond, the crown and table facets act as windows, driving light return and ultimately determining the brightness of the diamond. The crown facet also acts as a prism to disperse light giving off fire and the size and angle of the crown facet primarily determines the amount of fire a diamond gives off.
The crown facet has a third purpose which is to bend light so that what you see through the crown is a slightly shifted version of what you would see through the table. This shapes the arrow heads that you see through the crown. The crown facet creates more virtual facets and contributes to the structured contrast pattern in a diamond increasing its brilliance and sparkle.
The Pavilion
The pavilion and lower girdle facets of a diamond act as mirrors and a diamond’s ability to act as a mirror is determined by its refractive index.
Refractive index basically determines the angle that light is bent at when it enters a diamond. The angle is important because a diamond can only act as a mirror when light hits it at an angle that is greater than its critical angle. Basically the higher the refractive index, the steeper a gemstone can be cut before it begins to leak light.
It’s not something you need to know, but for those who are interested, the critical angle in optics refers to the angle of incidence above which total internal reflection occurs. The angle of incidence is measured relative to the normal.
Let me explain how this works in a diamond.
In a diamond with a pavilion that’s too deep, light entering perpendicular to the table facet is never steep enough to leak away from the diamond through the first pavilion facet. The problem is that the first pavilion facet does not bend light enough so that it leaks away at the opposite pavilion.
In a diamond with too shallow a pavilion, the light entering the diamond through the crown is bent too much so that instead of bouncing across a second pavilion, light reflects off of the opposite crown facet before leaving the diamond through the pavilion facet.
In the normal or ‘ideal’ case, light enters the crown facet and is bent just the right amount so that it doesn’t leak away from the opposite pavilion but is returned to the observer through the table facet. What we are looking for is a combination of crown and pavilion facets that produces a balance between brightness and fire while avoiding unwanted light leakage at the same time.
Ideal Pavilion Angles
Marcel Tolkowsky calculated the optimum pavilion angle to be 40.75. But the interesting thing is that diamond cutters were cutting diamonds like this way before it was determined mathematically. What diamond cutters have been saying for generations is that beyond 41-degrees is considered too steep.
Retailers selling poorly cut diamonds will try to tell you that a 41-degree cliff is ridiculous, but we know that in physics there is a critical angle before light leaks. What happens in reality is not so much a cliff, but a smooth transition from strong to weaker light return as more light rays leak away.
The thing to remember is that the transition occurs around 41 degrees so unless you’re looking at a super-ideal diamond cut to 40.9 degrees, then you’re far safer to go with something closer to 40.75 degrees.
With the help of light ray tracing, researchers have determined that a pavilion angle that is shallower than 40.5 degrees is considered too shallow and will lead to light obstruction or even light leakage. A 40.5 degree pavilion angle will be rounded up to 40.6 in a GIA lab report. So now we have a range (40.6 – 41 degrees) of acceptable pavilion angles. This then becomes the starting point for determining the range of acceptable crown angles.
Ideal Crown Angles
The crown angle can compensate for the bending of light by the first pavilion. The general idea is that if the pavilion angle is steeper, then the crown has to be shallower to compensate and vice versa. This suggests that there is a single crown angle that maximises the light return for any given pavilion angle.
Marcel Tolkowsky calculated that the ideal case is a 34.5-degree crown paired with a 40.75-degree pavilion. What you need to know now is that for a diamond with a 40.6-degree pavilion angle that bends light too much, you need to have a steeper 35-degree crown angle in order to compensate. In the same way for a diamond with a 41-degree pavilion angle that doesn’t bend light enough, then you need to have a shallower 34-degree crown angle to compensate.
The above analysis is how I arrived at 34 – 35 degrees for the recommended crown angles in my How to Pick a Diamond tutorial. Now that we have a range of acceptable crown angles, you should be aware of the differences between a 34 and a 35-degree crown angle.
Shallow-end of the Ideal Crown Angle
Within this range, a shallow crown angle is expected to have better light return as it ensures that there’s no leakage from the diamond. But apart from brightness, varying the crown angle changes how the diamond exhibits fire by changing its dispersion.
Dispersion is a material property but it is also affected by the angle of incidence of light rays that hits the crown as it leaves the diamond. Light is dispersed less with a shallower crown angle so a diamond with a 34-degree crown angle has less fire than one with a 35-degree crown angle.
If you have a preference for a bright diamond and do not mind sacrificing fire, then you can choose a diamond with a 34-degree crown angle provided that it is paired with a 41-degree pavilion angle. Bear in mind that in this combination, you need to make sure the diamond has excellent optical symmetry. Diamonds with a shallow crown (<33.5 degrees) will have significantly less fire. With a shallow crown, there's the benefit of having better spread. However, it is important to be aware that diamonds with very shallow crown angles (<32.5 degrees) have a durability issue when coupled with thin girdles due to the increased risk of chipping at the girdle edge.
Steep-end of the Ideal Crown Angle
For a fixed table percentage, a steeper crown means that the crown is higher and the crown facets are larger. This means more incident light rays can fall onto the prism-like crowns generating more dispersion so the diamond will have more fire.
The trade-off of having a steeper crown angles is that the lower girdles tend to begin leaking light once you go over a 35-degree crown even if you have a 40.8-degree pavilion. This happens because the lower girdle angles are dependent on the pavilion angle and the lower girdle length and a steeper pavilion causes even steeper lower girdle facets.
Even with a 40.5-degree pavilion and shallow lower girdles, you really do not want the crown angle to be over 35.5 degrees.
According to standard assessments, a steep crown angle will disperse light away from the observer in the assessment. This means that although you may not be able to see the diamond’s fire, other people looking from an angle might think it has a lot of fire. Also, a higher crown means that a lot of the diamond’s weight goes into the crown height rather than the width and hence reduces its spread.
If we are talking about a 34.5/41 CA/PA combination vs a 34/41 CA/PA, my personal preference is the 34.5/41. For me, the trade-off of decreased light return is more than made up for in the increase in fire. This is because weaker light return under the table can have a positive effect in terms of the contrast of the diamond.
You will even find that some super-ideal diamonds have crowns that are closer to 34.8-degrees. This is done to improve the fire in the diamond even further and is only something that should be done in a precision cut diamond. This is why super-ideals seem to contradict the general idea that there should be an inverse relationship between the crown and the pavilion angles.
Contrast Pattern
Before I finish, I will briefly mention how the crown angle affects the contrast pattern of a diamond. To be honest, the crown angle has very little affect on the face up appearance. In general, a shallower crown will make the diamond a bit bigger for the same carat weight, as it has better spread. In terms of the virtual facets, the shallower the crown angle, the closer the arrowhead is to the arrow shaft. On the other hand, for very steep crowns (>42 degrees), the arrowhead may begin to separate from the arrow shaft. Within the range of GIA ex/AGS0, the crown angle does not have much affect on the face up view. Also, for very steep or very shallow crowns, the impact on the diamond’s profile view is probably a bigger concern.
Conclusion
In conclusion, the range of acceptable crown angles is 34 – 35 degrees and the range of acceptable pavilion angles is 40.5 – 41 degrees. The ideal CA/PA is not surprisingly half way in between the acceptable range at 34.5/40.75 degrees.
Diamonds with very shallow (<32.5) or very steep (>36.5) crown angles affect a diamond negatively either by decreasing its fire or brilliance. Very shallow crown angles are also be prone to chipping.
A shallow crown angle (33.5 – 34) can increase light return, but a shallow crown coupled with a shallow pavilion (<40.5) can also lead to light leakage. Shallow pavilions generally tend to increase light obstruction in a diamond. A steep (35.5 - 36.5) crown angle side can maximize the dispersion from that diamond, but a very steep crown (>36.5) makes a diamond smaller and may even change the contrast pattern of the diamond. If you find that you need some help evaluating your diamond’s proportions, please don’t hesitate to contact me for assistance.