The crown facet also acts as a prism to disperse light giving off fire. The size and the angle of the crown facet determine the amount of fire a diamond gives off. The crown’s third purpose 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 creates more virtual facets and contributes to the contrast pattern in a diamond.
Crown/Pavilion Relationship
Up to now, you may have thought that our aim is maximum light return. But what we are actually 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.
In a diamond, the crown and table facets act as windows and the pavilion and lower girdle facets act as mirrors. A diamond’s ability to act as a mirror is determined by the refractive index (RI).
The RI basically determines the angle light is bent 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 it’s critical angle.
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.
In a diamond with too steep a pavilion, 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.
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.
Critics say that this 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 the top of the line BGD (which is 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. So now we have a range (40.5 – 41 degrees) of normal pavilion angles. This then becomes the starting point for determining the range of normal 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 34.6-degree crown paired with a 40.75-degree pavilion. What you need to know now is that for a diamond with a 40.5-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 one arrives at 34 – 35 degrees for the recommended crown angles in the "picking a diamond" tutorial. Now that we have a range of normal 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.
The point is that 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. With a shallow crown, you get an added benefit that the diamond has better spread.
It is important to be aware that diamonds with very shallow crown angles 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 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.
However, according to standard assessments, a steep crown angle will disperse light away from the observer in the assessment. This will mean that you may not be able to see the fire, but other people who see your diamond in real life will think it has a lot of fire. 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 most, 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.
The only time it would recommended to have a 41-degree pavilion angle is when the diamond is precision cut to tight tolerances. However, if you are not looking for a H&A diamond and also do not have detailed measurements on the diamond, it is much safer to get a 34.5-degree crown angle with no other information available to you. It is also safer to get a 34-degree crown angle than a 41-degree crown angle if you’re going by the numbers on the lab report alone.
Contrast Pattern
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 ideal combination of crown and pavilion angle is 34.6 and 40.75 degrees respectively. 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 slightly shallow crown angle (32.5 – 34) can increase light return, but a very shallow crown coupled with a shallow pavilion (<40.5) will also lead to light leakage. A slightly steep (35 - 36.5) crown angle side can maximise the dispersion from that diamond, but a very steep crown makes a diamond smaller and may even change the contrast pattern of the diamond.