Diamonds and total internal reflection
In 1919 Marcel Tolkowsky found that if a diamond was cut too deep or too shallow then light would escape out the sides or bottom of the diamond instead of reflecting back upwards through the top of the diamond.
Cut the diamonds at the correct angle to use total internal reflection and he found you could greatly improve the brilliance, fire and sparkle of a diamond.
This understanding of total internal reflection has been used ever since when cutting diamonds.
The correct way to cut a diamond so all the light reflects back upwards. The angle of incidence must be greater than the critical angle to create total internal reflection.
Even from the sides the diamond if cut correctly can reflect the light upwards.
This diamond has been cut too shallow and much of the light is refracted out the back of the diamond. The angle of incidence `(theta\i)` is less than the critical angle `(theta\c)`.
This diamond has been cut too deep and again most of the light refracts through the underside of the diamond. The angle of incidence `(theta\i)` is less than the critical angle `(theta\i)` as it refracts through the boundary of diamond to air.