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Asked in GSEB Board July 2017 · Total internal reflection and optical fibres
Given: the sparkle of a cut diamond.
Idea: light that has entered a diamond meets the faces from the inside, so the question at each face is whether the light gets out or is thrown back.
Diamond has a very high refractive index, n=2.42, so its critical angle is small: sin C=1/(2.42)=0.413, giving C=24.4°.
Almost every ray inside strikes a face at more than 24.4° and is totally internally reflected.
The light bounces from facet to facet and finally escapes in a concentrated flash through the few faces it can cross — that flash is the glitter.
The cutter chooses the facet angles precisely so that this happens.
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