A bout 15 years ago, I learned from a gemologist friend that the value of pearls is appraised by evaluating the following factors: Size; shape; colour and lustre (a term used for the quality of shinyness). The first three are easily quantified, but what about lustre? I decided to look into the problem as an intriguing piece of applied optics. Pearlescence? Iridescence? What optical phenomenon is responsible for the unique appearance of nacre (i.e. motherof-pearl)? The appearance of abalone shell, especially New Zealand Paua shell, gives a clue: Interference colours. So it must be something to do with the structure, maybe it is due to something like thin film interference? This is confirmed by scanning electron microscopysee Fig.1 – and explained by marine biologists as follows: Nacre consists of thin, tabular crystals of aragonite, which is Calcium Carbonate that the mollusk concentrates from seawater. But that is not all: aragonite normally forms needle-shaped crystals. However in seashells, it is constrained into tabular, platelet-shaped crystals by means of a protein secreted by the animal. This protein has dangling bonds with a spacing that is comparable with that of calcium carbonate molecules arranged in flat layers. So the biology of the situation constrains a change in crystal ‘architecture’ – from acicular, i.e. needle-shaped, to tabular. This, incidentally, gives the resulting composite structure quite remarkable mechanical strength, apart from the interesting optical properties. That seems to explain it, I thought: In abalone shells, the thickness of the “bricks” must be very uniform so that thin-film interference gives rise to iridescent colours. But what about ordinary nacre (mother-of-pearl) and indeed pearls themselves? My first thoughts were that maybe the layers are too thick or maybe of non-uniform thickness in ordinary nacre. I wasted a lot of time trying to calculate the reflection properties of thin films of slightly variable (i.e. poly-disperse) thickness. This turned out to be an interesting exercise, rather more difficult than I thought. I even enlisted the expert help of Professor John Lekner from Victoria University, New Zealand, who spent a brief Sabbatical with us in Melbourne and is a noted specialist in reflection phenomena, random matrices and so forth. It turned out to be a wild goose chase and eventually the real answer dawned on me and turned out to be much simpler than I had thought. Before coming to the real explanation, I must remind you why sugar, salt, snow, etc. are white. Rather surprisingly, many students and even more accomplished physicists are unaware of the answer. Starting with an analogy, the random walk of a drunk near a cliff-top, even if initially stepping away from the cliff face, inevitably ends up at the bottom of the cliff! In a completely analogous way, a photon (or a ray, if you prefer) entering a substance consisting of small transparent crystals gets randomly refracted (scattered) and ends up coming back to the surface, whence it emerges in some random direction, never to return to the bulk. This is a form of diffuse reflection, which – if the crystallites are totally non-absorbing – corresponds to 100% reflection. Even better than the best metallic mirrors! So, a white surface is a better reflector than a metallic surface. Even with a certain amount of absorption caused by impurities, this gives rise to strong diffuse reflection, hence the utility of white paint. The mean depth to which the photon (or ray) penetrates depends on the scattering power of the crystallites. This, in cartoon by melbourne artist Leunig
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