"Labradorescence" –  Intense colours shine from deep inside the mineral labradorite.  Imaged by Kevin Boyle.  ©Kevin Boyle, shown with permission.
 
Hold labradorite under a bright light and slowly rotate it. From deep within come flashes of peacock blue, greens, golds and rusts.

Labradorite is a feldspar, a sodium aluminium silicate with 50 to 70% of the sodium sites in the crystal lattice replaced by calcium. After it solidified from a melt, labradorite cooled and silicate compositions, albite NaAlSi3O8 and anorthite CaAl2Si2O8, that were miscible at high temperatures became incompatible and separated into two phases. The phases are arranged in stacked alternate layers or lamellae and it is these that produce the iridescent colours by multi-layer interference.

Labradorescence is an example of “structural colour” where hues derive not from pigment absorption but from wave interactions in nanostructures. These range in complexity from a single soap film to biological structures of astounding subtlety. The latter give the vivid hues of some butterfly wings, a peacock’s display and the silvery scales of fishes.

Interference across a single layer produces the colours of soap bubbles and oil films. Light striking the layer is part reflected from the front surface. Another part enters the film, reflects off the rear surface and leaves in the same direction as the front reflected wave.

The two outgoing waves combine. If their wave crests (shown red for positive and blue for negative at left) coincide then there is light. When they are out of phase there is destructive interference and there is darkness. The phase condition is wavelength dependent with the result that we see interference colours.

All this is enhanced when there are multiple layers. Light leaving the structure is the result of several reflections between layers, each with interference possibilities.

In Labradorite the alternate albite rich and anorthite rich layers have only a small difference in refractive index. Reflections at layer boundaries are weak and a large number of layers are needed to produce an intense reflection. This is an advantage because the bandwidth or wavelength range of the reflected light narrows and we see an almost pure colour. The bandwidth roughly halves for a doubling of the number of layers.  Tens perhaps hundreds of layers contribute to the intense colour flashes from deep within the stone.

Computing and predicting how multilayer films behave is complicated.  Not surprising considering the many branching network of possible wave paths to be considered.  Lord Rayleigh, the giant of optics and mathematical physics, developed a theory in 1917. Modern methods are numerical and are part of an important and growing area of optics and communications.

We can unweave the rainbow and for that matter a labradorite crystal also.   But contrary to poet Keats' oft quoted assertions, ‘charms [do not] fly at the mere touch of cold philosophy’. Scientific understanding enhances Nature’s wonder and beauty rather than clips or dulls it.

Atmospheric
Optics

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Single film interference:
Waves reflected from the two sides of the film combine and interfere.   In-phase waves give light.   The phase condition is wavelength and angle dependent. Hence we see coloured reflections in different directions.



Multiple film interference:
The interference principles are the same. There are more opportunities for interference. With the right layer thicknesses and properties, reflections of particular colours are intense and pure.