What is the colour of a peacock's feather?

D. Indumathi, The Institute of Mathematical Sciences, Chennai

``A peacock's feather has many colours,'' is the obvious answer to the question in the title. It turns out that a peacock's feathers are actually coloured brown due to melanin.
Then what causes the brilliant colours we associate with a peacock? The answer to this question first came from the scientists Isaac Newton and Robert Hooke many centuries before. The answer is ``structural colouration'', a phenomenon due to wave interference.
Wave Interference
You may have learnt that light can be thought of as a wave, just like water waves, with crests and troughs (peaks and valleys). The spacing between two peaks or two troughs is called the wave-length of the wave. Different colours of light have different wavelengths and they all travel at the same speed. 
When two identical sets of light waves travel in the same space in the same direction, they can add to each other or cancel out, depending on whether the peaks of each match (left side of Fig. 1) or whether the peak of one overlaps the trough of the other wave (right side of Fig 1). In the figure, the original waves are shown below and their resultant wave is shown at the top. Here both the waves have the same wave-length and so correspond to the same colour. If they had different wave-lengths they would never match exactly and so there would be a partial addition or cancellation of the two colours.

Iridescence
An oil film on the surface of a road, or the surface of a soap bubble has two surfaces which are very close together (because the film is thin). You may have noticed that such films also show several beautiful colours which appear to shimmer and change as you observe them from different angles. This happens because the light falling on the surface can reflect from both the top and bottom surface. Since the angle of reflection from both surfaces is the same, both the reflected waves of light are travelling in the same space, in the same direction. But the two waves have travelled different distances (as seen from Fig. 2) and so their peaks and troughs may not match exactly. This depends on the angle and the colour (wave-length) of the light.
For instance let us assume that you are watching the bubble and it is red in colour. This means that for this angle, the waves of red light reflected from the two surfaces have matched to give a strongly red colour. The waves of other colours do not match well and so more or less cancel out. If you look at it from different angles, different colours will be visible. This observation of shimmering colours that change with angle of observation is called iridescence.

Structural Colouration
This is a phrase that means that the colour comes from the structure of an object and not its pigmentation. An example is the iridiscence of a peacock feather. The feathers have several parallel lines on them formed by parallel thin layers which are microstructures not visible to the human eye.
The peacock feather has many branches, with ``twigs'' coming off them; these are called ``barbules''. The reflections from the front and back of these barbules interfere to give the colours we see. This was investigated in detail by researchers at Fudan University in China and Osaka University in Japan. They took photos of the barbules at very high magnification to see these effects.

50 times magnification
A ProScope is a handheld microscope that attaches to a computer via its USB slot. The software activates the ProScope which enables you to capture single snap shots. These images aretaken at timed intervals. 
The rows of colored elements are visible at 50 times magnification in a ProScope. See Fig. 3. These "barbules" can be considered to be arranged in regular horizontal or vertical layers.

100 times magnification
At 100 times magnification, the variations in the filaments are more evident and so the colors seem to shimmer. See Fig. 4. The visible color will be different at different angles of view. The structures which produce the colors have an array spacing of about 150 nm. (1 nm is 1/1000000000 m).

Other colourations
Structures in nature can be more complicated and elaborate than just a single thin film. For instance, many films can be stacked up to give strong iridescence. Each mechanism offers a specific solution to the problem of creating a bright colour or combination of colours visible from different directions. For example, diffraction is another property associated with light. When light falls on structures that have a regular or periodic arrangement, it can split into several beams, each with different colours. The skeletons of many insects contain chitin. Layers of chitin and air together makes a diffraction grating that gives rise to the iridescent colours of various butterfly wings.
Fig. 5 shows a butterfly wing at different magnifications. The rows of chitin can be clearly seen in the bottom part of the figure. This microstructur of chitin acts as a diffraction grating and gives the beautiful colour to butterfly wings.

Variable structures
In both cases, the animal has fixed structures that cause the colouration. In some animals, the structures are not fixed but can be changed. For example, in sea animals such as squid, there are reversible proteins which can switch between two shapes or configurations, depending on electric charge. One configuration is tighter than another and so the layer spacing changes and hence the colour that is reflected from the surface. The squid uses this to change its colour rapidly for camouflaging itself when prey is near. The blue-ringed octopus does something similar, contracting its muscles and changing to yellow colour with bright blue rings when provoked.
So next time you see an iridiscent butterfly or bird winging its way past you with its brilliant colours, think of the wonderful and marvelous properties of light!

Sources:
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/peacock.html
https://en.wikipedia.org/wiki/Structural_coloration