How come some examples of structural coloration (like peacock feathers) only shows certain colors (blue-green to violet) but others (like pearls) shows any color if looked at from the right angle? (Answer should include talking about the spacing between reflecting structures)
color in bird feathers is primarily due to the way they selectively reflect certain wavelengths of light. The phenomenon is similar to the way a thin layer of oil on the surface of water can appear to be a variety of colors.
In the case of feathers, the different reflective surfaces are closely-spaced and the wavelengths of the reflected light can interfere with each-other—constructively and/or destructively. This causes very bright iridescent colors that appear and can change dramatically with only the slightest movement of the bird and its feathers.
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