Wednesday, September 9, 2015

Double Supernumerary Rainbow

Double rainbow at sunset (Osokorky district, Kyiv). This is a panoramic image made from three pics taken using Canon IXUS 132 [08 SEP 2015 ~18:06 EEST]

Note that colors of the fainter secondary rainbow are in reverse order (because of double reflection of sunlight inside the raindrops -- see graphical explanation at the end).



The bright primary rainbow is supernumerary: you can see additional narrow faint rainbow(s) on the inner side of the primary one; this effect is better seen in the picture with enhanced contrast:


An appearance of the supernumerary rainbow is explained by interference of sunrays:
It is not possible to explain their existence using classical geometric optics. The alternating faint rainbows are caused by interference between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in phase, reinforcing each other through constructive interference, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interference, and creating a gap. Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow. Supernumerary rainbows are clearest when raindrops are small and of uniform size. [https://en.wikipedia.org/wiki/Rainbow]
Here is an explanation how primary and secondary rainbows appear.
In the figure beneath paths of rays, which form primary and secondary rainbows are shown (from Wikipedia):
(7) primary rainbow; (8) secondary rainbow

The next figure is René Descartes' sketch of how primary and secondary rainbows are formed (from Wikipedia):