Rainbows over London

Imaged near sunset by Chris Tuckley. The highly reddened sunset rays have given an equally reddened rainbow. What is extraordinary is the number and wide spacing of the supernumerary bows inside the main primary.

©Chris Tuckley, shown with permission.


Atmospheric
Optics

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Supernumerary bows result from the wave nature of light. Waves radiating out in a particular direction to form a rainbow have taken two routes through a raindrop. The routes have different path lengths. Consequently the two outgoing waves can be in-step, out of step or at some state in between. In-step waves give brightness while out of phase waves cancel and produce no light.

As the deflection angle from the drop changes so does the phase condition of the two waves. The outcome is a set of interference fringes supernumeraries inside the primary bow.

The fringes are always generated but those from large drops they are closely spaced and the non-parallel rays from the sun blur them out. Smaller drops give wider spaced fringes but even then it is necessary for all the drops in the shower to be similarly sized if the fringes are to be visible.

This London bow was made by small raindrops, perhaps less than 0.5mm diameter. The supernumerary fringe spacing tends to increase with height indicating that higher up the drops were smaller.


Waves emerging in a particular direction have taken two different paths through the drop. The two waves are not always in phase. They interfere producing fringes inside the primary bow and outside the secondary