Namib Rainbow

Captured by Luc Perrot on a very stormy day in the Namib Desert of southern Africa.   The average rainfall grades from only 5mm per year near the barren Atlantic coast to ~100mm inland.   The actual rainfall is quite variable.    

Virga likely made this rainbow leaving the desert unwetted.    The many supernumerary fringes inside the main primary bow testify to small droplets of uniform size.  Many or all would evaporate before reaching the ground.

Image ©Luc Perrot, shown with permission
Reflection caustics
Rays through a raindrop. The bright arcs are caustics.

Caustics around shadows of petals floating on water.

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Supernumeraries are diffraction effects associated with a light caustic.

Light rays reflected once inside a raindrop form a primary rainbow. The once reflected rays emerge in a number of directions. As they do so they fold over and intersect each other. The surface where the rays cluster and intersect most densely marks the rainbow’s bright rim.

It is a caustic sheet that divides space where there are no rays and where rays intersect.

Caustics occur elsewhere, below sunlit wavy water giving dancing ripples along swimming pools or in stream beds, in the atmosphere to give strongly twinkling stars and in strong gravitational lensing of galaxies.

Close to the raindrop caustic sheet, each intersecting ray/wave pair coalesces and interferes. Coincident wave crests give brightness, out of phase crests give darkness. The result is a set of light and dark diffraction fringes parallel to the caustic sheet – The rainbow’s supernumerary arcs.