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   Supernumeraries & Drop Size

 
  Supernumerary bows and raindrop size.   Mouse over the slider to see the effect of changing raindrop size when the droplet size distribution is narrow**. The simulations were calculated by AirySim. The scale has steps of 1º.
  
 
   As drops become smaller, several things happen: supernumeraries become more widely spaced, the primary bow broadens, its colours become less saturated. Eventually there is no longer rainbow but instead a cloudbow or fogbow.

Supernumeraries are less obvious when the rain has drops of widely different sizes. Each drop size produces differently spaced fringes which overlap to a blur. The broader supernumeraries from smaller drops are more tolerant of variations in drop size.*  

The top of a rainbow often has more distinct supernumeraries than lower down. The drops higher up are possibly smaller and their size variation then has a less critical effect on the supernumerary bows' visibility than does the same percentage size variation in the larger drops lower down.

There is another another effect at the upper parts of a bow. Larger raindrops are slightly flattened and rays forming the top of a rainbow have to pass through the flattened vertical cross section. It so happens that when the drop size distribution is very broad, as in a shower, the combination of flattening and supernumerary spacing versus drop size produces a persistent fringe spacing of about 0.7°. The downside is that little information about the raindrop size can then be gained from the fringes. The effect does not occur at the base of the bow because those rays pass through the horizontal circular section of the flattened drops and the fringes of different spacings from the many sized drops overlap and cease to be visible.
  

The drop size distributions in the simulations above were set to preserve the visibility of about three supernumerary bows. Drops of 0.40 mm mean diameter had a standard deviation of 14%, drops of 0.86 mm diameter 6% and 1.50 mm drops 4%.
** Showers often have very wide drop size distributions and then, particularly at the top of the bow the droplet flattening effects described in the last paragraph operate.