The Mie algorithm assumes that the incident light is in the form of a plane wave (e.g. from a point source of light at infinite distance). 

Natural phenomena, such as rainbows or glories, are caused by light from the sun or, more rarely, from the moon.  The sun and the moon are circular light sources with a diameter of about 0.5°, rather than point sources.

The above control in the MiePlot program selects the size of the light source.  Fig. 1 compares MiePlot calculations of a monochromatic primary "rainbow".  The red line shows the results for a point source of light, whilst the black line shows the results for the Sun (0.5° diameter source).

The main rainbow occurs around 138.6° with supernumeraries at 140.2°, 141.3°, 142.3° and so on.  The averaging processes caused by the  0.5° source remove most of the "unnatural" ripples predicted for a point source.