Today at 1338 I saw part of a rainbow against what appeared to be
a clear blue sky. It extended from the horizon to an altitude of
about 10° then continued upwards against the backdrop of the rear end
of cloud from a shower retreating to the east. There must have been a
very thin area of rain falling, but it was not enough to noticeably
change the colour of the blue sky. When the bow disappeared (after no
more than about a minute) there was no change as far as I could detect
in the blueness of the sky yet the bow had been easily bright enough
to be seen.
It is all the more puzzling because one could argue if there is
sufficient density of reflecting surfaces, either by number or size,
to form a rainbow then that reflectance (and scattering) would be
enough to obscure a blue sky. Obviously not, and most intriguing.

Tudor Hughes, Warlingham, Surrey, 556 ft, 169 m.