So I've seen lots of rainbows. And on more than one occasion, I've seen a ring around the moon and even around the sun at mid day. What I don't understand is why these rings around the moon or sun don't appear prismatic like I would expect them to be.
Quadrillian
There actually are colours (ie prismatic) in the rings around the moon and around the sun. Just a few days ago I was shown a beautiful picture of a coloured ring around the sun. I have often seen rings around the moon at night, and unless my eyes are playing tricks, there are colours in that too.
But some of the other answers here are (at least partially) correct. Rings around the sun tend to be formed by ice crystals. Personally I find that rings around the moon are caused by normal water clouds most of the time. But maybe I live in an atypical part of the world! 8---)
Rainbows and haloes are all really different manifestations of the same laws of optics involving reflection and refraction combined with dispersion. So the colour effects are present in all these apparitions. Just sometimes the colours are more noticeable than at other times.
Cheers!
quantumclaustrophobe
Actually, it sort of *is* a rainbow.... or, an 'ice'bow, anyway - it's usually formed due to ice crystals high in the atmosphere; a rainbow forms due to how light refracts through rain droplets; the ring around the moon is due to the same reason - only, it's not water but ice.
oyubir
In fact, yes, it is.
But first, there is a scale problem. It is thiner. And you notice far more the discontinuity in the brighness between the two areas (inside and outside the ring). That also exist with raibows. But few people notice it, because the frontier (the rainbox is thicker).
Another reason is, of course, because the light from the moon is not as intense. So you don't see color as well. And besides, is already quite shifted.
But with a very bright moon, you can clearly see the rainbow
See those:
http://en.es-static.us/upl/2016/11/supermoon-11-14-2016-Sheryl-R-Garrison-Idaho-e1479205813436.jpg
http://en.es-static.us/upl/2014/11/moon-halo-north-dakota-e1425569741200.jpg
(for the second one, clearly, the settings of the camera must help. It wasn't probably so visible with naked eye).
Those ring, are, roughly, a kind of rainbow anyway (forming with ice hexagonal crystal), and not with spherical drop of water. But yet, there is a dispersion of the light.
Anonymous
There is no water there to form the 'rainbow' effect.
OldHippie
Because the moon has no atmosphere. Because there's no moisture. https://scijinks.gov/rainbow/