A sundog, or parhelion, is a rainbow-coloured patch of intense light that can often be seen to the right or left of the sun (sometimes on both sides) when it’s at a fairly low angle in the sky.
Often the sun is surrounded by a complete ice halo, but this is usually less distinct. The conditions obviously need to be clear, and (from our own amateur observation) there needs to be fairly thin, high cloud for the effect to form. We’ve observed them mostly in cold, calm weather.
Sun dogs are always red nearest the sun, progressing through the colours of the rainbow to violet on the outer edge. The effect can be breathtakingly bright, almost creating a second sun in the sky for a few minutes.
When I first found out about sundogs, I thought they must be quite rare, but once you’ve seen one and you know what to look for, you will see them quite frequently!
More information: Atmospheric Optics