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Halos and parhelia (more commonly known as sundogs or mock suns) are formed by refraction and reflection through ice crystals high in the atmosphere. They are surprisingly common once you start looking for them -- indeed, we'd both gone through our lives not seeing a single one, but since we saw the first we've been seeing one a week or so.
The best conditions for their formation are high, thin cirrus cloud on a sunny day. Both halos and sundogs can be coloured, like rainbows; sundogs can be extremely bright. Unlike rainbows, no rain is involved in their production.
There are many different halos, but by far the most common is a 22° circle around the sun. Surprisingly, the exact production mechanism of this most common halo is unclear. Circumzenithal arcs are like a short rainbow almost directly overhead (who looks there?), seen when the sun is fairly low; there is a rarer counterpart arc, below the sun when it's high. Sundogs are at the same height as the sun, 22° on either side; they are sometimes seen with part or all of a halo. One or both may be visible. They can be very bright and vividly coloured. To find them, stretch out your hand at arm's length -- from thumbtip to fingertip is about 22°.
As always, be very cautious when looking at or near the sun, especially through optical equipment (including camera viewfinders).
For further information about halos, visit the superb Atmospheric Optics web site. This site has many spectacular images -- look particularly for the shots of the astonishing 1999 halo display, seen at the South Pole -- and also has a halo simulation program (sadly only available for Windows platforms).
Click on an image for a full-size picture and description
Lunar 22° halo
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Scottish halo
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Partial halo
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Circumzenithal arc
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Sundog 1
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Sundog 2
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Sundog 3
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Double sundog
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