The picture above was taken while I was cross-country skiing in Trollheimen, a Norwegian mountain region, a weekend late in November 2005. The picture is taken from an altidude of 1243 m, and the horizon is between 1400 and 1671 m and roughly 13 km away. The temperature was below zero and the wind was moderate. Note the pillar of light that rises vertically above the position where the sun has just disappeared below the horizon. This is called a sun pillar. It has the same width as the sun diameter, and was impressively sharp in this case. By clicking on the picture you will see a larger version where the solar diameter (0.54°) is indicated.
Sun pillars arise due to flat ice crystals that are falling slowly through the atmosphere. If the air is calm or the wind is steady most of the crystals will be oriented horizontally, perpendicular to the gravitational force (similar to a ship without any motors or sail, which after a while will end up perpendicular to the wind direction). Sunlight that is reflected from below these ice flakes will not change direction sideways, and we will therefore see the reflected light only vertically above the sun, appearing as a pilar on the sky. The less intesnse reflections that we can see to the left and right of the pillar must be reflected from ice crystals and other particles that are oriented more randomly, so that light is scattered in many directions. If you read the text below you will see that the crystals that contribute to the sun pilar must have an orientation that deviates from horizontal by less than 2 to 4 degrees.
Ice crystals can also produce other strange atmospheric phenomenons, like a halo (bright ring) around the sun with 22 degrees radius and "sun dogs", which are bright spots 22 degrees away from the sun on each side. These phenomenons are related to the special hexagonal symmetry of the ice crystals. If you follow the links at the bottom of this page you can read more about them and see example pictures .
The illustrations below show the ray traces for sunlight that are reflected towards an observer from different positions on the sky. The size of the crystals is strongly excagregated. The left figure shows the ray traces seen from a point far behind the observer. When viewed from this direction the reflecting surfaces of the crystals are perpendicular to the ray traces, and therefore parallell to circles with center at the sun position. The pilar is rather weak and diffuse near the top of the photo above, and the apparent width of the pilar seems to have increased to about twice the width near the horizon. The distance from the horizon to the edge of the picture is 7.2 degrees while one half solar diameter is 0.26 degrees, so that crystals that are one half solar diameter outside the "real" edge of the pilar must be tilted by 2.1 degrees (arcsin(0.26/7.2)) in order to reflect any sunlight to the observer. This means that a relatively large fraction of the crystals must be tilted by less than 2.1 degrees.
The figure to the right below illustrates that it is actually necessary with some spread in the crystal tilt for the pilar to be visible far above the horizon. Prallell rays from the sun are comming in from the right. The observer cannot see the sun directly due to the curvature of the earth. By studying the reflection angles relative to the crystal surfaces one may deduce that the crystal surfaces must tilt slightly towards the observer to guide the light towards her/him. Since the angle from the horizon to the top edge of the picture is 7.2 degrees, the crystals that contribute to the pilar near the top of the picture must tilt by about 7.2/2 = 3.6 degrees.
The pilar on the picture is much brighter near the horizon than at higher altitudes. On reason for this is that relatively few crystals have enough tilt to reflect from high altitudes. The most importan reason, however, is probably that we are looking throughmuch more of the atmosphere when looking close to the horizon than when looking higher up. Many more ice crystals will therefore contribute with reflections along a longer path.
Links and references
Erlend Rønnekleiv, www.eronn.net erlend.web&eronn.net [replace & with @]