Sun halos and sun dogs are very different things. Similar to sun halos, sun dogs form when ice crystals with diameters larger than 30 micrometers form and lie flat on the broad end of the crystal. Light double refracts through the ice crystal, but because of the different size and orientation, a brighter "spot" is now visible within the halo. But ice crystal orientation is important: if they are randomly-oriented, then just a halo will appear. If the ice crystals are lying flat on the broad end of the crystal, then sun dogs will form as well as the halo.
A mix of chemistry, physics and geometry are the main components for sun halos.
Recall that the atmosphere is a mix of gases, including oxygen, nitrogen and water vapor. At high enough altitudes in the sky, the water vapor condenses and then freezes into ice crystals. As sunlight passes through the ice crystals, the geometry of the crystals cause the light to refract, similar to what happens when light passes through a prism.
The process works for any celestial light source, which means moon halos form under the same physical and geometrical properties. In addition, the process is similar to how rainbows are formed, which is why colors can sometimes be seen in the rainbow.According to the University of Illinois at Urbana-Champaign, randomly-oriented hexagonal ice crystals with diameters less than 20.5 micrometers are responsible for the halo observed in the sky. This geometric size and shape causes light to undergo two refractions, or bends, as the light passes through the ice crystal. Once the second bend is made, the light appears as a halo in the sky.
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