|White Dog & Blue Spot
Imaged by Kim Thomas at Salt Lake City, Utah on December 31, '09 with the sun 26° high.. ©Kim Thomas, shown with permission.
|When there are halos about, especially sundogs, look at right angles to the sun at the same level, Then cast your eye a little further away from the sun. A 120 degree parhelion might well be seen as a white patch.
They are not readily visible against a whitish sky and usually must be searched out. Not here - Kim’s shines brightly and hugely on the parhelic circle, both halos were generated by ice crystals in cirrus haze and thicker cloud wisps.
The 120° parhelion is formed by plate crystals. In one route, a ray enters the top face, reflects internally from two side faces and finally leaves through the lower face - path 1,3,8,2. The overall light deflection is always 120° regardless of the crystal orientation. The colour dispersions at ray entry and exit are in opposite directions and cancel to yield a white halo. The ray path needs several optically perfect faces, freedom from internal defects and thick plates. Therefore rare.
Blue Spot: The parhelic circle is similarly mostly generated by ray paths where there is only reflection or no net refraction. It is therefore white – but not always! Look at the extreme left of the upper image or that at lower right. There the parhelic circle becomes fainter and slightly bluish.
The colours and sudden fall off in brightness are linked. They are both readily visible in the HaloSim tracing using 60 million rays through relatively thick plate crystals. Two versions are at right, an all sky view centred on the zenith and one approximately centred on the camera direction.
The colour and brightness fall off arise from a transition between partial and total reflection within the crystal of rays contributing to the parhelic circle.
When a ray internally reaches a crystal face at a steep angle (close to the normal of the surface) a part is internally reflected and a part leaves the crystal.
As the angle of incidence becomes less steep a certain critical condition is reached (calculable from the refractive index) after which the reflection is total and no light leaves the crystal. This accounts for the sudden fall off in parhelic circle brightness.
And the blue spot? The critical condition is wavelength dependent and blue rays reach it farther from the sun.