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   Parhelic Circle Formation ~ A halo of many paths  

The parhelic circle is produced when sunlight or moonlight reflects from near vertical faces of ice crystals.

Plate, horizontal columns and Parry oriented crystals all make it.

The reflection from the outside of a crystal or one more times within it.

The parhelic circle appears simple yet more ray paths contribute to it than in any other halo. Some are very intricate.

The circle is white (or very nearly so) because the angle of the exit rays is almost always equal to that of the rays entering the crystal. There is therefore no net refraction and colour dispersion produced as the ray enters is cancelled on exit.

External and internal reflections make the parhelic circle. External reflections contribute most near the sun. Rays reflected once inside a crystal produce much of the halo intensity. Opposite the sun, rays internally reflected twice or more add their brightness. The relative contributions depend on the sun's altitude and the crystal thickness. Unfiltered (left) and filtered (right) fisheye HaloSim ray tracings for a 30 high sun.
  
 


External reflection       

Rays reflect off any near-vertical face. Most effective when rays graze the surface. They therefore contribute most near to the sun

1 internal reflection      

Rays enter a nearly horizontal upper face, reflect off a side face and leave through a lower face.
 

A route through side faces only. The ray path has right-left symmetry and the halo is white.

2 internal reflections      

The ray path is asymmetric, the entrance and exit rays make different angles to the faces. There is therefore net refraction and some separation of colours.

3 internal reflections      

A tortuous path contributing to intensity away from the sun.

5 internal reflections      

This ray travels right around the crystal. Another contributor far from the sun.

There are even more ray paths in plate crystals and further ones involving the near vertical end faces of column crystals!   Find them with HaloSim by using the ray filters and the ray tracer.