Reflection occurs when light bounces off of the surface of the ice crystal and refraction occurs when sunlight is bent to a different direction or angle as it passes through the crystal and comes out a different side. Halos can occur at either 22 or 46 degree angles from the sun. A 22 degree halo occurs when the refracted light passes through the sides of ice columns and a 46 degree halo occurs when the light is refracted through one side and the end of an ice column. 22 degree halos are the more common because the small range of size of ice columns that is needed to produce a 46 degree halo.
Tangent arcs can take a wide variety of shapes and orientations around the halo.
Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.