The geometry for the secondary bow is similar except that there are two internal reflections inside the drop. This geometry results in the appearance of the secondary rainbow at an angular distance of about 51 degrees, outside the primary bow. The secondary rainbow is much less brilliant than the primary because each time a ray crosses the surface of a drop from either side, part of it is reflected and part is refracted. Tertiary bows are apparently seen only rarely for three reasons. First, they appear as a circle at an angular distance of about 40 degrees from the sun.
Few people think to look in the direction of the sun when they are viewing an ordinary rainbow.