One of my favorite websites, Atmospheric Optics, says that secondary rainbows or “double rainbows” feature a secondary bow that is nearly always fainter than the primary, with colors reversed and more widely separated:
Light can be reflected more than once inside a raindrop. Rays escaping after two reflections make a secondary bow.
The secondary has a radius of 51º and lies some 9º outside the primary bow. It is broader, 1.8X the width of the primary, and its colours are reversed so that the reds of the two bows always face one another. The secondary has 43% of the total brightness of the primary but its surface brightness is lower than that because its light is spread over its greater angular extent. The primary and secondary are are concentric, sharing the antisolar point for a center.
Steve took this photo last month & you can see more in his Michigan Skyscapes gallery on Flickr.
Lots more rainbows on Michigan in Pictures!