Atmospheric Optics from the UK is far and away the best website for rainbow science as well as other atmospheric optical phenomena. Regarding primary rainbows as seen in Noah’s photo from Frankfort, they say:
To see a rainbow we need sunshine and falling rain. Rainbows are rarer than might be thought … Halos occur much more frequently.
Early morning and late afternoon are the best times to see them because the sun must not be too high. Rainbows are always opposite the sun and their centres are below the horizon at the the antisolar point. The lower the sun the higher is the bow.
Red is always outermost in the primary bow with orange, yellow, green and blue within. Occasionally, when the raindrops are small, fainter supernumerary arcs of electric greens, pinks and purples lie just inside the main bow.
A rainbow is not just a set of coloured rings. The sky inside is bright because raindrops direct light there too. The primary bow is a shining disk brightening very strongly towards its rim.
Lots more rainbow information and more summer wallpaper on Michigan in Pictures!