Should Rainbows Have Reflections?

By Timothy Raub Ph.D. — Dec 22, 2020
The rainbow that hung over Scotland’s Kingdom of Fife for a half-hour yesterday stunned me.

As I drove north, dark-gray haar stretched up, tumbled over, and rolled around: frozen wisps and bulges above broccoli-colored hills.  The fog was renewed by the cold water of the Firth of Tay and sustained by windless stillness.  Behind, the sun burnt through weaker haar on inland hills.  Approaching the solstice, its low illumination cast a yellow glow on glistening, dewy swales and green-brown braes.  The resulting rainbow was complete, crystal clear, and flanked by an inverted secondary rainbow on both sides.

So far, so beautiful.  But when I reached the Tay, I saw something new.  The Tay Road Bridge, almost 1.5 miles long, is a human feat worth marveling at.  Yesterday the bridge was mere foreground.  From a vantage near the commuter parking lot, beneath the bridge but perched 100 feet above the river, I saw the rainbow and its reflection.

Why is there a rainbow?  White sunlight bends through the surface of microscopic, suspended water droplets.  Different colors of light diffract more or diffract less, separating into a microscopic rainbow.  A tiny fraction of this light totally internally reflects on the backside, inner surface of the water droplet.  About a picosecond later, this internal rainbow emerges and diffracts once more, separating its color beams still further, and a few – only the least part of the original sunlight - aim straight at my eye.  Because there is a special angle (42°) between entering sunbeams and exiting color beams, and because the sky is full of water droplets, I see the rainbow arch everywhere those droplets happen to cast their light at my eye.  I don’t see any rainbow emerging from droplets whose doubly-diffracted, reflected color beams bounce back toward my daughter’s eye beside me or toward the broccoli plant in the hill next to us.

Why is there a reflection to this rainbow?  I have no idea.  Can you figure it out?

The reflection seems straight; it is not arched like the rainbow it seems to reflect.  Therefore I must only see reflections from the rainbow’s very end, somehow extended over the expanse of water between me and it.  However, no still water can reflect more than one ray path to one receiver.  The buildings’ reflections across the river are singular and clear.

At my college graduation long ago, Alan Alda, the actor and great enthusiast for science communication, exhorted us: “If you can’t explain your science to your grandparents, you don’t understand it!”  I cannot even explain this science to myself.

I’ve puzzled over this twenty-four hours.  Now I realize.  If it is possible to understand the reflection, that knowledge seems less beautiful than the mystery of unknowing.