Skyman Bob Sets Me Straight

New Bern, NC

Long time readers of this blog are familiar with the picture above taken by Brian McPhee.  I blogged about it here.  Yesterday I was stunned to learn some very subtle points about physics that are evident in that photo.  I'll share them with you.

I learned these things at skymanbob.com in Bob Berman's blog.  Bob Berman is a famous astronomer and explainer.  The blog post's title was "Can Rainbows Cast Reflections?"  "Of course then can," I thought, "Just think of this rainbow picture on my own blog."  But I read further, and of course Bob was right.

Look more closely at the picture above.  You can not see recognizable reflections of the sky, or the clouds, or even of Tarwathie sitting in the foreground, but you can see a very recognizable rainbow image on the water surface.   What's going on?

First, a rippled water surface reflects light, but it does not reflect recognizable images very well.  It is analogous to a heap of broken mirror glass fragments.   In the extreme, it is like the surface of frosted glass.   So the surprising answer is that the image of the rainbow you see in the water is not a reflection, it is a segment of rainbow refracting sunlight back toward your eye.

Like a vampire in a Hollywood movie, a rainbow can not be reflected in a mirror.  Wow!  I never knew that before..  Here it is in Bob Berman's words.

If you and I look at a car, we both see the same object. But a rainbow is a specific set of reflections and refractions within water droplets that essentially appear on the surface of an invisible cone whose radius is 42 degrees, whose orientation is the antisolar point, and whose apex is your eye, and your eye alone.
An apparent rainbow reflection in a mirror or on a lake, is that of a different rainbow. It may not even look like yours, since if it intercepts larger droplets it will be brighter but also deficient in blue. It is a different rainbow. Moreover, if the rainbow you’re seeing is nearby (as from a lawn sprinkler) then a mirror just ten feet to either side of you will show no reflection of it at all — no matter how the mirror is angled. It’ll show the same water droplets but with no rainbow within it.

Try it sometime. Or at least, think about it, and you’ll understand why you can never see a rainbow and also the reflection of that same rainbow.

Some readers have noted that they’ve seen or captured rainbows using cameras or reflector telescopes. But I never said that photons from rainbows somehow cannot bounce off glass: In these cases you’re seeing the rainbow, but not simultaneously seeing its reflection. The central point is that you cannot see a rainbow AND this same rainbow’s reflection. That’s because any reflection of an object is that object viewed from a different angle — and a rainbow, not being a real 3D object, cannot be viewed from any other angle except exactly where your eye (or camera) is located, completing the required geometry.