How are rainbows made?

Physics Forums. January 5, 2016, written by anorlunda

For several years, I have been contemplating this beautiful picture by photographer Brian McPhee. I have a personal interest in the photograph because that boat is my year round home. I also have a scientific interest in the photograph because of what it teaches me about rainbow physics. The simplest explanation of rainbow physics is based on internal reflections in the near-spherical shape of a raindrop….

credit: Brian McPhee

Look carefully at the photo with the boat. You will see that the sky inside the arc is much brighter than the sky outside the arc. Some scientists claim that no such effect exists, but it’s pretty plain in the picture. The explanation is that raindrops inside the arc reflect sunlight toward me, while drops outside the arc reflect sunlight away from me. The colors appear in the transition region where only certain colors are reflected towards my eye.

More challenging physics comes from the image of the rainbow seen on the surface of the water. At first, I assumed that it was a reflection of the rainbow in the sky, just like reflections of blue sky and white clouds one sees on a calm day in a reflecting pool.

But then I came across Can Rainbows Cast Reflections? on the web site of noted astronomer Bob Berman. Paraphrasing Berman. “No, they do not. Rainbows are not 3D objects and they do not cast reflections. In the water you see a different rainbow, not a reflection.”

I spent a lot of time puzzling over that, because I didn’t understand Berman’s explanation. I also doubted its truth because I’m sure that I have seen rainbows in the rear view mirror as I drive. It sounds like the Hollywood version of vampires that don’t make reflections in mirrors.

At first, I thought that Berman meant that the image in the water was sunlight hitting the surface and creating a rainbow effect as it was refracted back to my eye. But no, that won’t work because water in the lake is not in the form of spherical droplets.

After much thinking, I think I’ve got it. No vampire magic is required. The colored light you see from a rainbow is not omnidirectional, it is a unidirectional beam aimed at your eye.

By analogy, imagine a man at the far end of a hall of mirrors holding a laser pointer pointed at your eye (assume a laser suitably attenuated for safety). The mirrors on the walls, ceiling and floor of this hall will show many images of the man, but they will not show the red dot of the laser because the laser beam doesn’t hit those mirrors.

However, if you turn your back, step to the side, and hold up a rear view mirror, you’ll see both the man and the red dot. That is because the rear view mirror is inside the cone of light from the laser pointer.

So, to say that the red dot (or the rainbow) does reflect, and that it does not reflect are both true statements depending on which mirror it refers to. Yet, the image of the man appears in all the mirrors. The man is a 3D object, but the red dot is not….

Read the rest of the article here: Rainbow reflections: rainbows are not vampires

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A related article with a good (and short) explanation:

Reflected Rainbows: Atmospheric Optics

And the original post which inspired this:

Can rainbows cast reflections? By SkyManBob

…Bob Berman

{regarding a reflection of a rainbow seen in a mirror} How can we tell if it’s the same rainbow?

First: Every rainbow is a set of refractions and reflections precisely beamed in one direction — the eye of the observer. The person next to you is at the apex of a different set of light rays emanating from different droplets, making it a separate rainbow on two counts.

Second, the rainbow seen in a mirror is coming from a different part of the sky where the raindrops may be smaller or bigger or incomplete, changing the appearance (larger drops makes the rainbow more vivid, while robbing it of blue.)

Third, try it with a nearby rainbow like from a lawn sprinkler a few feet away. Now have someone hold a mirror. You’ll see the spray but no rainbow at all in this reflection….

…A traffic light sends photons in all directions. But a rainbow sends its light only to your retina, and nowhere else.

A person next to you is receiving the photons from an entirely separate rainbow (meaning a different set of raindrops, which may have different properties from the ones you are seeing.)