Aug 30, 2009
Can rainbows cast reflections?
Many people are puzzled by my writing that a rainbow cannot cast its reflection. Some say they’ve seen rainbows and reflections, and wonder if I’m wrong, or else maybe I meant something else.
Nope. It’s true. You cannot see a rainbow and the reflection of that rainbow.
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.
Try this link to an image and good explanation.
The point is, you CAN see a person and her reflection; the reflection is that person viewed from a different angle. Since a rainbow is not a real 3-D object, but just light rays aimed at your eyes, it has neither a reflection or a shadow. Making it simple, look at: http://www.atoptics.co.uk/rainbows/rflctd.htm
I came up with a design for an two-mirror optical setup using a combination of a half-silvered mirror and a standard mirror, through which any given photon reaching my eye from the rainbow has an equal chance of either being viewed directly or of reflecting off the half-silvered mirror, bouncing off the full mirror and back to my eye. Simply position yourself directly behind the half-silvered mirror and be able to look either directly through it, or at the regular mirror which will contain a 3-D, reflected, virtual image of the rainbow. Since I can see a reflection of the bow and the real bow simultaneously, and since I could even use the photons to create an interference pattern this would seem to meet the criteria of seeing truly the same bow truly reflected. Alternately, by using a half-silvered concave parabolic mirror, I could create a real image which could be project. This projection could be done simultaneously with my direct view through the half-silvered parabolic mirror.
If you make the claim that you cannot see the reflection of a rainbow, then you must also make the claim that you cannot see A rainbow at all. Your two eyes are in two different spacial locations and thus viewing the rainbow from two different angles and thus seeing two “different” rainbows. However for each eye, the top of the eye’s lens is in a different spacial location than the bottom of the eye’s lens. Thus, each eye actually sees an enormous number of rainbows. If I place a very small mirror directly under one eye, the reflection I see with that same eye is more similar than the image I see with my other eye. Thus to the extent we can claim to see a single rainbow, we can also claim that we can see the reflection of a rainbow.
After I read the thing about the rainbow I went to the internet and for several hours tried to come up with an answer that made sense. I gave up in frustration. I even ask the question on Yahoo. Nobody could answer it, except to repeat the same things I had read on the internet. Noplace could I find any mention of holding a mirror in my hand and looking over my shoulder to see if the rainbow could be seen. I live in western Oregon and thus I should not have to wait very long to try it myself. Then I happened to see the “skymanbob.com” on your page in Astronomy Magizine…..Now I understand. Thank you.
Bob, if I could see your point of view:
Do you meant that if I am looking a rainbow and someone close to me “see” the bow reflected in my eyes it is not the same bow that I am seeing?.
Or do you meant that in my eyes (even when they “converted” suddenly in glasses) nobody could see the bow (or the “same” bow) that I am seeing?.
Thanks a lot.
Excellent point. I never thought about a reflection in the observer’s eyes. But to answer: Yes, the reflection of the rainbow in your friend’s eyes is the same rainbow they are seeing. However, notice that you are then facing away from it, so YOU are still not seeing a rainbow and the reflection of that rainbow simultaneously. The whole thing has to do with angles, since a rainbow is nothing more than a converging group of light rays, reaching convergance at a camera or an eye but nowhere else. Hope this helps.
I loved your thought-provoking remark, which I read in “Astronomy”, Oct 2009 (yes, I’m living halfway around the world from the US). Your explanation is correct, of course, but the controversy shows just how careful you must be about how you state a fact. Your statement in “Astronomy” is wrong as it stands: “… vampires don’t have a reflection in a mirror. Neither do rainbows.” This is not the same as stating, for example: “The rainbow reflection that you see, is not that of the same rainbow that you see.”
I agree. And I wish I’d had more space to elaborate. However, I may be splitting hairs here, but: If a rainbow was sentient and could look in a mirror, in truth it would NOT see any reflection. Certainly not of itself, and probably of no other rainbow either, since the angles would be so off.