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# Where is a rainbow? Answered

As you may be aware, your reflection in a mirror appears to be behind the mirror.

But, where is a rainbow?

The Sun is over your shoulder, the cloud of raindrops is in front of you, but what is the apparent location of the rainbow?

Is it between the observer and the water droplets, in the same location as the water droplets, or behind the water droplets (from the POV of the observer)?

Or is it at some indefinably infinite location?

I should know this...

(a sketched-out ray diagram would be greatly appreciated)

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## 17 Replies

Take a look at a similar phenomenon: Simple reflection. The light is bounced off the mirror, but your eyes think the image is behind the mirror. Also keep in mind, the distance from the reflecting point is preserved in this illusion -- the distance between your eyes and the mirror plus the distance between the mirror and the reflected image. Even though it's in the wrong place, your eyes can still tell it's that distance away.
With rainbows, a water droplet acts as a mirror. The fact that the light is refracted is irrelevant and only complicates thinking -- suffice to say that because of refraction, the angle will be different. But the apparent distance remains the same -- that of the sun. You'll have to fly your RC helicopter 93 million miles before it's "in" the rainbow.
Probably the confusion comes from not being able to see past the thick curtain of rain or droplets that casts this reflection.

Kiteman (author)2010-06-22

But...

For a normal reflection, the rays are diverging from a (virtual) point.  It's the divergence that gives the impression of distance.

Looking at your second diagram, the rays are converging, and the rainbow is in front of the cloud.  For the bow to appear to be at any great distance, the rays should be parallel, or diverging minimally.

Where did you find that second diagram?

Kiteman (author)2011-07-20

Looking at this diagram again, a year late, I've realised that the rays are not converging, but that they have only included the rays that reach the eyes.

rojo.balloon (author)2011-07-19

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind at a low altitude angle. The light is first refracted entering the surface of the raindrop, reflected off the back of the drop, and again refracted as it leaves the drop.

Kiteman (author)2011-07-20

I was asking where the image of the rainbow appears to be.

Sorunome (author)2010-11-01

It is actually the watter drops, because the light is there spread out into the colores, that is wy a rainbow seems to apper neerer to you if the water that breaks the light is neerer to you. Thats what I think. :)

Kryptonite (author)2010-06-22

A rain bow (as you know) is white light being split through a prism. I think this should answer it.

porcupinemamma (author)2010-06-22

All I know is "ROY GBV" red orange yellow, green blue violet/indigo

PKM (author)2010-06-22

From what I think you mean judging by your example concerning the mirror reflection, I have the nasty feeling that it's a some kind of negative distance.

Bear with me- when you move your head to the left, objects in front of you appear to move to the right, due to parallax. The more they move in angle for a certain displacement of the observer, the closer they are. An object that doesn't appear to move at all when you move your head, like a star, is effectively at infinite distance.

A rainbow is centred on the shadow of your head cast by the sun. If you moved far enough to the left to observe parallax with the sun, your shadow would appear to move to your left, and with it the rainbow. I suspect this means the rainbow's location is actually behind you at the sun.

A simpler example is the effect you get when you are sufficiently far away from a concave shaving mirror for it to turn your image upside-down. The image, as well as being inverted, moves in "the wrong direction" in response to parallax.

Is that the answer you were looking for? The answer you can say with certainty it is not is in the raindrops forming the image- if that were the case you could find the end of a rainbow, leprechaun treasure and all.

Kiteman (author)2010-06-22

That does sound negative...

Maybe a clearer way of asking the question is;

If I flew a radio-controlled helicopter until it appeared to be in the colours of the rainbow, would the helicopter be between me and the raindrops, in the raindrops, or beyond the raindrops?

lemonie (author)2010-06-21

Where is dictated by the relative positions of the sun, water and observer (it's about 50o or something).
It's virtual really, the real "where" is "inside your head".

(You know where Wikipedia is)

L

Kiteman (author)2010-06-21

The angle Sun-Rain-Viewer is 42° - it's easy to find information on how a single raindrop generates a spectrum (it was the first lesson I ever taught as a student teacher!), but your eye only receives a single colour from each raindrop (dispersion means the other colours pass on either side of your head, so to speak).

I'm starting to wonder - are the rays from each raindrop effectively parallel?  If so, that would put the rainbow at "optical infinity".

(Why do I only think of these things late at night?)

lemonie (author)2010-06-21

No, the light is not parallel and there's a fixed (apparent) distance, which I haven't researched this morning before I finish coffee and leave...

L

Re-design (author)2010-06-21

I don't have an answer yet but I know a lot more about rainbows well at least I've read a lot about them.

Devrimm (author)2010-06-21

Mr. Kiteman; I really don't know about the physical part of the rain. But, I love to have a caffee and watch with all my quiet, while it is raining. I think ( becouse I saw so) they are dropping " parallel". I hope, it is important if they are falling parallel or not for you...

seandogue (author)2010-06-21

In the water in which you're seeing it. I believe there's a critical angle at which rainbows are visible, although I can no longer recall the exact number it was, I believe somewhere in the neighborhood of 55 degrees...Now, the problem is I don't remember if that's that angle of incidence form the observers pov or the sun inclination with respect to the water "column".

idk if any of these will help:

http://www.geom.uiuc.edu/apps/rainbow/

http://www.webexhibits.org/causesofcolor/13.html

I collected them using the following search "Geometry of rainbows"

best of luck!

JavaNut13 (author)2010-06-20

Isn't the rainbow colours (not colors, they don't work) reflecting off, or travelling through water droplets. So I guess it is located in the water, because if there is not water, the white light cannot split into multiple colours.