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When I searched on the Internet for the reason of formation of rainbows, I got many explanations like this one & this. All the explanations consider only one spherical water droplet (like this one).

Why don't the refracted waves coming from the adjacent droplets interfere with each other? For example, why doesn't a red ray coincide with a violet ray coming from another droplet at a suitable position?

How are we able to see rainbows with distinct colors? Since there are thousands of raindrops in the sky when it is raining, shouldn't it be a mess due to overlapping of different wavelengths?

Please explain.

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Even when there are lots of droplets still rays of any particular color coming from different droplets would be parallel to each other. –  user10001 Aug 31 '12 at 14:33
    
@dushya Why is that so? Can you elaborate? –  Green Noob Aug 31 '12 at 14:53
    
Think of two droplets for example. Since source of light (sun) is very far away, so irrespective of different positions of these two droplets, the rays of white light entering into them would be parallel, and so reflected rays of same color would also be parallel. Look at second picture in @CrazyBuddy 's answer below. –  user10001 Aug 31 '12 at 15:15

3 Answers 3

There was a recent paper published in the computer graphics literature that discusses non-spherical raindrops and clearly explains a lot of real-world rainbow phenomena:

Sagdehi, et al, "Physically-based Simulation of Rainbows," ACM Transaction on Graphics 31(1), Jan 2012.

Here's the official web link to the paper: http://dl.acm.org/citation.cfm?id=2077341.2077344 But if you don't have an ACM Digital Library subscription, it's a paywall, so here's a link to the author's page which has a preprint available: http://zurich.disneyresearch.com/~wjarosz/publications/sadeghi11physically.html

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To understand the property of refraction through rainbows, first you could think Raindrops as falling prism-like objects... The same answer here - Refraction & Dispersion of light

(Wikipedia & Howstuffworks has a pretty good article on it...)

These images show the refraction and dispersion of light by raindrops (just like an optical prism). But, it has a small difference from a prism.. The refraction occurs twice inside a raindrop... (due to the spherical shape I think so). For a typical rainbow, the angle of refraction at which light would enter and exit the raindrop is 40°-42° for colors in the order violet-red. This 2° range is due to increasing wavelengths of different colors...

Single raindrop

Howstuffworks shows a good comparison for the image below:

When A disperses light, only the red light exits at the correct angle (42°) to travel to the observer's eyes. The other colored beams exit at a lower angle, so the observer doesn't see them. The sunlight will hit all the surrounding raindrops in the same way, so they will all bounce red light onto the observer. But, B is much lower in the sky, so it doesn't bounce red light to the observer. At its height, the violet light exits at the correct angle (40°) to travel to the observer's eye. All the drops surrounding B bounce light in the same way. The raindrops in between A and B all bounce different colors of light to the observer, so the observer sees the full color spectrum.

Rainbow due to collection of raindrops

Also If you were above the ground (at some pretty higher altitude), you would be able to see the rainbow as a full circle. On ground, only the arc of rainbow which is above the horizon is visible.

  • A rainbow doesn't depend upon where ever you are... Even if you're above the ground, you could be able to see the colors in the same order VIBGYOR... It depends on whether the sun is at the horizon or not, whether the environment has a fog, mist or rain

But, in case of Twinned rainbows, double reflection is supposed to happen... It depends upon the difference in size of the drops and the angle of refraction would be within 50-53° range... A wonderful thing is for a twinned rainbow, an inverted rainbow would be above the real one at some distance (each being separated by a common base...

Supernumerary rainbows have a collection of bright and dark bands from violet to red due to interference. At angles very close to the required rainbow angle, two paths of light through the droplet differ only slightly, and so the two rays interfere constructively. As the angle increases, the two rays follow paths of substantially different lengths. When the difference equals half of the wavelength, the interference is completely destructive. And at even larger angles, the beams reinforce again. The result is a periodic variation in the intensity of the scattered light, a series of alternately bright and dark bands.

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A nice lecture which maybe helps you is "Walter Lewin: MIT Physics Lecture: Electromagnetism - 31 - Rainbows". When i remember right your questions get mostly answered in this lecture.

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