How is a rainbow formed?

Yes, I know that raindrops act as prisms, but exactly how are all those prism spectrums organized into a rainbow with red and green being where they are in the smaller prism spectrum?

This doesn’t really answer your question but it is relevant.

Using Snell’s law one can produce a function that computes the output angle of a ray of light given the input angle after the light refracts on the way into a water drop, reflects off the far side, and refracts again on the way out. This function has a critical point near the output angle of 42 degrees. What this means is that a wide range of input angles all have output angles near 42 degrees. This is the angle at which the rainbow appears in the sky.

Two internal reflections gives us a different function with a different critical point. This is where the dimmer and upside down double rainbow appears.

There are many examples with diagrams and photos on the web that will explain far better than I can in text.

But basically, sunlight gets bent by prisms. Raindrops act as a prism. The light always gets bent by the same angle, so to see light that’s been bent, we need to look a fixed number of degrees from the sun. Because we’re looking a fixed number of degrees from the sun, that makes a circle around the sun. Except half the circle would need to be under ground where there’s no rain and we can’t see anyway, so we just see an arc. White sunlight is actually made of all the colours of the spectrum, and the different colours get bent by slightly different amounts, making slightly different sized circles from colour to colour, giving the arc we see a multi coloured appearance.

Yeah. I forgot to add that refraction index is dependent on wavelength which is why the output angles for different colors of light are slightly different.

You totally should have titled this thread “how is rainbbow formed?”

Nitpick - since the angle from the sun is > 90 deg (actually 138 deg), it makes more sense to say it makes a circle around a point opposite to the sun.

Anyways, all you ever wanted to know about rainbows or any other optical atmospheric phenomena:

There are plenty of sites on rainbows and meteorological optics that will tell you exactly what’s going on, but here’s the brief rundown:
1.) Geometrical Optics – If you trace a light ray through a raindrop, one of the possible paths it can take is for light to enter at one point, get refracted (bent) and travel through the drop until it strikes the side. Some of the light will exit the drop at this point, but quite a bit will be reflected at the interface and travel again through the drop until it strikes the outside again. Some will continue to be reflected, but some will pass through the water/air interface and be refracted again.

Depending upon how far from the center of the drop the ray first strikes the raindrop (which is nearly a perfect sphere, and not “teardrop” shaped), the ray can emerge at any of several different angles. If you make a plot of the point it strikes the drop at against the emerging angle, you find that there is a maximum angle of divergence, and most of the light impinging on the raindrop exits at close to this angle. This is where the rainbow occurs. As others have noted, the angle of refraction is wavelength dependent, so different colors come out at slightly different angles. Furthermore, in this geometrical optics limit, the angle is completely independent of the size of the raindrop. So you get red light coming out about 42 degrees from the point (below the horizon, unless you;'re on a mountain or in a plane) on the sky opposite where the sun is. Orange is a little bit less, yellow at even less of an angle, and so on. Because the entire arrangement is symmetrical, you get a circle. Intercepted by the horizon, it forms an arc.

2.) Physical optics. – Because the function described above has a maximum, and because the raindrops are usually pretty small and the path length difference between these two paths is less than the coherence length of the light, the wavefront will interfere with itself. a rainbow is really an interference phenomenon, just as Young’s experiment is. In fact, Thomas Young pointed out the rainbow as another example of the wave nature of light. This is something that gets far too little treatment in Optics classes, and it deserves better, since it has a fully-developed solution, and illustrates some fascinating physics.

Unicorn farts.

From a mountain/tower top or an aircraft it is possible to see the entire circle. (well, most of it anyway, for the mountain) It forms around your shadow on a cloud, and is called a “glory”. This is only possible when you are above the cloud.

A Glory is not the same thing as a rainbow – it’s formed by a different mechanism, and forms a very tight circle around your shadow as seen on a cloudbank below. It used to be that you had to be on a mountain looking down into a valley of mist with the sun behind you to see these (as Wilson did, which inspired him to build his Cloud Chamber. Or as the name “Specttre of the Brocken” implies, the Brocken being an Alpine peak), but nowadays you can easily see these against the clouds below you on an airplane flight.
You can indeed see more of a circle if you’re elevated (as I note above), but you can only see a complete circle if you’re high enough and the sun is low enough to get the entire circle above the horizon. Except very close to sunset, that’s pretty hard in most cases.

They aren’t organized. You only see the ones that are in the exact position to form what your eyes interpret as a rainbow. The guy standing next to you sees a different rainbow.

A rainbow is centered exactly opposite the sun, exactly where your shadow would fall if there were a surface close enough for it to fall on. Normally when you see a rainbow, the mist is beyond the range of your umbra, and the mist is not solid enough to see it even if it were close enough.

When the local sun is high and bright enough to see your shadow, you will find that any rainbow seen will have it’s apparent center at your shadow’s head.

That’s the best fucking rainbow I’ve ever seen.

(Close enough, Clockwork? :D)

All of this is true, but doesn’t change the fact that a rainbow and a glory are two very different things. A rainbow is a circle that’s about 42 degrees from the anti-solar point. The glory is a very tight circle about 5-20 degrees that is very concentrated around the anti-solar point. The path of the rays through the drop is completely different from those in a rainbow.

In addition, rainbows aren’t seen in clouds, but are most visible with relatively large drops. Glories can easily be seen in mist or clouds with smaller drops.
And the appearances are clearly extremely different.



I saw one like that, once. I was commuting home from Stockton to Sacramento and it momentarily made me glad that I had an hour plus commute. I’d seen rainbows before, even complete doubles, but this thing GLOWED.

But what about double rainbows?

Ohhh… (Sob, sob, sob…) double rainbows man!

Sooo, beautiful. But what does it mean… ohhhhh… man.
Double rainbows!!!

Man, I hate being forgotton: What causes double rainbows? Why is the order of the colors reversed? - The Straight Dope