What is the reason for the rainbows to be circular?

[Robertoalva]

a friend of mine asked me this question after i told her that the rainbows were a phenomenon made by the sun and the rain, and also told her, that the rainbow, in fact was a full circle, but it seems to be an arch because the other half of the rainbow is "underground" and so she asked me why it was circular and not a square, or a rectangle.

 

[H2Bro]

I'd explain it to her like this.

Take a pair of compasses (the kind you use to draw circles etc, not magnetic). Place the point on the paper and make an angle of ~40 degrees. Rotate the pencil around the center and draw a circle. Pretend the center point is the rays of light and the paper is a wall of water droplets. The line of the circle you made is the area where incoming light will get bounced around inside the droplets and separated then reflected back to you.

Now, why is it a circle? Seems obvious when you do it yourself. The area with a separation of 40 degrees from the incoming light makes a circle.

I once saw a full rainbow. It was from a plane as we descended towards some cloud cover. At first it was really broad, then as we got lower to the clouds it converged around the shadow of the plane, then the shadow of the plane blocked it out entirely.

 

[acesuv]

Because rainbows are caused by such a particular light angle (40-42 degrees) relative to the observer, only a certain strip of the sky will appear to be a rainbow. Light is able to enter the observer's eye from up, down, left, right, and any other direction in between. If light from the sun were only to enter the observer's eye from the bottom, then the observer would see a straight rainbow band (or something that isn't a circle at least). Essentially what I'm trying to say is, there are only certain paths that light can take in order to appear as a rainbow, and those paths are within 40-42 degrees of the observer's line of sight.

I hope this helps - I may have done a bad job explaining this.

 

[Robertoalva]

Thanks! both explanations are very good! thank you!

 

[Bobbywhy]

I once saw a full rainbow. It was from a plane as we descended towards some cloud cover. At first it was really broad, then as we got lower to the clouds it converged around the shadow of the plane, then the shadow of the plane blocked it out entirely.

“A rainbow gets its traditional semicircle shape from the horizon, which makes it seem as if it is half a circle. So when the same atmospheric conditions that create a rainbow are observed from an airplane, a rainbow can appear to be a full circle. This is called a glory, which NASA defines as an optical phenomenon that “looks like small, circular rainbows of interlocking colors.””

http://www.mnn.com/earth-matters/climate-weather/photos/10-stunning-images-of-rainbows-and-their-less-famous-cousins-4

 

[A.T.]

"...a rainbow are observed from an airplane, a rainbow can appear to be a full circle. This is called a glory..."

That's is not quite correct. Full rainbows and glories are not the same thing.

http://www.badastronomy.com/bad/news/marilyn3.html

the glory is not due to the simple refraction of light like a rainbow; the light is also "back-scattered".

They also look quite different (angular size and order of colors):

Full rainbow (http://en.wikipedia.org/wiki/Rainbow):

http://linein.org/blog/wp-content/uploads/2007/02/circle_rainbow.jpg

Glory (http://en.wikipedia.org/wiki/Glory_(optical_phenomenon)):

http://www.weatherquesting.com/2008-03-17-glory.jpg

 

[A.T.]

she asked me why it was circular and not a square, or a rectangle.

You could create other shapes, if:
- the raindrops where not spherically symmetrical, but had more distinct reflection directions.
and:
- you could orient the raindrops in certain ways depending on their position.

Ice crystals are less symmetric than drops, and if air resistance orients them in certain ways, they create non-circular shapes:

http://en.wikipedia.org/wiki/Light_pillar

 

[H2Bro]

What I saw was definitely a glory.However, is there a physical difference between the two i.e. in how the light is reflected, or is it just a difference in name?

 

[A.T.]

However, is there a physical difference between the two i.e. in how the light is reflected, or is it just a difference in name?

The physics of the rainbow is understood well. About the Glory there seems to be some debate. I'm not sure there is a final conclusion.
http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-27-16-1379
http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/rainbow_glory_review.pdf