What Makes a Rainbow?

Quick self-test to check if you really understand what makes a rainbow

Looking at Meric's diagram http://www.freecoders.co.uk/pics/rainbow1.jpg which correctly shows a light ray entering a raindrop at the top and exiting as separate colours below, it is true that the blue ray exits ABOVE the red ray. Can you see in your mind why the outer (upper) edge of the rainbow therefore appears red? If you can't, this may be one of those lovely, humbling, enlightening moments when we discover that we actually don't understand something we've been "explaining" for years.

Try thinking of a tall column of distant raindrops, into which parallel, horizontal rays of sunlight are shining, above your head with the sun behind you. Now can you see that the drops sending red rays back down to you are higher than the drops sending blue rays back down to you...? Which raindrops appear red and which raindrops appear blue?

The shadow of your head is always at the centre of the rainbow, and the imaginary raindrop-column can be pivoted in your mind around that point to sweep out the arc of the rainbow.

Few people notice how strikingly brighter the sky appears inside the arc, presumably because textbook diagrams make no reference to what is otherwise very obvious. It never ceases to amaze me how much 'explanations' condition, and often limit, what we educated people actually SEE.
http://www.brantacan.co.uk/images/Rainbow.jpg

ian@interactives.co.uk
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http://www.interactives.co.uk
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Give people facts and you feed their minds for an hour.
Awaken curiosity and they feed their own minds for a lifetime.
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Ian Russell

...but there is a crucial link missing between the two which makes this a very partial explanation. The diagram shows only one ray entering the drop, but in reality the drop is illuminated over its entire cross-section by parallel rays from the Sun. So you don't get a single spectrum leaving the drop, you get a whole pile of them, overlapping each other to various degrees, each corresponding to a different point of entry of a ray of light to the drop. You now need to explain why this optical mess still results in a nice tidy rainbow.

If you look at the exit angles of rays as a function of where they enter the drop, an interesting pattern emerges. A ray aimed exactly at the centre of the drop will be (partially) reflected straight back. Rays off-axis emerge at an angle from the drop, and as you move the entry point further off-axis, the angle of deviation increases. However this rate of increase slows down, until, with rays aimed near the edge of the drop, the angle of deviation reaches a maximum of about 40 degrees, and then starts to decline again for rays even further off-axis. The result is that, of all of the rays entering the drop at different places, surprisingly many of them exit the drop at an angle of about 40 degrees. So evenly-illuminated raindrops preferentially reflect light back at about 40 degrees, and this angle varies a little with wavelength, being greater for red and less for blue.

        At this point we can rejoin Ian's explanation:

        >Now can you see that the drops sending red rays back down to
        >you are higher than the drops sending blue rays back down to
you...?

At the same time we get an explanation for why the sky inside of the rainbow is lighter than the sky outside. Rays entering a raindrop are reflected back at all angles up to about 40 degrees, but at no greater angles (unless they undergo 2 internal reflections), so no raindrop more than about 40 degrees from the centre of the bow reflects sunlight into the observers eye.

The rainbow should be considered as a disc of light with a bright rim.

Ben Craven
Glasgow Science Centre