Finding Rainbows

i-e161656a2f74f476de423583f4afd0bd-sm_rainbow.jpgGoogle the title phrase, and you’ll find a bunch of New Age twaddle. This is a physics blog, though, so here’s a reliable scientific method for finding the location of a rainbow, such as this one seen over Chateau Steelypips after the thunderstorms that went through earlier this evening (it was much brighter half a minute before the picture was taken, but faded as the camera was fetched):

  1. Stand so you can see your shadow in front of you.
  2. Spread the fingers on both hands, and hold them so your thumbs just touch.
  3. Hold your hands so one pinky finger is just on the head of your shadow.
  4. Keeping that finger where it is, swing your hands so the other pinky finger traces out an arc. If there’s a rainbow to be seen, it will appear more or less along that arc.

If you don’t want to wait for a convenient thunderstorm to produce a rainbow up in the sky, you can always test this with a garden hose. This offers the additional advantage of not producing giant piles of hail:

i-5a075819b2553abb636872c3e9262308-sm_hail.jpg

The spread-finger trick works because the arc of a rainbow is determined by the optics involved– the angle of the sun, the index of refraction of water– and appears at around 40 degrees from the path of a straight ray from the sun. This happens to be just about the width of two spread hands held at arm’s length, regardless of your size. My hands are considerably larger than Kate’s, for example, but her arms are considerably shorter than mine, so the angular size of a spread hand at arm’s length is roughly the same for both of us.

So, the next time you want to know where to look for a rainbow, you can use your hands to work it out.

(See also this video demonstration, which doesn’t go into the angular details, but does show that you need the sun at your back, and you can probably estimate the angle from the video.)