Wonder Why Wednesday: How Big Is A Rainbow?

Rainbows are pretty amazing things. We have urban legends about them, viral videos featuring them, and even cereals based on them.

But how much do we really know about rainbows?

I, for one, know very little. I know they are colorful (kinda like hipsters) and they like to come out in the rain (kinda like hipsters).  But, honestly, I don’t spend much time thinking about them (unlike hipsters, apparently).

Until now.

The other day, my grandma sent me an email saying she had a suggestion for a Wonder Why Wednesday question. She said she was wondering about rainbows and if it is possible to measure the size of a rainbow. I am not sure what inspired her question (I like to imagine that it had something to do with her eating Lucky Charms), but I think it is a great one.

Let’s see if we can answer it for her.

Wonder Why Wednesday: How Big Is A Rainbow?

Before I could figure out if it is possible to measure a rainbow, I had to determine just exactly what a rainbow is. Here’s what I learned,

Rainbows appear when light originating from the sun is refracted and reflected by small water droplets suspended in the air.”

Next, I had to look up what refracted means.

After that, I learned that the size of a rainbow has more to do with how we see it than actual length. The size we see depends on three things: how many particles there are for light to refract off, the angle in which it reaches the eye, and any objects that obscure the view of the rainbow.

Finally, after much searching on the Internet, I learned that measuring the actual size of a rainbow is very, very difficult. One site puts it this way:

It’s probably not impossible, but it is difficult. A rainbow looks circular because it’s basically the circle where a cloud of rain droplets intersects with your cone of vision, like the circle on the end of an ice-cream cone. Imagine said ice-cream cone with the point in your eye (don’t actually try this experiment unless you’re looking for a career in piracy). Now make the cone bigger and bigger until the round end hits the cloud of raindrops that are reflecting the sun’s light. The big circle on the end of that cone is where the rainbow appears to be — as someone else pointed out, you can only see the top half of it (because the other half is below the surface of the earth). The raindrops reflect light at about a 40 degree angle, so you can calculate the diameter of the circle if you also know the height of the cone (because the height of the cone, the radius of the circle, and the 40 degree angle are all part of a right angled triangle). The challenge is knowing the height of the cone, which is how far away the cloud of raindrops is from you. If you can work that out then, yes, you can measure the diameter of the rainbow (diameter = (2*distanceToCloud) / tan 40).”

Now, if you are anything like me, your mind started to wander after you read ice cream cone. But he’s what I think we learned:

  • we only see half of a rainbow, the other half is underground
  • we can determine the size of a rainbow if we can figure out its height
  • to find out the height, we need to know how far we are from the cloud of raindrops
  • not sure how you do that, but if you can, then you use the following equation: diameter = (2*distanceToCloud) / tan 40

Got all that, Ma??

In short, rainbows are really complicated and figuring out their size is probably not worth our brainpower.


Sources: Scientific American, Ask Philosophers, Answers.com

Photo credit: Wikipedia