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Q & A: Why are rainbows curved as semicircles?

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Q:
Why does the rainbow seem curved as a semicircle?
- Anonymous
A:
Nice question! Rainbows are a product of sunlight passing through small droplets of water suspended in the atmosphere (or even falling through it!). Not only are they beautiful, but they are usually rare because you need a rainy day and a sunny day at the same time to make one appear -- the sun has to be shining from one part of the sky, and the rain in another part of the sky before a rainbow can appear.

The sunlight takes a complicated path through each water droplet. It comes in the side closest to the sun, bends because the index of refraction in water is bigger than that of air (you can see this effect by putting a pencil in a glass of water so that some of it sticks out and looking at it from different angles -- the pencil will apppear "broken" at the place it crosses the water surface). The sunlight, passing through the water droplet, bounces off the back surface of the droplet, travels back to the other side, and bends once again on its way out.

The reason why the rainbow is curved is because all the angles in the water drop have to be just right for the drop to send some sunlight to you, standing on the ground. So, with the sun *behind* you, only those water droplets that have the same angle formed by you, the drop, and the sun (this angle happens to be approximately 42 degrees) will contribute to the rainbow. Other droplets send their light somewhere else, and if you move to a different location, new droplets are needed to make the rainbow you see in the new location. This is why you canít go to the end of a rainbow to find the mythical leprechauns and pots of gold; anywhere you stand, the rainbow is formed by faraway drops of water reflecting and bending sunlight. The rainbow is curved because the set of all the raindrops that have the right angle between you, the drop, and the sun lie on a cone pointing at the sun with you at one tip. The rainbow may look semicircular if the sun is setting or rising (a good time to see a rainbow because the sunlight at that time can get under rain clouds because it is traveling horizontally). If the sun is higher in the sky, the earth gets in the way and you may see less than a semicircular rainbow.

The rainbow is colored because the water drops act like little prisms -- how much the light bends when it enters and exits the drop depends on its color, and light from the sun contains contributions from light of all colors. So that 42 degrees above is a bit different for red light and different still for blue light -- you have to look in a different place to see the red rainbow arc and the blue rainbow arc, so you see them as arcs in the sky of different sizes and the rainbow is striped with colors.

You can make your own rainbows with a lawn sprinkler or even a water spray-bottle that can make a fine mist. On a bright, sunny day with the sun at your back, spray some water in front of you in different directions to see where the best rainbows can be seen. Can you make one go all the way around in a circle? Rainbows crop up in the nicest places -- you can see them sometimes at the bottoms of waterfalls and even briefly in the splashes of divers at the swimming pool.

(republished on 08/01/06)

Follow-Up #1: missing link

Q:
it is to inform you that the link u have give is no longer available online so kindly remove the reference as it may cause inconvenience to others
- Anonymous
A:
Thanks- notes like this help us keep things up-to-date.

Mike W.

(published on 03/14/09)

Follow-Up #2: rainbows in space?

Q:
Would a rainbow still appear to arc in the vacuum of outer space? Does our atmosphere or the curvature of the earth have anything to do with it?
- Ben (age 32)
Salt Lake City, UT
A:

Rainbows are made by the way light curves in many small drops of water.  So unless you had a way to get a spray of little raindrops near you in space, you wouldn't see a rainbow. I think it would be hard to do, because any little random or systematic velocity that the drops had relative to you initially would soon carry them away.

Our atmosphere is important for a couple of reasons here. It includes the water vapor that forms rain drops when it coools at high altitude. The friction between the drops and the air then keeps them from falling out of the atmosphere more quickly.

The curvature of the Earth is indirectly connected. If the Earth's surface didn't curve then the Earth would be infinite. Its infinite gravity would make the whole situation impossible.

Mike W.


(published on 07/12/14)

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