Date: Thursday, August 22, 2002
Why is a rainbow curved/round?
A rainbow is round because the process is based on angles. Light from the
sun hits the little water droplets after a rain. The water droplets act
like little prisms. Different colors are sent out at different angles. The
sun must be behind you. Imagine a narrow triangle. The narrow angle is at
the water drop. One side points toward the sun. One side points toward
your eye. The drops for which this device works form a circle. The center
of this circle lines up with you and the sun. If the Earth were not in the
way, a rainbow would be a complete circle. This is why you can never find
"the golden pot at the end of the rainbow". A rainbow is really a complete
Dr. Ken Mellendorf
Illinois Central College
This one was a "toughie". I had to do a little looking. I had plenty of
info on "why" rainbows, but not so much on "why round" rainbows. This is
from Hewitt, Suchocki, and Hewitt's Conceptual Physical Science, second
edition, p 293. It is published by Addison, Wesley, Longman, copyright1999.
(You might try your local library if you wish to learn more; and if you want
to see the really good diagrams that Mr. Hewitt draws.) Anyway, here goes:
Why does the light dispersed by the raindrops form a bow? The answer to
this involves a bit of geometry. First of all, a rainbow is not the flat
two-dimensional arc it appears to be. It appears flat for the same reason a
spherical burst of fireworks high in the sky appears as a disk-because of a
lack of distance cues. The rainbow you see is actually a three-dimensional
cone with the tip (apex) at your eye. Consider a glass cone,the shape of
those paper cones you sometimes see at drinking fountains. If you held the
tip of such a glass cone against your eye, what would you see? You would see
the glass as a circle. Likewise with a rainbow. All the drops that
disperse the rainbow's light toward you lie in the shape of a cone-a cone of
different layers with drops that deflect red to your eye on the outside,
orange beneath the red, yellow beneath the orange, and so on all the way to
violet on the inner conical surface. The thicker the region containing the
water drops, the thicker conical edge that you look through, and the more
vivid the rainbow.
Your cone of vision that intersects the cloud of drops that creates your
rainbow is different from that of a person next to you. So when a friend
says, "Look at the pretty rainbow," you can reply, "Okay, move aside so I
can see it too." Everybody sees his or her own personal rainbow.
I hope that casts "light" on your rainbow query.
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Update: June 2012