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You see a rainbow when the sky in front of
is full of raindrops and the sun is at your back. The parallel rays
from the sun pass over your head and strike the raindrops, which
act like prisms. As a ray of light enters the drop, it is broken
into its consistuent colors red, orange, yellow, green, blue, and
violet. Each of these colored rays then strike the back wall of
the raindrop and is reflected back toward the front. These
reflected colored rays leave the raindrop at a certain angle,
and they can be seen only when they enter the eye at the same
angle; just as a small object can be seen in a tiny mirror only
when the viewer moves so that the object's reflected image
enters the eye at a certain angle. Therefore, in order to see
the colored rays reflected out of a single raindrop, the eye,
the sun, and the raindrop must be at one specific angle. And
to see the reflected rays coming from millios of raindrops, this
angle of reflection must be exactly the same for each drop.
If you were asked to arrange several million raindrops so that the
the angle between the sun, the drop and the viewer's eye was always
the same, you would find that you had to arrange the drops in a
circle. A circle is the only arrangement that would allow the angle
to stay the same. To see this, imagine a cone placed flat-end down
in a drinking glass. Note that the angle between the sides of the
cone and the sides of the glass remain the same only because the cone
is circular. Any changes in the shape of the cone would clearly change
the angle. In this analogy, the sides of the glass represent the
parallel rays of the sun, the bottom rim of the glass represents the
field of raindrops, the sides of the cone are reflected rays of colored
lights, and the tip of the cone is the viewer's eye.
This means even though all the raindrops before you are reflecting
the colors of the rainbow, your eye can only see those that are arranged
in a circle. And you can only see half of the circle that appears
above the horizon.
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