Rainbow

Think back for a second to the last time you saw a rainbow. Where were you standing relative to the sun? Were you looking toward the sun or away from it? You were looking away from it.

In fact, the sun was directly behind you, while the rain was somewhere in front of you. The light from the sun was bouncing off the raindrops and reflecting back into your eyes. How is color seen? The colors are present because both reflection and refraction is taken place (see the drawing).

Notice in the drawing how the raindrop acts like a prism, splitting the white light from the sun (on the left) into it's component colors. For simplification, the red and the blue beams are shown.

When the white light from the sun hits the raindrop, the light is first refracted as it enters the raindrop. Then separate colors are reflected from the backside of the raindrop and refracted once again, due to the change of index of refraction between the water and the air. The angles at which each color emerges is obviously different (or else you wouldn't see different colors!): red light emerges at 42^° and blue light emerges at 40.6^° relative to the incoming ray of sunlight. This is due to the index of refraction which is greater for blue light and for red light.

Each raindrop is emitting the full spectrum of colors, but surely a normal rainbow is far too large to be created by just one raindrop! We find that we are seeing only one color (indeed, only one tiny beam of light!) from each raindrop. We must be seeing the refracted light contributed from many different raindrops. Within the arc of the rainbow, the rain drops farther in the rainbow contributes to blue, green and violet light and rain drops further in contributes to red, orange, and yellow light.

If we look at every raindrop within 40° of the antisolar line, we would see a circle of raindrops centered on the line. Unfortunately, the horizon blocks off most of the rain, so only the an arc or a bow is visible; however, some people have reported seeing full rainbows from airplanes and mountain-tops. Another example of a full rainbow is at the bottom of the waterfall where a complete circular rainbow would occur.

Remember that the rain does not fall in a flat sheet, but in varying distances from you. This causes the "rainbow circle" to form at varying distances. An interesting question to ask is: What shape is made by circles at varying distances from an apex (in this case, your eye)? Since the raindrops contribute to the rainbow you see they are all lie on a cone with its apex at your eye, the scientific jargon might say: The rainbow is an optical phenomenon caused by the refraction and reflection of light by the locus of raindrops between 40.6 and 42° of the observer's antisolar line.

Rainbow

One last thing to remember: when you see a rainbow, you are looking at the collected light from many raindrops which, for a fleeting moment, collectively produce a "cone of color" with its apex at your eye. If you move to the left or the right, you are looking at new raindrops, and hence, a new rainbow! If you are admiring a rainbow with a friend, you are both seeing different rainbows.

Each rainbow is your own.


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