Analysis of rainbows (Part I)
- David Chandler
Rainbows are caused by light that enters a water droplet, bends upon entering, reflects off the back surface, and bends again, symmetrically as it exits. Some of the light simply goes straight through. Some reflects several times, but the beam that undergoes a single reflection inside the drop is the one that creates what we know as a rainbow. This demo allows you to experiment with the single and double reflection beams, which produce the primary and secondary rainbows.
In the single reflection case, notice: --If the beam enters through the center, it reflects straignt back. As you sweep further from the center, the beam deflects to the side. The more you displace the beam, the more it deflects until you come to a place where deflection is maximum. At this point the beam further offsets cause the beam to deflect less. --If you have both colors turned on notice that the red and violet rays follow close to the same path but red refracts as it enters and leaves the droplet a little less than the violet. The result is that the maximum deflection is a little greater for red than violet. --There is a checkbox that displays the maximum deflection on both sides. Since all the colors reflect back inside the cone, the droplet scatters back white light. However at the surface of the scatter cone the colors separate out. --Notice that only the red rays reach the maximum deflection for red, but both red and violet reach the maximum for violet. Therefore we would expect the rainbow to produce a clear red, but progressively more washed-out colors toward the violet. --Notice that if you consider rays beyond maximum defletion they reflect into the cone. Each of these rays is paired up with another ray prior to maximum deflection. The paths they travel inside the droplet are different, so the waves interfere. The result is interference colors: the alternating greens and purples (non spectral colors) that you would see in a soap bubble or an oil slick. In the double-reflection case, notice: --Light entering near the center of the droplet scatters forward instead of back. As the entering beam is offset from the center it deflects from the forward direction until it reaches a maximum angle from the forward direction, or minimum angle from the sun. --Notice that red, again, has a larger maximum deflection, measured from the forward direction, or smaller maximum deflection, measured from the backward direction, so the order of colors appears reversed. A second demonstration will show you how this analysis produces the rainbow itself.