Why Are Rainbows Circular?
Short and sweet answer: Because raindrops are spherical
The popular conception of a raindrop is what we call a "tear drop:" pointed at the top and round on the bottom. But a droplet of water tends to round itself out when nothing else is around it, unless its wind resistance, but that can be discussed elsewhere. This tendency to become spherical is due to the surface tension of the water, and because water particles are attracted one to another, so all parts of the H2O droplet are drawn in as close to the center as possible.
Next, there's the issue of refraction by the water droplet. You've seen how a prism refracts white light and separates it into its component colors. Within white light are various wavelengths of energy. The human eye/brain system can detect the different wavelengths and can therefore interpret them uniquely. The end result is - we see colors. Some wavelengths are stronger than others. When light passes through glass, it tends to slow down. If light passes through glass at an angle, it tends to bend the light as well. Some wavelengths, being stronger, will bend less than others. Think of light waves as a series of dominoes, as shown in Figure 2. While the dominoes are marching along in a vertical attitude, then they're going straight ahead. But if they run into a piece of glass at an angle, as shown here, the foot of the first domino will strike the glass and tend to tip over toward the glass. It's then facing downward a little, and will therefore continue through the glass at that downward angle. When it leaves the glass, the foot of the domino will be the first to exit, so it will speed up before the topside of the domino. Therefore, it will continue on in the same direction it was going before it entered the glass, but at a lower level. This is why when we look at objects in a glass of water, or a fish in a stream, they are not where we think they are. If you were to cut the glass so that the top of each domino leaves the glass, then the dominoes (light rays) will continue to bend downwards, and because each color has a different resistance to this bend, the colors will spread further apart. This is why a prism, being triangular, can separate light into its component colors.
A water droplet does the same thing as a prism, but with one variation: after the light enters the droplet, some of it bounces off its inner surface. The back of the droplet acts like a mirror. Look at the diagram (Fig. 1) to the right, and you will see how the various light rays bend on entering the water, then, after being reflected off the back, are bended further as they leave the droplet (I left out some of the in-between colors to not jumple them together). Red is the strongest, so it bends the least. This puts the red coming out of the bottom of the droplet.
In the diagram, there's a text that says "We see red on the top." One may wonder at that, considering that red is coming out the bottom of the droplet. So do it this way: Right now, the eye is receiving the violet rays. In order to see the red rays, what must you do? You must raise the drop of water. The eye won't see the red until the drop of water is higher up. Therefore, those droplets that are higher up, or above those whose violet rays are seen, are the ones showing you the red part. This explains why red appears at the top of all rainbows.
Light enters each drop of water at all levels, not just where the diagram shows. But the more you approach the center, the more you'll see that the rays are bending less, due to the more vertical attitude of the walls of the droplet. For this reason, colors are concentrated basically in their own general refracted angles, thus showing the distinct bands. If you were to look head-on into the droplet with the sun behind you, there would be colorful rings coming out at you. When light enters the droplet right through its center point, then it will bounce straight out again, because the walls of the droplet are basically vertical at this point. This means that the colors won't separate, and you'll see white light. Think of this the next time you look at a rainbow: It will be brighter within the circle of the rainbow than outside of it.
Back to the rainbow's curvature: because colors are coming out of each raindrop in a cone shape, then in order to keep seeing the same color in one drop as you move it, you will have to move that drop in an arch. The arch is inverted as it comes out to you, which means you have to move it up and over in order to keep seeing that same color.
You could also try this: The mouse pad on my computer has a light that goes on when I freeze the pad so that when I type, I won't move the cursor if I accidentally touch it. If you have such a light on your computer, draw an inverted arch on a piece of paper, then slide the line over that light. While you're moving the paper, put one finger at any point on that inverted arch. You'll see that your finger has drawn an imaginary regular rainbow-type arch.
You don't see droplets of water moving in arches, when you look at a rainbow, and you don't need to, because there will be a droplet of water at any point at all times, if there's constant rain.
Great Hub - Photos of Different Types of Rainbows:
If you saw a rainbow from an airplane, and if you were high enough (which depends on how close the rainstorm is), then you'd see a full circular rainbow. If you were on a building, you wouldn't see the whole thing, because the sun needs to be behind you in order to see a rainbow, and the building would block it at some point.
Sometimes you can see a double-rainbow. The next time you see one, note that the red band is inside the arch, this time. This is due to a double reflection inside the raindrop. In other words, light not only bounces off the back of each droplet, but it can bounce off the inner front side as well, then off the back again before emerging in refracted angles. Just as two mirrors will put your right arm to your left, so will a double-reflection in a raindrop put the red band on the bottom of a secondary rainbow.
I hope I have given you something that will help you find more joy and discovery in this world when you look at your next rainbow.