When you spray water from a garden hose into the air, with the sun behind you, you see a rainbow which appears to stretch right across the sky, in the same way that rainbows form by normal rain appear. In the garden hose case, the water droplets are only a few feet in front of the observer. Is the image of a normal rainbow also only a few feet away or is it formed by droplets within the total volume of the rain shower? If this latter case is true, does the rainbow in fact form a complete circle that is cut off by the horizon? — RP, Solihull, England
A rainbow isn’t an image that originates at a specific distance away from your eyes. It consists of rays of colored light that travel at particular angles away from the water droplets that produce them. You see red light coming toward you from a certain angle because at that angle, the water droplets are all sending red light toward you. In the garden hose case, the water droplets are so densely arranged that they are able to create a brilliant rainbow in only a few meters of thickness. In a typical rainstorm, sunlight must travel through hundreds or thousands of meters of raindrops to produce an intense rainbow. When you look up toward the red arc of the normal rainbow, you are seeing light directed toward your eyes by millions of water droplets, some close and others distant, that are all sending a part of the red portion of the sunlight striking them toward you and the other wavelengths of sunlight elsewhere.
You are correct that a normal rainbow is cut off abruptly by the horizon and that it would continue down below to form a full circle if the ground weren’t in the way. People in airplanes sometimes see full 360° rainbows.