Have you ever wondered how would the rainbow look like as seen by an animal that has different vision spectrum than human? Just posing this simple question should lead to a quick conclusion that we see just a part of the rainbow – the part that shines with the colors we can perceive. The rainbow extends both into infrared and into ultraviolet and the only reason we can’t see it, is because our eyes can’t perceive these “colors.”
If you were able to see all parts of the electromagnetic spectrum, you would see that the rainbow is made of a number of separated arcs of different width and brightness. This is because the Earth’s atmosphere is opaque to many light frequencies, for example high energy ultraviolet and most of the infrared spectrum. Also, keep in mind that the reason why rainbow emerges in the first place is because light rays going through water are scattered. Anything that cannot be scattered by water droplets is then out of the picture too. This includes some microwaves (water is opaque to microwaves, this is why microwaves boil water, duh!) and radio waves (anything with wavelength comparable to or exceeding the size of a droplet cannot be scattered by it).
As a matter of fact, if the lens in your eye was not opaque to ultraviolet light, you would be able to see it (and some people do, after removal of their lenses)! An interesting fact is that ultraviolet is not perceived by cones (which are the cells responsible for perceiving color) but lower wavelength ultraviolet is perceived by rods (which are the cells which perceive light intensity). Thus, if not for the lens, something glowing in ultraviolet would just look brighter, but would not give it any distinct color you could name. Your brain would not be able to distinguish between something glowing green and ultraviolet and something brighter glowing just green (or glowing green and white). If you looked at the rainbow, the arc next to violet would just make the colors of the background brighter.