How wide is the rainbow?

Light colour is made by its frequency and as you write correctly, light is a type of electromagnetic wave and is specific "only" by that it is about the frequencies we see. The frequency of the electromagnetic waves can be arbitrary and so our perception is limited to a narrow part of the spectrum (in frequencies 1014 Hz). We do not perceive the remaining frequencies with our eyes, but we know that they exist (e.g. the mentioned IR and UV radiation). Because it's still an electromagnetic wave, the invisible frequencies conduct even to us just as light. Therefore, the so-called dispersion, will also occur with IR or UV. This is a phenomenon in which light decomposes into different colours (more precisely frequencies) and which we can observe at the formation of the rainbow. This phenomenon is caused by the fact that refraction index (a quantity that describes how the light, as it passes from one environment to another, refracts) depends on the light frequency. In general, the higher the frequency of a given colour, the more it refracts. And because the individual colours break at a different angle, we can observe the mentioned rainbow. This phenomenon occurs in any electromagnetic wave, therefore we could see an infrared arc over the red colour of the rainbow and an ultraviolet radiation arc under the purple colour of the rainbow. This is a physical simplification. In fact, all the substances have the ability to absorb radiation and this ability is not the same for all frequencies (e.g. here). Even though water absorbs the least regarding visible light, it absorbs significantly more in other areas. Therefore, the dispersion at other frequencies would not be that noticeable. The more the frequency differs from visible light, the less radiation would pass through the drops of water and the less noticeable the arch would be on the rainbow for a given frequency. And you need to realize that, for example, infrared light has a frequency range of approx. 1,000 times higher than visible light, therefore, without absorption, the infrared band would be 1,000 times wider and would contain 1,000 times more "sub-colours". The fact, that the IR and UV frequencies are also included in the rainbow, can be seen, for example, here.