The spectrum ranges from radio waves at the long end to gamma rays at the short end. In between are microwaves, IR, visible, UV and X-rays. All part of one spectrum.
IR was obviously part of the visible spectrum from the way it was discovered. But who figured out that X-rays, gamma rays, etc. were all electromagnetic radiation? And how did they do it?
Well, both the X-ray and gamma ray stories are rather messy.
In the case of X-rays, the overwhelming prejudice was, not only that they were vibrations of the aether, they were longitudinal vibrations. This was the opinion of Roentgen in his original paper and it was quickly backed up by the likes of FitzGerald, Boltzmann and Oliver Lodge. So while the early concensus was that this was EM radiation, it wasn’t quite analogous to visible light (which, on all interpretations, is transverse). Even in 1896 we find J.J. Thomson declaring “Though there is no direct evidence that the Roentgen rays are a kind of light, there are no properties of the rays that are not possessed by some variety of light.” The sticking point seems to be whether X-rays reflected and refracted as light. As a partial result, in 1906 Barkla showed that you could get partial polarisation of X-rays. But it was only in 1912 that von Laue, Friedrich and Knipping published the results that showed that X-rays refracted off crystals. That seems to have killed the debate.
Gamma rays are different in that the phenomenon they could possibly be subsumed under was beta rays. Rutherford still though they were just such a particularly energetic form of beta rays in 1902. The problem became that while beta rays could be deflected in a magnetic field (c.f. Thomson’s experiments on the electron a decade earlier), it became increasingly clear that this wasn’t as easy with gamma rays. Yet even in 1912, while believing that gamma rays were akin to X-rays, Rutherford still allowed that they could be different. But in 1914 he and Andrade showed that gamma rays reflected from crystals.
The endgame in both cases was thus rather similar: how did they interact with crystals.
The main source for the above is Inward Bound (Oxford, 1986) by Pais. Rather conventional, but thorough for the period in question.
And a further question. How did they figure that light is an electromagnetic wave? Once it was obvious it wasn’t a wave in the ether, it must be a wave in something. But who got the idea it was alternating magnetic and electric fields?
With radio waves, it was a case of Hertz deliberately looking for electromagnetic radiation of this type. Maxwell had already suggested that visible light was alternating magnetic and electric fields, on the basis of his general description of electromagnetism. From what came to be called Maxwell’s equations, he’d shown that such an interaction between magnetic and electric fields would propagate at a speed close to the experimentally determined speed of light. Maxwell thus suggested that that was what light was. What Hertz did was realise, from Maxwell’s work, that you could build pieces of electrical equipment to generate and detect such waves. It so happened that the wavelengths involved were those associated with what we now call radio waves. No doubt if Hertz’s experiment had been able to generate visible wavelengths, he’d have been happier. After all, he was trying to prove Maxwell right and what better proof could there have been than to have directly generated visible light from electrical equipment. As it was, he was generating and detecting radio waves.
On the further question, well Maxwell (and Hertz) already thought that light was an electromagnetic wave. (Indeed, offhand, I’m pretty sure that Faraday had already suggested something like this.) The problem is that he thought that an electromagnetic wave was a wave in the aether/ether.
The key shift is post-1905 and Einstein. He makes this idea of EM waves being waves in a substance irrelevant. That gives way to the modern conception of fields that just are. Electric and magnetic fields don’t summarise some mechanical substructure; electric and magnetic fields are just examples of the handful of fields that pervade the universe.
It actually strikes me that there’s a quite a profound historical issue here. Plenty of people describe the before and after, but, for all the literature on the history of relativity, I can’t think of any attempt to construct an account of how this shift from field as aether disturbance to field as field happened in detail.