How did James Clerk Maxwell conclude that Visible Light was a form of EM rays?

When studying the propagation of an Electromagnetic field, Maxwell noted that its speed was about the neighbourhood of that of visible light, and concluded that this was no coincidence. He hypothesised that Visible Light was part of an Electromagnetic Spectrum and then he predicted the existence of other waves*.

Now I am physics genius or a physics anything, but this seems, well a pretty big leap of faith. It could well be a coincidence. At that time Fizeau had come up with the first useful and reasonably accurate or the speed of light (320,000 km/s if memory serves, which is a bit faster than what it is actually at 299,000 km/s), but the differences should have tripped him up. What was the inspiration?

*In his day the wave theory was ascendant and the wave-particle duality was not known. Do other parts of the spectrum exhibit a similar duality?

I know this bit! Yes, all of it does. That’s why we can talk about all of it having photons (when the behavior we are describing makes sense in a particle kind of way), but also of those photons having an associated frequency and wavelength (which are wave properties).

He couldn’t be sure-- That’s why it’s called a hypothesis. But if they aren’t the same, then you’d have to ask where all the electromagnetic radiation is, and why there doesn’t seem to be any evidence of it. So it was a pretty reasonable hypothesis.

And while light of any frequency (as well as, well, pretty much everything else) exhibits wave-particle duality, the frequency is certainly relevant. The sorts of situations where the wave nature is relevant are much more likely for low-frequency, long-wavelength light like radio waves, and the sorts of situations where the particle nature is relevant are much more likely for high-frequency, short-wavelength light like X-rays and gamma rays (or really, anything in the visible range or above).

Note that Rømer came sort of close to the actual speed of light in 1676 (only 22% low). Later measurements refined things but the magnitude was long known.

Young started measuring the wavelengths of visible light in 1802. (It’s a direct consequence of the double slit experiment. We measured the wavelength of red light in a Physics lab in college that way.)

Given those two numbers the frequency of visible light easily follows. And holy cow: from 430–770 THz! That was an amazingly high frequency for Maxwell to ponder.

It wasn’t until Hertz in 1886 (about 20 years later) was able to build the equipment to generate and test the properties of EM waves. That they moved at the speed of light was a big boost to Maxwell’s hypothesis. Better still, he showed that his EM waves were reflected and refracted just like visible light.

Maxwell didn’t like the idea of waves just propagating through nothing. There had to be some medium through which the waves were propagating. With electromagnetic waves and light both propagating at the same speed, it wasn’t really that much of a stretch for him to conclude that they were both waves propagating through the same unknown medium. Other physicists would call this the “aether”.

Kirchoff (a name familiar to all of us EE folks) had also previously noted that the speed of a signal along an electrical wire was the same as the speed of light, so there was already an idea out there that light and other electromagnetic waves were related. Maxwell didn’t need to come up with the idea completely on his own.

Maxwell later backed away from the “aether” idea since parts of it did not make sense with his conclusions. Instead, he focused less on whatever medium these waves might be traveling through and instead focused on how those waves behaved.

Maxwell was this close to figuring out the fundamentals of the wave nature of the interaction of light and matter, and with it, the quantization of light. Given another productive twenty years, he would probably have determined the quantization of light before Max Planck, and with his mathematical acumen, perhaps even the quantum wave function long before Max Born and Louis de Broglie.


It’s not unusual for physicists to make the assumption that simplicity is the key to understanding how the universe works, looking for a common explanation for things rather than establishing many different explanations. What might look like a meaningless coincidence to a layman may very well be a huge clue to a working physicist.

Maxwell published the conclusion in his 1864 “A Dynamical Theory of the Electromagnetic Field”. For the velocity of light in air he quotes a value of 314,858,000 m/s by Fizeau and a “more accurate” 298,000,000 m/s by Foucault, together with a value of 308,000,000 m/s deduced from aberration for which he doesn’t give a reference. By contrast he has to rely on Weber and Kohlrausch alone for the electromagnetic equivalent of 310,740,000 m/s.

(p86 in the 1982 Scottish Academic Press edition.) The bit I’ve omitted makes the point that the two types of experiments involved are completely independent in terms of the physics involved.

Stranger, I’ve often commented that it’s a tragedy that the fourth-greatest physicist in history was eclipsed a scant few decades later by one of the only three who was greater.

Nitpick: Signals travel slower than c through real wires; I think speeds of 0.6c to 0.8c are typical. The 370/168 Multiprocessor had the clock in its Main Memory module wired upside-down compared with the clock in a Uniprocessor: this gave an extra 40 nanosecs in-bound and 40 nanosecs out-bound for delays through the very long wires connecting that $7 million beast to its memory.

Maxwell was eclipsed by Einstein — do I guess right? Newton … who’s the 4th?

True, but I am referring to what Kirchoff published at the time, which was relevant to what information Maxwell had available:

… 1856, when Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio
of the electromagnetic and electrostatic units of charge, by discharging a Leyden
jar, and found that its numerical value was very close to the speed of light as measured by
Fizeau. So its not Maxwell who first thinks “hey that number in the Leyden jar equation is the speed of light !”

Maxwell then predicts EM waves …
So he knew the magnetic field was so very similar to the electric field. inverse square law, energy potentials and all that. So similar. And they were related eg changing the medium where the field was would affect both the electric and magnetic fields. (That Leyden jar constant… ), in a symettric way, same but different.
Now go back to newton’s spectrum from a prism… There was some connection there, as the more metallic glass (Lead crystal), meant greater prism… the properties of the material affected light , and it affected the static electric and magnetic fields. why ? The same properties control both ?
And then he realised the magnetic field was the change in electric field just by observing all the experiments that showed electromagnetic properties.

So he concluded that the electric field is d/dt of the magnetic field.

And then he considered, well these fields store energy. So the electric field goes to zero, all the energy must now be in the magnetic field. But the magnetic field is changing fasted at that point, so the energy must be flowing back. What rate does this swapping occur at ? But the prism produces the spectrum while the electric and magnetic properies of the prism’s material are not related to frequency, they are the DC properties, yet control the swapping between electric and magnetic ?

Well laplace had solved the differential equations, and the solution was sine curves.

here he had evidence that simplest and most accurate and most whollistic description of the electric and magnetic fields was the two differential equations… he modelled what this meant if there was a fast change in very strong electric fiend, and the result, that energy would spear out in a straight line, the fields cancelled elsewhere.
Now back to the prism … so the speed was irrespective of frequency, but the that explains why the prism worked. the light was different frequencies but the same speed … and a wave… so the waves bent differently.
While he may not have provided formula for diffraction , light wavelength and photon energy, he could see that it was all coming together. His EM waves had the same speed no matter frequency, and would diffract through a prism to show their spectrum… just like light.

As it happens, Maxwell also decided on how colour mixing works and how to make a colour photograph. So I am sure he was thinking all about why a prism would work. As it happens, his particular photographic film for red was in fact only sensitive to infrared instead of red. But the red in his test subject (a red coloured ribbon) was strong in infrared as well … so the resuling image showed red where he expected. He also seems to have invented false colour photography of infrared, by accident.

Prisms do in fact rely on different speeds for the different frequencies. The speeds are all the same in vacuum, but they typically differ in materials, like glass.

EDIT: Oh, and the other physicist I’m putting in the Top 3 is Archimedes.

Archimedes, Newton, Maxwell, and Einstein are generally considered the top four. Maxwell is generally placed in fourth place despite being the first person to express the rules of classical electrodynamics in a rigorous mathematical form (and in the more complex original 20 equation quarternion formulation rather than the highly simplified 4 equation vector formulation which was actually codified by Oliver Heaviside as taught to undergraduates) and of course his other fundamental contributions to thermodyanmics and statistical mechanics, optics, and of course color photography.

Maxwell worked in an effective vacuum with few comtemporary physicists even conceeding that electricity and magnetism were manifestations of the same phenomenon, and his most notable theoretical accomplishments not being widely understood or disseminated until well after his death. Maxwell was highly productive throughout his relatively short lifetimeand despite frequent illness, and given what he did accomplish with the primitive knowledge and tools of his day, had he lived longer I suspect he would be known as the “father of quantum mechanics” and possibly special relativity. He was as accomplished a mathematician as a physicist, if not moreso, and had a rare intellectual curiosity even by the standards of great physicists.


Well, not exactly. In fact, it hasn’t really been established that Young ever did perform the famous Double Slit experiment – it may only have been a thought experiment. I know that sounds like heresy, but it’s true.

Young WAS the first to measure the wavelength of light, and he did it by using a diffraction grating. He didn’t even have to construct it, or to have it constructed especially for him – he used a very finely ruled instrument ruling, which had very fine lines equally spaced at a very short distance. In other words, he used OTS (Off The Shelf) equipment. But it was a multiline grating, not a double slit.

Actually, Young was very nearly beaten out by an underappreciated American scientist, David Rittenhouse. Rittenhouse’s friend and associate, Francis Hopkinson, had observed a weird optical effect when he looked at a distant light source through his handkerchief. Rittenhouse got hold of the finest-pitch screws that he could (106 threads to the inch, then later with 250 threads to the inch) and carefully wound threads between two of these, thus guaranteeing equally-spaced fibers. It was the first deliberately created diffraction grating. With it, Rittenhouse observed that a distant white light was separated into its constituent colors. He carefully measured the angles that the colors were deflected by. He now had all the data her needed to calculate the wavelengths of the different colors of light – the grating pitch, the angles, a basic theory. Only he didn’t. In his own words:

That was in 1785, some twenty years before Young. Using his measurements, you can, indeed, calculate the wavelengths of light. Rittenhouse never found the leisure to go back and re-study light. It’s another of the many tantalizing and frustration "What If"s of the history of science, like Claudius Ptolemy’s refusing to follow up his experiments on the refraction of light.

Actually, Young “checked” the results he got against an earlier series of experiments – by Isaac Newton, who didn’t even believe in the wave theory of light! Newton had calculated characteristic lengths associated with the colors, based upon his experiments with “Newton’s rings”. But, since he stubbornly refused to consider the wave theory, he had nothing to peg these lengths to. Young was an indefatigable crusader for the wave theory, and looked for examples of it everywhere (including the rainbow, where he found further evidence), so it’s not surprising that his experiment gave good reasons for the wave theory.

I wrote up an article about the Hopkinson-Rittenhouse experiments, and later expanded that into a chapter in my book “How the Ray Gun Got Its Zap!”

On Young not actually doing a “double slit” here’s one reference that quotes directly from Young:

My favorite physics lab I’ve taught uses a machinist’s rule (a metal ruler with the markings engraved into it) marked in millimeters (or perhaps even less finely-- We’ve got some as coarse as an eighth of an inch) to measure the wavelength of a laser to within a few nanometers. You hold the ruler so the laser hits it at a grazing angle (a few degrees), and it splits it into a bunch of separate spots on a screen. I just find it endlessly fascinating that you can use a measurement tool to measure with a precision six orders of magnitude finer.

Granted, this is a lot easier with a bright monochromatic source like a laser, but you can do the same thing with sunlight split into a spectrum: Measure the difference between one red part and the next to find the wavelength of red light, and so on.