Electromagnetic waves and light

Your router fills the room with WiFi. A microwave oven cooks with the same kind of wave at a nearby frequency. Sunlight warms your skin and, at a slightly higher pitch, burns it. Radio, light, and X-rays feel like completely different things. They are the same wave, and only one number tells them apart.

In the last lesson, a changing magnetic field pushed charges - it created an electric field. There is a twin fact, equally experimental: a changing electric field creates a magnetic field. Put those two together and something remarkable becomes possible, a disturbance that needs no wire, no magnet, nothing but empty space to keep itself alive.

Literally the same wave. Radio, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays are all one thing - an electromagnetic wave - and the only thing that changes across that entire list is the frequency, how fast the fields wiggle.

Why it keeps itself alive

Here is the self-propagation, built from the two facts you already have. Wiggle a charge and you make a changing electric field. That changing electric field creates a changing magnetic field right next to it. But a changing magnetic field creates a changing electric field a little further along. Which makes another magnetic field further still. Each field's change births the other, leapfrog after leapfrog, marching outward through empty space with nothing carrying it but the two fields taking turns. This is what light is.

James Clerk Maxwell wrote down the four equations governing electric and magnetic fields, and found that they force exactly this travelling wave - moving at one fixed speed set by two measurable constants of empty space. That speed came out equal to the already-measured speed of light, which is how we learned light is an electromagnetic wave^[1]. We call it $c$, about 300 million metres per second. Maxwell's equations we take as stated; the payoff is what they predict.

One dial across the whole spectrum

Because every electromagnetic wave travels at the same speed $c$, its frequency and wavelength are locked together: fast wiggles leave no room, so the wavelength is short, and slow wiggles stretch long. Sweep the dial below from radio up to gamma and watch the wave tighten, the wavelength shrink, and the band name change - all one continuous thing.

The lock is a single equation, the same $v=f\lambda$ you met for any wave, with the speed fixed at $c$:

So higher frequency means shorter wavelength, always. And there is a second quantity riding along that the dial also tracks: each wave delivers its energy in lumps whose size grows with frequency, $E=hf$. That is why radio passes through you harmlessly while ultraviolet burns and X-rays ionise - not because there is more of it, but because each lump packs more energy. That lump is the photon, and it is the whole subject of a later lesson; here just notice the trend the dial makes visible.

Check yourself