A wave that carries itself

An electromagnetic wave is a pair of oscillating fields: an electric field and a magnetic field, mutually perpendicular and both perpendicular to the direction of travel. That last part makes light a transverse wave, which is why it can be polarized.

Nothing material has to move. The changing electric field sustains the magnetic one and the changing magnetic field sustains the electric one, so the wave propagates itself.

Transferring the mechanical-wave rule to light is what makes people fill space with a thin something for light to travel through. The clean test is the pair of everyday observations:

1. Sound stops at the edge of the atmosphere. It is a displacement of air, and there is no air.
2. Light crosses the vacuum unaffected. It is a field oscillation, and fields exist in vacuum.

Which is why the Sun is blindingly bright and completely silent.

Every electromagnetic wave travels at the same speed in vacuum:

$$c = 3.00\times10^8 \ \text{m/s}, \qquad c = f\lambda.$$

Radio, visible light and gamma rays all cross a vacuum at exactly the same speed. What distinguishes them is the frequency, and therefore the wavelength.

Because $c$ is fixed, $f$ and $\lambda$ are locked together in inverse proportion: longer wavelength always means lower frequency, with no exceptions anywhere on the spectrum. That single fact converts any ordering by wavelength into an ordering by frequency for free.

In a medium the speed drops to $c/n$, which is the previous unit's material. Frequency still belongs to the source, so the wavelength is what shortens.

From longest wavelength to shortest:

radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

And within the visible band, longest to shortest: red, orange, yellow, green, blue, violet.

Ordering by how dangerous or powerful a band sounds is the error, and it produces X-rays filed as long waves because they penetrate deeply, or blue placed at the long end because it looks bright. Penetration and perceived brightness are not the axis being sorted.

The way to hold the list is to anchor it at both ends and walk across: radio wavelengths measured in kilometres, gamma wavelengths measured in picometres, everything else in order between. Then apply $c = f\lambda$, which makes the short-wavelength end the high-frequency end and the high-energy end. You are asked for the ordering, never for exact wavelength ranges.

The applications follow from the wavelength, which makes them a check on the ordering rather than a separate list to memorise.

1. Radio has wavelengths comparable to buildings and hills, so it diffracts around them and reaches receivers out of line of sight.
2. Microwaves are absorbed efficiently by water molecules, which is what heats food.
3. Infrared is emitted by everything near room temperature, which is what a thermal camera sees.
4. Ultraviolet and beyond carry enough energy per photon to break chemical bonds, which is why the short end is the damaging end.
5. X-rays have wavelengths comparable to atomic spacings, which is why crystals diffract them.

Notice that the deep penetration of X-rays comes from their short wavelength and high photon energy, not from a long one. That single observation kills the order-by-feel error at its source.