Wavelength (EM)

The wavelength λ of an electromagnetic wave is the spatial period of the sinusoidal oscillation — the distance between two successive points of equal phase along the propagation direction. In vacuum, λ = c/f, where f is the frequency in hertz and c = 2.998 × 10⁸ m/s. In a medium with refractive index n, the frequency is unchanged but the wavelength is reduced: λ_medium = λ_vacuum/n. Visible wavelengths span roughly 400 nm (violet) to 700 nm (red); radio wavelengths from metres (FM) to tens of kilometres (submarine VLF); X-rays at tens of picometres; gamma rays below a femtometre.

Wavelength controls which physical effects dominate at a given frequency. When the wavelength is much smaller than the obstacle or aperture under consideration, geometric-optics approximations (ray tracing, shadows with sharp edges) work well; when the wavelength is comparable to or larger than the obstacle, diffraction and interference dominate. This is why visible light casts sharp shadows past a door (λ ≈ 500 nm ≪ 1 m) but long-wave radio (λ ≈ 1 km) bends easily around buildings. Wavelength also sets antenna size: efficient radiation requires antenna dimensions on the order of λ/2 or λ/4, which is why AM radio antennas are tens of metres tall while Wi-Fi antennas are a few centimetres.