λ × f = c

For any wave, the basic relation v = fλ ties speed, frequency, and wavelength together.

For EM waves in vacuum, v is fixed at c ≈ 3 × 10⁸ m/s. So f and λ are INVERSELY proportional.

Frequency f is the number of full cycles passing a point per second (Hz = s⁻¹). It is set by the source.

Wavelength λ is the spatial period — the distance between two consecutive crests of the wave.

Period T = 1/f is the time for one full cycle; angular frequency ω = 2πf.

When an EM wave enters a medium of index n: f stays the same, v drops to c/n, so λ shrinks to λ_vac/n. Wave-number k = 2π/λ therefore GROWS in the medium.

Photon energy is fixed by f, not λ: E = hf. So in a medium, photon energy is unchanged — only wavelength is.