WaFE   Wavelength / frequency / energy equivalents

Conversion between equivalents of wavelength, frequency, and photon energy

This concerns the propagation of harmonic electromagnetic waves in vacuum. In standard complex notation, electric and magnetic fields depend on coordinates x in space and t in time as

∼ exp(i ω t - i k x),

with wavenumber k, and angular frequency ω. Related quantities are the wavelength λ, the spectroscopic wavenumber ν̄, the frequency f, the period in time T, and the energy E of photons associated with the electromagnetic wave.

The converter script accepts simple C-style expressions, as processed by the Teval script. The calculations are based on the equations

c = λ f,    k = 2π/λ,    ν̄ = 1/λ = f/c,    ω = k c = 2π f,    T = 2π/ω = 1/f,    E = ħ ω = h f,

or on equivalent expressions. Values for π and the physical constants originate from The NIST Reference on Constants, Units, and Uncertainty, Physical Measurement Laboratory, National Institute of Standards and Technology, USA (09.2015); see Teval → Constants for the implemented values. This concerns the speed of light in vacuum c, the elementary charge e, and the Planck constant h, with ħ = h/(2π).

Quantities are shown in SI units, applying prefixes as far as reasonable. Note that units of radians for wavenumbers and angular frequencies are not shown.

The (largely heuristic) recipe for the conversion to RGB color levels, for visible light, originates from a Fortran code on a site on color science by D. Bruton, Department of Physics and Astronomy, SFA State University, Texas, USA. The division into spectral regions follows the scheme as given on the page on the electromagnetic spectrum on Wikipedia, English section, and on referred pages on the separate spectral regions.