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A quantity related to the wavelength is the angular wavelength (also known as reduced wavelength), usually symbolized by ƛ ("lambda-bar" or barred lambda). It is equal to the ordinary wavelength reduced by a factor of 2π (ƛ = λ/2π), with SI units of meter per radian. It is the inverse of angular wavenumber (k = 2π/λ).
where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres. Usually, it is sufficient to use a two-term form of the ...
where R is the Rydberg constant, and n i and n f are the principal quantum numbers of the initial and final levels respectively (n i is greater than n f for emission). A spectroscopic wavenumber can be converted into energy per photon E by Planck's relation: = ~. It can also be converted into wavelength of light:
The refractive index, , can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ 0 /n, where λ 0 is the wavelength of that
An expression for n as a function of photon energy, symbolically written as n(E), is then determined from the expression for k(E) in accordance to the Kramers–Kronig relations [4] which states that n(E) is the Hilbert transform of k(E). The Forouhi–Bloomer dispersion equations for n(E) and k(E) of amorphous materials are given as:
In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. [2]: v1:376 He noticed that lines came in series and he found that he could simplify his calculations using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement.
A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency.
The phase velocity is given in terms of the wavelength λ (lambda) and time period T as v p = λ T . {\displaystyle v_{\mathrm {p} }={\frac {\lambda }{T}}.} Equivalently, in terms of the wave's angular frequency ω , which specifies angular change per unit of time, and wavenumber (or angular wave number) k , which represent the angular change ...