Abstract
The refractive index n depends on the wavelength λ of the radiation; it exhibits “dispersion”. Dispersion is closely related to the absorption of radiation, and it, in turn, depends strongly on the wavelength. In the following Sects. 27.2 through 27.5, we will consider the empirical evidence relating dispersion and absorption. Then we will treat quantitatively the wavelength dependence of refraction and absorption. This will show close ties to our quantitative treatment of scattering in Chap. 26.
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Notes
- 1.
The justification of this statement will be seen later in Eq. (27.7). n attains high values only when the difference of the squared frequencies, that is \(\nu_{0}^{2}-\nu^{2}\), is very small. In solids and liquids, with their broad absorption bands, this leads into regions where the material is opaque.
- 2.
This is a simplifying hypothesis. In fact, this phase difference of \(-90^{\circ}\) results from the summation of all the secondary waves along the path of the primary waves.
- 3.
Here, as always, ‘molecule’ refers to the smallest independent unit; this could often be also atoms or ions.
- 4.
The quotient \(\frac{n^{2}-1}{n^{2}+2}=R^{\prime}\) is known as the refraction.
- 5.
In solutions, \(n=\dfrac{n_{\text{solution}}}{n_{\text{solvent}}}\) , and it thus represents the refractive index that is due solely to the dissolved molecules.
- 6.
F centers. Considered chemically, a K\({}^{+}\) ion together with an electron forms a neutral potassium atom. H. Pick, “Struktur von Störstellen in Alkalihalogenidkristallen”, Springer Tracts in Modern Physics (Springer-Verlag Berlin, Vol. 38, p. 1 (1965)).
- 7.
Note that the measurements on mercury in Fig. 27.18 were carried out at a pressure of \(30\cdot 10^{5}\) Pa.
- 8.
The eigenfrequency ν0 of such a dipole (resonator or oscillator) corresponds in quantum mechanics to the frequency \(\nu_{0}=\Updelta W/h\) when the energy of the molecule changes by \(\Updelta W\).
- 9.
The oscillation period T = 1 ∕ ν for the fundamental mechanical vibration of a rod is \(=\leavevmode\nobreak\ 2D/u\). This means that a longitudinal elastic perturbation passes along the entire length D of the rod twice during the time T, namely going forward and then returning. The velocity of sound within a solid body is nearly always quoted as the special case of its value along the length of a rod, without further comment (cf. Vol. 1, Fig. 12.42 and Eq. (11.5)). In Eq. (27.22), however, a valid average value for a three-dimensional body must be used.
- 10.
It follows from Eq. (25.15) for an imaginary refractive index n that the reflectivity is \(R=(E_{\text{r}}/E_{\text{i}})^{2}=1\) (numerator and denominator have the same magnitude).
- 11.
This detection of single particles is called “ultramicroscopy”.
- 12.
E. Mollwo (Dr. rer. nat. Göttingen, 1933), Zeitschrift für Physik 85, 56 (1933).
- 13.
The extinction curves of the fine colloids in Fig. 27.21 are not “optical resonance curves”; their shapes are instead determined by the curves of the optical constants of the material of the particles.
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Lüders, K., Pohl, R.O. (2018). Dispersion and Absorption. In: Lüders, K., Pohl, R. (eds) Pohl's Introduction to Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-50269-4_27
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