Abstract
In Volume 1, interference is treated in detail within the framework of the general topic of waves (Chap. 12). There, we considered two conditions, which can usually be fulfilled to a good approximation:
1. Pointlike wave centers, i.e. their diameters must be small compared to the wavelength of the radiation.
2. Wave trains of unlimited length and a single frequency. Only with such wave trains can we produce interferences between two independent emitters with the same frequency, e.g. two whistles.
If these two conditions are not sufficiently well fulfilled, we can obtain clear-cut, spatially fixed interference patterns only by taking special measures. This is the case for light, in particular; that is why we have postponed the treatment of such measures to the section on optics.
Wave trains of limited length are generically called wave groups. They always have a corresponding frequency range; the term ‘frequency’ then refers only to the midpoint of that range. Strictly monochromatic wave trains cannot be produced in a finite experiment.
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Notes
- 1.
They should preferably be called single-frequency. The term monochromatic , that is with a single color, is an unhappy choice of wording: Monochromatic light usually includes a broad range of light frequencies, up to half of the visible spectrum! (Sect. 29.10).
- 2.
If one measures \(\Updelta s\), the difference in the lengths of two paths along which two wave groups propagate to the point of observation, as multiples of their wavelength λ, then \(m\lambda\) is called their path difference.
- 3.
Thomas Young, 1773–1829, studied in Göttingen and lived in London where he had a medical practice. He was a natural scientist with unusually broad interests, and he also made an important contribution to deciphering Egyptian hieroglyphic writing. In 1802, Young was the first to determine the wavelengths of individual spectral regions, by making use of interference fringes in thin wedge-shaped glass plates (Sect. 20.7). He found for example the wavelengths at the ends of the visible spectrum to be 0.7 \(\upmu\)m (red) and 0.4 \(\upmu\)m (violet). He also photographed the interference fringes from ultraviolet light as early as 1803 using paper dipped into a silver nitrate solution! (See R.W. Pohl, Physikalische Blätter 5, 208 (1961)).
- 4.
Some authors refer to Eq. (20.1) as the spatial coherence condition to distinguish it from a temporal coherence condition, \(\Updelta\nu\cdot\Updelta t\ll 1\). This second inequality, however, does not characterize a property of the radiation which is limited to a certain angular range, as in Eq. (20.1). It simply limits the permissible path difference for the occurrence of interference fringes between the wave groups that are to be superposed. This path difference must be small compared to the lengths of the wave groups, as shown in Sect. 20.2.
- 5.
See the footnote at the end of Sect. 20.2, and also Comment C12.3 in Vol. 1.
- 6.
This approximation neglects small differences in the angles of inclination β for rays separated only by the angle \(2\omega\), and in addition refraction is neglected, as also in the later Figs. 20.12, 20.13 and 20.32 ; and finally also the phase jump of the waves upon reflection from an optically denser material, which is quite unimportant in the above connection,C20.3.
- 7.
Compare Fig. Fig. 27.1 for NaCl, the best-known of the alkali halides.
- 8.
This radiometer is therefore not selective for radiations in different wavelength regions like the human eye, which reacts to some regions in varying ways (chromatic hues! Sect. 29.9), and to some regions not at all.
- 9.
Jumps of λ ∕ 2 are included in the path differences Δ; these are due to reflection by a more optically dense material.C20.2
- 10.
Comptes rendus, Paris, 66, 934 (1868), and J.M. Stephan, ibid., 78, 1008 (1873).
- 11.
To show this demonstration to a large audience, the surface of a glass plate is covered with a layer of glued-on glass powder and then moved back and forth perpendicular to the beam axis of a beam of light which is projected onto a wall screen.
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Lüders, K., Pohl, R.O. (2018). Interference. In: Lüders, K., Pohl, R. (eds) Pohl's Introduction to Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-50269-4_20
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