Editing Augustin-Jean Fresnel (section)

=== Dispersion ===

The analogy between light waves and transverse waves in elastic solids does not predict ''[[Dispersion (optics)|dispersion]]''—that is, the frequency-dependence of the speed of propagation, which enables [[Dispersive prism|prisms]] to produce spectra and causes lenses to suffer from [[chromatic aberration]]. Fresnel, in ''De la Lumière'' and in the second supplement to his first memoir on double refraction, suggested that dispersion could be accounted for if the particles of the medium exerted forces on each other over distances that were significant fractions of a wavelength.<ref>Darrigol, 2012, p.&nbsp;246; Buchwald, 1989, pp.&nbsp;307–308;{{tsp}} Fresnel, 1822a, tr.&nbsp;Young, in ''Quarterly Journal of Science, Literature, and Art'',{{tsp}} Jan.–{{hsp}}Jun.{{tsp}}1828, at pp.&nbsp;[https://books.google.com/books?id=SbJMAAAAYAAJ&pg=PA213 213–215].&nbsp; Whittaker, 1910, p.&nbsp;132; Fresnel, 1866–70, vol.&nbsp;2, p.&nbsp;438.</ref> Later, more than once, Fresnel referred to the demonstration of this result as being contained in a note appended to his "second memoir" on double refraction.<ref>Fresnel, 1827, tr.&nbsp;Hobson, pp.&nbsp;277n,{{px2}}331n; Lloyd, 1834, p.&nbsp;316.</ref> No such note appeared in print, and the relevant manuscripts found after his death showed only that, around 1824, he was comparing refractive indices (measured by Fraunhofer) with a theoretical formula, the meaning of which was not fully explained.<ref>Fresnel, 1866–70, vol.&nbsp;1, p.&nbsp;xcvi.</ref>

In the 1830s, Fresnel's suggestion was taken up by Cauchy, [[Baden Powell (mathematician)|Baden Powell]], and [[Philip Kelland]], and it was found to be tolerably consistent with the variation of refractive indices with wavelength over the [[visible spectrum]] for a variety of transparent media {{crossreference|(see [[Cauchy's equation]])}}.<ref>Whittaker, 1910, pp.&nbsp;182–183; Whewell, 1857, pp.&nbsp;365–367; Darrigol, 2012, pp.&nbsp;246–249.</ref> These investigations were enough to show that the wave theory was at least compatible with dispersion; if the model of dispersion was to be accurate over a wider range of frequencies, it needed to be modified so as to take account of resonances within the medium {{crossreference|(see [[Sellmeier equation]])}}.<ref>Darrigol, 2012, p.&nbsp;252.</ref>