Dispersion and the speed of light
Dispersion and the speed of light
“So far as problems involving light are concerned, the electrons (in atoms) behave as though they were held by springs”.Feynman “In a microscopic but otherwise classical analysis, the electric field in electromagnetic radiation accelerates electrons held by springs in the atoms of a piece of glass, and these accelerated electrons re-radiate in all directions. The observed light is the superposition of the electric (and magnetic) fields of the incoming light and the re-radiation.
In the backward direction we normally call the re-radiation "reflection," but this labelling obscures the fact that this is new light radiated by all the atoms in the glass, not old light that has magically
"bounced off" the front surface due to some unknown mechanism.
In the forward direction we speak of "refraction," and we say that "the speed of light is slower in the glass," but in fact, the speed of light does not change in the material. Rather, Feynman shows how the superposition of the incoming light, travelling at speed c, and the light re-radiated by the atomic electrons, travelling at speed c, shifts the phase of the radiation in the air downstream of the glass in the same way that would occur if the light were to go slower than c in the glass, with a shorter wavelength and an index of refraction greater than one for frequencies below the natural frequency of the oscillators (otherwise the phase shift corresponds to a speed greater than c in the material, with index of refraction less than one). At a fundamental level this phase velocity, greater or less than c, is of no particular physical significance, because it only applies to the overly-simplified case of singlefrequency sinusoidal radiation permeating all space, and such radiation cannot carry a meaningful signal.” Bruce Sherwood. Fig 3.38 from Hecht.
“The index of refraction is specified by the speed of light in the glass, which depends, in turn, on the way
the
“So far as problems involving light are concerned, the electrons (in atoms) behave as though they were held by springs”.Feynman “In a microscopic but otherwise classical analysis, the electric field in electromagnetic radiation accelerates electrons held by springs in the atoms of a piece of glass, and these accelerated electrons re-radiate in all directions. The observed light is the superposition of the electric (and magnetic) fields of the incoming light and the re-radiation.
In the backward direction we normally call the re-radiation "reflection," but this labelling obscures the fact that this is new light radiated by all the atoms in the glass, not old light that has magically
"bounced off" the front surface due to some unknown mechanism.
In the forward direction we speak of "refraction," and we say that "the speed of light is slower in the glass," but in fact, the speed of light does not change in the material. Rather, Feynman shows how the superposition of the incoming light, travelling at speed c, and the light re-radiated by the atomic electrons, travelling at speed c, shifts the phase of the radiation in the air downstream of the glass in the same way that would occur if the light were to go slower than c in the glass, with a shorter wavelength and an index of refraction greater than one for frequencies below the natural frequency of the oscillators (otherwise the phase shift corresponds to a speed greater than c in the material, with index of refraction less than one). At a fundamental level this phase velocity, greater or less than c, is of no particular physical significance, because it only applies to the overly-simplified case of singlefrequency sinusoidal radiation permeating all space, and such radiation cannot carry a meaningful signal.” Bruce Sherwood. Fig 3.38 from Hecht.
“The index of refraction is specified by the speed of light in the glass, which depends, in turn, on the way
the