Plasma Theory of Redshift and Deflection of Light

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
At ground level, the average distance between two molecules is 1/250 of the wavelength at 5000 A, so the relative statistical variance is 1/sqrt(250)=6*10^-2. Now the Fraunhofer criterion for a perfectly smooth surface (i.e. perfectly coherent scattering) says that the variance has to be less than 1/32 of the wavelength.
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I had not understood your error: you suppose that the molecules are synchronous while they are only if they are on a considered wave surface. Therefore, to apply Fraunhofer criterion, you must add the path from a wave surface to the molecules to the path from the molecule to an other wave surface. Only the fluctuations of density break the coherence adding the incoherent Rayleigh scattering to the coherent (which is at the origin of the refraction).

The coherent Raman effect is weak because the sum of these paths is not constant, so that the coherence is destroyed unless the observation is done using a small laser beam, for scattered light propagating along a convenient cone which does not exist for all frequencies .

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by JMB</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
At ground level, the average distance between two molecules is 1/250 of the wavelength at 5000 A, so the relative statistical variance is 1/sqrt(250)=6*10^-2. Now the Fraunhofer criterion for a perfectly smooth surface (i.e. perfectly coherent scattering) says that the variance has to be less than 1/32 of the wavelength.
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I had not understood your error: you suppose that the molecules are synchronous while they are only if they are on a considered wave surface. Therefore, to apply Fraunhofer criterion, you must add the path from a wave surface to the molecules to the path from the molecule to an other wave surface. Only the fluctuations of density break the coherence adding the incoherent Rayleigh scattering to the coherent (which is at the origin of the refraction).
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I don't know why you think the Fraunhofer criterion can not be applied here. The situation of a randomly un-smooth surface should be exactly identical to the scattering of randomly distributed air molecules. In both cases you will have a phase-incoherent reflection/scattering if the wavelength is smaller than the size of the irregularities, but phase-coherent scattering/reflection if the wavelength is larger. In fact, if this wouldn't be so, there should not be any specular reflection be possible at all (even for a perfectly smooth surface) as all the scattering electrons in the surface are in random places. So the very fact that mirrors exist proves my point.

Thomas

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>

I don't know why you think the Fraunhofer criterion can not be applied here. The situation of a randomly un-smooth surface should be exactly identical to the scattering of randomly distributed air molecules. In both cases you will have a phase-incoherent reflection/scattering if the wavelength is smaller than the size of the irregularities, but phase-coherent scattering/reflection if the wavelength is larger.
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Fraunhofer criterion applies on the wave surfaces, but not easily: you have a lot (almost infinite) of wave surfaces on which there are scattering molecules which perturb locally the wave surface, but the addition of the perturbations for all wave surfaces statistically cancels.

To take into account ALL scattering molecules whose radiated field arrives to the observation system, it is much easier to add all scattered fields to the direct field at the point of observation or close to it. Thus, in the focal plane of the telescope looking at a star, you have a point where all scattered paths are equal, while at a small distance, just out of the image, they differ of a fraction of wavelength. With photocells, this fraction is shorter than with Fraunhofer criterion. A smooth decrease of the intensity from the centre of the image requires a large number of scattering molecules, but does not depend on their distances.