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In a Scientific American article from 1968 in which he explains classically how light interacts with matter, Victor Weisskopf states that "the reflection of light on the surface of a solid or liquid involves only the oscillators (electrons) located in a small, pillbox-shaped volume at the surface of the material". He then says the pillbox has a thickness corresponding to half the wavelength of incident light and an area he calls the first Fresnel zone.

I think I found a way to make sense of the area of the zone where reflection occurs (if you compute the phase for every possible path from source to surface to observer and add them, only paths close to the center will contribute significantly to the sum and the area will be larger for larger wavelength), but I have no idea where the half-wavelength thickness might come from.

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I found this paper: http://users.aims.ac.za/~jweiner/AJPIAS_64_8_986_1.pdf

The authors mention that Weisskopf says that a layer of thickness λ/2 at the surface of an object is responsible for the reflection of light upon it. They then take the microscopic perspective in which the reflection and transmission result from the scattering of light by the atoms (which become dipoles when light is incident on them) making up a dielectric. They show rather convincingly that no finite surface layer of dipoles can produce the field outside the dielectric. It thus seems that the reflection comes from the whole volume of the object and that Weisskopf was wrong.

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