Fresnel zones in classical reflection from solid surfaces

[damosuz]

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 have searched for Fresnel zones and I have not found anything related to the reflection of visible light on surfaces. Does anybody know anything about an explanation along these lines?

 

[tech99]

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 have searched for Fresnel zones and I have not found anything related to the reflection of visible light on surfaces. Does anybody know anything about an explanation along these lines?

This topic comes up in microwave engineering when a ray is reflected from the ground at an oblique angle. I think he is saying that the oscillating electrons occupy just a small depth, like skin effect, but the diameter is equal to one Fresnel Zone.
If the ray arrives at an oblique angle, you may notice that, for geometrical reasons, the phase will alter across the surface of the material due to the varying distance travelled. If you consider a single "ray", as in school optics, the Fresnel Zone is an elliptical shape which surrounds it on on the surface and within which the phase error is less than 180 degrees. (Actually, I would have expected 90 degrees for the present purpose). Outside this zone, the phase is reversed, so it must be dependent on another pill box.

 

[damosuz]

Thank you for your answer.

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 am not sure about the half-wavelength thickness. If you compute the phase for layers parallel to the surface, you find that it varies sinusoidally as you go deeper in the material, and that it varies faster for shorter wavelengths. If you add those phases, they will then interfere destructively in every full cycle and you end up with a maximum of half a cycle that interferes constructrively and contributes to reflection. You thus have a thickness of effective reflection that is proportional to wavelength, but I don't know why Weisskopf says half a wavelength.

 

[tech99]

Thank you for your answer.

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 am not sure about the half-wavelength thickness. If you compute the phase for layers parallel to the surface, you find that it varies sinusoidally as you go deeper in the material, and that it varies faster for shorter wavelengths. If you add those phases, they will then interfere destructively in every full cycle and you end up with a maximum of half a cycle that interferes constructrively and contributes to reflection. You thus have a thickness of effective reflection that is proportional to wavelength, but I don't know why Weisskopf says half a wavelength.

I think the thickness is equal to the skin depth, which for a conductor is very small.

 

[damosuz]

Weisskopf talks about reflection on a transparent dielectric like glass.

 

[tech99]

Weisskopf talks about reflection on a transparent dielectric like glass.

Thank you, now I understand your point.