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Can anyone please explain why light reflects at the boundary between two regions with different impedances? This sounds very simple but I got confused when I tried to think of how light and atoms interact with one another at the boundary.

This question can actually be generalised to the reflection of all types of waves. I have to admit I have no understanding of the microscopic detail of reflection.

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The way I would recommend you approach this question is to look at the derivation of Fresnel's Laws of Reflection, as is shown in detail at this link. The key here is that there must be a continuity of the electric field across the boundary between the regions of different refractive index - but since such regions have different amounts of polarization for the same electric field (that is pretty much the definition of relative dielectric constant...) the only way that this can happen is if part of the electric field "stays outside" while another part penetrates into the second medium. Which is what we call "partial reflection".

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  • $\begingroup$ It also obeys Fermat's principle. $\endgroup$ – lemontwist Sep 7 '15 at 16:24
  • $\begingroup$ Thank you very much for the answer but it still does not quite clarify my confusion. I would love to see a microscopic expaination where individuals photons and atoms+electrons are taking into account. I am probably asking for too much through $\endgroup$ – ErwinNK Sep 8 '15 at 15:20
  • $\begingroup$ The electrons move in response to the electric field from the EM wave. This response is a function of frequency. The polarization this gives rise to is expressed in the dielectric constant. And from there, you use Fresnel's equations. Does that help? $\endgroup$ – Floris Sep 8 '15 at 15:31
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In addition to all that has been said, maybe the following will help the intuition: The electrons around the atoms at the surface of the glass is set in vibration by the oscillating electric field of the light beam. But a vibrating electric charge will itself send out an electromagnetic wave. This secondary wave generated at the surface will propagate not only into the glass, but also into the air and give rise to the reflected beam.

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  • $\begingroup$ Now, let's consider light inside the glass. Electrons in the glass would be excited and behave like dipoles, sending out light in both forward and backward directions. However, there is no reflected light in a uniform medium. The Huygens–Fresnel principle assume an inclination factor of K=(1+cos x)/2 so that there is no backward propagating wave in a uniform media, but I could not find a good explanation why it is the case. This is what I am confused about. $\endgroup$ – ErwinNK Aug 29 '16 at 1:12
  • $\begingroup$ The book "Optics" by Born and Wolf has a chapter of classical dispersion theory. Maybe that would help? $\endgroup$ – Halvor Heier Aug 30 '16 at 17:21
  • $\begingroup$ The Huygens-Fresnel principle belongs to the wave-optics model of light and can be used for studying diffraction and interference. The obliquity factor and also the phase of the secondary waves are introduced ad hoc to make the model work. Reflection from a surface is studied by the electromagnetic wave optics model based on Maxwell's equations, in the way described by Floris above. In the electromagnetic model the dipoles radiate in all directions, an obliquity factor is not used. $\endgroup$ – Halvor Heier Sep 1 '16 at 6:19

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