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The boundary conditions, namely enter image description here

were all these, realized only by looking at Maxwell's equations? Or is there a physical reasoning behind them? For example, Why does the component of the electric field parallel to the surface of interface remain unaltered? I also read that the reason light bends when it passes through another medium is because only the normal component gets altered and the horizontal component remains the same(whereas the velocity gets altered because of the other electrons in the material that are driven by the source and produce a separate wave with a different phase and the superposition of these two waves seem to alter the speed of light in a medium $^\dagger$).

My question in short is, What would be my answer,if someone asked me, to explain the boundary conditions, without equations*.

*If that's purely based on equations, please ignore "without equations", but there's got to be something that's physically occurring which led us to create a model, right?.

$^\dagger$Is that right?

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In short: Yes.

Those equations can be understood as boundary conditions, but they can also be understood as being valid between any two points inside the domain. This is because they result from integrating the Maxwell equations over an arbitrary test volume, and hence link the quantities at either end of this test volume.

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  • $\begingroup$ :( Okay, I agree that the result is purely a consequence of the equations. But is there any physical interpretation? Like(don't mind this, I'm giving some random interpretation, for example), the charges in the medium move only normally and produce an opposing field, that reduces only the normal component of the incoming field. $\endgroup$
    – Aravindh Vasu
    Nov 12, 2019 at 12:21
  • $\begingroup$ @AravindhVasu: It has the same interpretation as the original Maxwell's equations. Just the differential form of the equations is valid for infinitesimal steps or "the microscopic world", while the integral form is integrated over a finite volume, so it is valid for "the macroscopic world". $\endgroup$
    – AtmosphericPrisonEscape
    Nov 12, 2019 at 13:19
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Consider an electrically polarized continuous medium. In its volume it is neutral but at its boundary a charge appears. For a magnetically polarised medium a current appears. This is why there is a jump in the fields.

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  • $\begingroup$ Can you please elucidate, why would the be a charge at the boundary? $\endgroup$
    – Aravindh Vasu
    Nov 13, 2019 at 1:02

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