A ray crossing 2 media of different indices and energy conservation

  • #1
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The ##I_i## are the intensity of the rays, in other words energy per surface units per radians by seconds.

The d##\Omega## are the solid angles

The equation p75 isis what I don't understand. I suppose that each side represent the energy going and out of the surface dS but I don't understand why it has this form. It looks like the projection of the intensities along the x-axis, as if energy was a a vector quantity (like the momentum, for which the three components are conserved separately). But only the total energy going through dS should matter and I don't understand why it has this form.

If we say that ##I_1## is independant of the spacetime coordinates and is large enough to wrap around dS, the energy going in should be ##I_1 d\Omega dS## since the surface is totally exposed to the ray. I am probably wrong but I don't know why.
 
  • #2
Some energy is reflected.
 
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