I A ray crossing 2 media of different indices and energy conservation

AI Thread Summary
The discussion centers on the behavior of a ray crossing two media with different indices of refraction and the implications for energy conservation. Participants express confusion about the equation presented on page 75, particularly regarding its representation of energy flow through a surface area (dS) and the role of intensity (I_i) and solid angles (dΩ). The equation appears to suggest that energy behaves like a vector quantity, which raises questions about the conservation of total energy versus its directional components. The conversation also touches on the assumption that intensity (I_1) is constant and how it affects the energy entering the surface, acknowledging that some energy is reflected. Overall, the thread highlights the complexities of understanding energy transfer across media boundaries.
Paulpaulpa
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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.
 
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Some energy is reflected.
 
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