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SunMesa
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My first (successful) post, hope this isn't silly/trivial. Also hope this is the appropriate area for optics-related questions.
While debugging some code that applies the Fresnel equations to transmission of light through multiple layers of planar media, I encountered an interesting feature that I had not previously noticed. Specifically, consider the transmission of a ray from medium 1 through a finite layer of medium 2, which re-emerges into medium 1 again (e.g., sunlight passing through a pane of glass in air).
It turns out that the reflection coefficient at the entry (1->2) interface is just equal to the reflection coefficient at the exit (2->1) interface. This regardless of the respective indices of refraction of the two media, the initial angle of incidence, or the polarization of the ray.
What surprises me about this symmetry is that the angle of incidence at the two interfaces is generally quite different... the refraction at the first interface just happens to produce the proper angle of incidence at the second such that the reflection coefficients are equal at both.
I guess my first question would be, is this simply wrong (i.e., am I using the wrong equations or made some other error), or, if not wrong, is there some broader (e.g., conservation or continuity) principle that makes more obvious why this would be the case?
Thanks for any info/insights-
While debugging some code that applies the Fresnel equations to transmission of light through multiple layers of planar media, I encountered an interesting feature that I had not previously noticed. Specifically, consider the transmission of a ray from medium 1 through a finite layer of medium 2, which re-emerges into medium 1 again (e.g., sunlight passing through a pane of glass in air).
It turns out that the reflection coefficient at the entry (1->2) interface is just equal to the reflection coefficient at the exit (2->1) interface. This regardless of the respective indices of refraction of the two media, the initial angle of incidence, or the polarization of the ray.
What surprises me about this symmetry is that the angle of incidence at the two interfaces is generally quite different... the refraction at the first interface just happens to produce the proper angle of incidence at the second such that the reflection coefficients are equal at both.
I guess my first question would be, is this simply wrong (i.e., am I using the wrong equations or made some other error), or, if not wrong, is there some broader (e.g., conservation or continuity) principle that makes more obvious why this would be the case?
Thanks for any info/insights-