Deflection of wave in dissipative media with a complex refractive index

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Homework Statement


A monochromatic plane wave with wavelength 500µm is propagating through a dissipative medium with refractive index 1-0.0002i. It approaching the edge of the medium, and will pass out into free space. If the angle of incidence is not 90°, how much will the wave deflect as it passes out into free space?

Homework Equations


Snell's Law:
b5a73124df21668801a4d20054bb1b13f6709752


The Attempt at a Solution


The refractive index of free space would be 1-0*i so so far I have 1-0.0002i/1. But I don't know how to find the angles.
 

Answers and Replies

  • #2
Charles Link
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I haven't previously worked this type of problem, even though I have an Optics background, but I can give you a couple of inputs to it. In a medium with complex ## n ##, the wave will propagate as ## E=E_o e^{i( n_r k_o x-\omega t)} e^{-n_i k_o x} ##. I don't think the ## e^{-n_i k_o x } ## factor will affect the boundary value conditions that determine which direction the wavefront emerges when it encounters a boundary. I think that is simply determined by ## n_r ##. If my inputs are indeed correct, the answer to this problem, for which ## n_r=1 ##, should be obvious.
 
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I haven't previously worked this type of problem, even though I have an Optics background, but I can give you a couple of inputs to it. In a medium with complex ## n ##, the wave will propagate as ## E=E_o e^{i( n_r k_o x-\omega t)} e^{-n_i k_o x} ##. I don't think the ## e^{-n_i k_o x } ## factor will affect the boundary value conditions that determine which direction the wavefront emerges when it encounters a boundary. I think that is simply determined by ## n_r ##. If my inputs are indeed correct, the answer to this problem, for which ## n_r=1 ##, should be obvious.
Thank you this makes a lot of sense
 
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Charles Link
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Thank you this makes a lot of sense
A google of this question shows there seems to be a couple of different schools of thought on the subject. There are a couple of postings that talk about the Descartes-Snell law of refraction, but there are other postings that interpret it exactly like I did. I leave the question open to further discussion, but I don't know that there is a definitive answer to this one that everyone will agree upon. ## \\ ## Unless ## n_i ## is considerably greater than ## 0 ##, it may be difficult to experimentally verify any result that would show ## n_i ## could cause some effect, but if ## n_i ## gets to be significant, the wave doesn't propagate very far through the material.
 

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