# Deflection of wave in dissipative media with a complex refractive index

## 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?

Snell's Law:

## 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.

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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.

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

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.