# 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?

## Homework Equations

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.

• Tinaaaaaa
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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