- #1

- 10

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## Main Question or Discussion Point

Hi,

Got a problem with the following derivation:

Coming from the Helmholtz equation one gets:

[itex]\textbf{n}^2[/itex]=[itex]\mu[/itex][itex]c^{2}[/itex]([itex]\epsilon[/itex]+i[itex]\frac{\sigma}{\omega}[/itex])

which is of course something like:

[itex]\textbf{n}[/itex]=n+i[itex]\kappa[/itex]

My question is, how do you obtain the following relations?

[itex]n^{2}[/itex]=[itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]c^{2}[/itex][itex]\epsilon[/itex]([itex]\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}[/itex]+1)

[itex]\kappa^{2}[/itex]=[itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]c^{2}[/itex][itex]\epsilon[/itex]([itex]\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}[/itex]-1)

Maybe it's obvious, but I am arriving at everything but this. Enlighten me guys and thanks if you do.

Got a problem with the following derivation:

Coming from the Helmholtz equation one gets:

[itex]\textbf{n}^2[/itex]=[itex]\mu[/itex][itex]c^{2}[/itex]([itex]\epsilon[/itex]+i[itex]\frac{\sigma}{\omega}[/itex])

which is of course something like:

[itex]\textbf{n}[/itex]=n+i[itex]\kappa[/itex]

My question is, how do you obtain the following relations?

[itex]n^{2}[/itex]=[itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]c^{2}[/itex][itex]\epsilon[/itex]([itex]\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}[/itex]+1)

[itex]\kappa^{2}[/itex]=[itex]\frac{1}{2}[/itex][itex]\mu[/itex][itex]c^{2}[/itex][itex]\epsilon[/itex]([itex]\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}[/itex]-1)

Maybe it's obvious, but I am arriving at everything but this. Enlighten me guys and thanks if you do.