Derivation of complex refractive index

[OneMoreName]

Hi,

Got a problem with the following derivation:

Coming from the Helmholtz equation one gets:

$\textbf{n}^2$=$\mu$$c^{2}$($\epsilon$+i$\frac{\sigma}{\omega}$)

which is of course something like:

$\textbf{n}$=n+i$\kappa$

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

$n^{2}$=$\frac{1}{2}$$\mu$$c^{2}$$\epsilon$($\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}$+1)
$\kappa^{2}$=$\frac{1}{2}$$\mu$$c^{2}$$\epsilon$($\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}$-1)

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

 

[andrien]

$$n$$=n+ik, put into $$n^2$$ and you will have two eqn ,one equating the real part and other equating the imaginary part which you can solve to get.if that is what you are asking.

 

[OneMoreName]

That's right, but the problem is you cannot separate n or κ out. For example you get something like

$n^{2}$($n^{2}$-$\mu$$c^{2}$$\epsilon$)=($\frac{μc^{2}σ}{2ω})^{2}$

and I don't see how to get to n².

Oh, OK, just have to solve the quadratic equation after substitution and one gets to the results, duh! Thanks!