That's right, but the problem is you cannot separate n or κ out. For example you get something like
n^{2}(n^{2}-\muc^{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...