# Phase shift of reflected wave

## Homework Statement

An EM wave normally shed on a conductive material ($\tilde{\epsilon}=\epsilon+i\epsilon_i,\mu_0$). Calculate the phase shift of the electric field of the reflected wave relative to that of the incident wave.

## Homework Equations

$\nabla^2\textbf{E}=\mu\epsilon\frac{\partial^2\textbf{E}}{\partial t^2}+\mu\sigma\frac{\partial\textbf{E}}{\partial t}\Rightarrow\tilde{\textbf{E}}=\tilde{\textbf{E}}_0e^{i(\tilde{k}z-\omega t)}$

$\nabla^2\textbf{B}=\mu\epsilon\frac{\partial^2\textbf{B}}{\partial t^2}+\mu\sigma\frac{\partial\textbf{B}}{\partial t}\Rightarrow\tilde{\textbf{B}}=\tilde{\textbf{B}}_0e^{i(\tilde{k}z-\omega t)}$

$\tilde{k}=k+i\kappa\qquad;\qquad k=\omega\sqrt\frac{\epsilon\mu}{2}\left[\sqrt{1+\left(\frac{\sigma}{\epsilon\mu}\right)^2}+1\right]^{\frac{1}{2}}\,,\qquad\kappa=\omega\sqrt\frac{\epsilon\mu}{2}\left[\sqrt{1+\left(\frac{\sigma}{\epsilon\mu}\right)^2}-1\right]^{\frac{1}{2}}$

## The Attempt at a Solution

If I express $\tilde{k}$ as $\tilde{k}=Ke^{i\phi}$ where $K$ is a constant, I have a phase difference $\phi=\tan^{-1}\frac{\kappa}{k}$. This however seem to be the phase difference between the E and B field and not between the incident and reflected wave. I am the grader of a course using the second half of Griffiths' EM text book, but I don't seem to be able to find the solution to this question there.