Home exercise 6.3.1: Reflection from a copper surface

A uniform plane wave in air is normally incident on a flat copper surface ($\sigma =5.8\times 10^7$ S/m, $\mu ={\mu }_0$) at $f=10$ GHz.

1. Show that for a good conductor ${\eta }_2\approx (1+\mathrm{j})\sqrt{\omega {\mu }_0/2\sigma }=(1+\mathrm{j})R_s$, and evaluate $R_s$ and the skin depth.
2. Find $\Gamma$.
3. Show that the fraction of the incident power absorbed by the copper is $1-|\Gamma {|}^2\approx 4R_s/{\eta }_0$, and evaluate it.

Adapted from: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Problem P.8-28.