Surface-plasmon dispersion relation from the reflectivity of parallel-polarized light

We show that a very general method of deriving the surface-plasmon dispersion relation, $\omega =\omega \mathrm{}\left(Q\right)\mathrm{}$, for a semi-infinite metal is to set either $r_p\left(q_z\right)=\infty$ or $r_p(-q_z)=0\mathrm{}$, where $r_p$ is the reflected amplitude of parallel-polarized light and $q_z=i{(Q^2-\frac{{\omega }^2}{c^2})}^{\frac{1}{2}}$. This method is applied to get a new formula for the dispersion in the retardation region for a surface with a continuously varying electron-density profile, and it reduces to the Harris-Griffin result in the $c\to \infty$ limit.