The Drude model for a free-electron metal (Chapter 5) gives the complex relative…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

What an Instrument Can See, Ch The boundary as a two-port

Problem

The Drude model for a free-electron metal (Chapter 5) gives the complex relative permittivity

\tilde\varepsilon(\omega) = 1 - \frac{\omega_p^2}{\omega^2+i\omega\gamma},

where

\omega_p

is the plasma frequency and

\gamma

the damping rate. For silver,

\omega_p = 1.37\times10^{16}\ \mathrm{rad\,s^{-1}}

and

\gamma = 2.73\times10^{13}\ \mathrm{rad\,s^{-1}}

. ((a)) Find silver's complex refractive index

\tilde n = n+i\kappa = \sqrt{\tilde\varepsilon}

at a vacuum wavelength of

589\ \mathrm{nm}

(the sodium D line). ((b)) Compute the normal-incidence reflectance

\mathcal{R}

from air onto this surface.