Introduction to Electrodynamics · Problem 9.15

Electromagnetic Waves — David J. Griffiths

Physics · reflection-transmission-normal-incidence

Problem

In writing Eqs. 9.76 and 9.77, I tacitly assumed that the reflected and transmitted waves have the same polarization as the incident wave---along the

x

direction. Prove that this must be so. [Hint: Let the polarization vectors of the transmitted and reflected waves be

\hat{\mathbf{n}}_T = \cos\theta_T\,\hat{x} + \sin\theta_T\,\hat{y}, \quad \hat{\mathbf{n}}_R = \cos\theta_R\,\hat{x} + \sin\theta_R\,\hat{y},

and prove from the boundary conditions that

\theta_T = \theta_R = 0