Pre-Quantum Electrodynamics

Interesting question: what happens to an EM wave as it passes from one medium to another? Incident wave: produces reflected and transmitted waves. Detailed study: starts from boundary conditions disc_nfc,

\begin{align*} (i)~~ &\varepsilon_1 E_1^{\perp} - \varepsilon_2 E_2^{\perp} = 0, \nonumber \\ (ii)~~ &B_1^{\perp} - B_2^{\perp} = 0, \nonumber \\ (iii)~~ &{\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0, \nonumber \\ (iv)~~ &\frac{1}{\mu_1} {\bf B}_1^{\parallel} - \frac{1}{\mu_2} {\bf B}_2^{\parallel} = 0. \end{align*}