Problem 5.78

An electromagnetic wave falls normally on the boundary between two isotropic dielectrics with refractive indices \(n_{1}\) and \(n_{2}\). Making use of the continuity condition for the tangential components, \(\mathbf{E}\) and \(\mathbf{H}\) across the boundary, demonstrate that at the interface the electric field vector \(\mathbf{F}\) (a) of the transmitted wave experiences no phase jump; (b) of the reflected wave is subjected to the phase jump equal to \(\pi\) if it is reflected from a medium of higher optical density.