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.