Question

Demonstrate that at the boundary between two media the normal components of the Poynting vector are continuous, i.e. `S_(1n) = S_(1n)`.

Answer 1

Let `oversetrarr(n)` be along the `z` axis. Then
`S_(In) = E_(1x) H_(1y)-E_(1y)H_(1x)`
and `S_(2n) = E_(2x)H_(2y) - E_(2y)H_(2x)`
Using the bounadary condition `E_(1t) = E_(2t), H_(1t) H_(2t)` at the boundary `(t = x` or `y `) we see that
`S_(1n) = S_(2n)`.