# Energy flows of reflected/refracted waves

1. Apr 5, 2010

### fabpan

In this topic, I repeat a question I posted in an old topic trying to make it more understandable and hoping to receive some answer.

In case an electromagnetic plane wave meets an interface between 2 different dielectrics, the flow of energy of the incident wave through the xy-plane is equal to the sum of the flows of the reflected and transmitted waves through the same plane. This relation seems intuitive for the conservation of energy.
If $$\vec{S}_{I}, \vec{S}_{R}, \vec{S}_{T}$$ are the vectors of energy flows (Poynting vectors) of the incident, reflected and transmitted waves, then $$\left|\vec{S}_{I}\right|\times\cos{\theta_{I}}=\left|\vec{S}_{R}\right|\times\cos{\theta_{R}} + \left|\vec{S}_{T}\right|\times\cos{\theta_{T}}$$.
Many books show how to prove this relation starting from the Maxwell's equations.

Instead, I couldn't find any indication about the flows of energy along the y-direction. Surprisingly for me, in the y-direction it seems that the flow of energy of the incident wave be not equal to the sum of the flows of energy of the 2 resulting waves. Please, could anybody give me some explanation about these energy flows and their relationship or sugest me a reference to a book that deals with them?
[URL]http://einstein1.byu.edu/~masong/emsite/S5Q60/Brewster.gif[/URL]

Last edited by a moderator: Apr 25, 2017