# Energy flows of reflected/refracted waves

1. Apr 2, 2010

### fabpan

The reflection/transmission of an EM monochromatic plane wave when meets obliquely a plane boundary between two linear homogeneous isotropic means is clearly explained in many textbooks.

One of the results that is often shown is that the energy flow normal to plane (let say xy plane) between the 2 means produced by the incident wave is equal to the sum of the energy flows normal to the same plane produced by the reflected and transmitted waves.

No surprise, just conservation of energy.

Since the incident wave produces a flow of energy also on a direction parallel to the boundary plane (let say x direction) I would expect the same result also in this direction, but I couldn't find any textbook that deals whit this aspect.

Since the flow of energy normal to the boundary plane is $$S\times\cos\theta$$, where $$S$$ is the flow of energy in the propagation direction and $$\theta$$ is the angle of incidence, I tried just to change $$cos$$ into $$sin$$ to get the flow of energy on the x direction.

Doing this, the result is not what I expected. The flow produced by the incident wave seems not equal to the sum of the others two flows.

Of course I am wrong, but where?

Thank you