Originally Posted by **morrobay** Then with the units of the Poynting vector, **S** = dU/dtA=1/uo **E**x**B**
in units watts/meter^2. When the incidence is at an angle, then **S** like
intensity is less in the medium. So it seems refraction here is a boundary
correction. |

I just found the equations I was looking for. For the electric field we have boundary conditions: E1_n - E2_n = 0, where E1_n is the normal component of the incident electric field at the surface, and E2_n is the normal component of the outgoing electric field. The tangential E field (along the surface) is continuous.

The magnetic field has the same boundary condtions.

Important note: None of these equations hold for a situation where there is a surface charge density or an electric current on the surface. If you want a partial (meaning simplified) analysis, see

here. (Warning! Calculus involved.)

-Dan