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Old Dec 1st 2013, 04:38 PM   #11
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Then with the units of the Poynting vector, S = dU/dtA=1/uo ExB
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.

Last edited by morrobay; Dec 1st 2013 at 05:25 PM.
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Old Dec 1st 2013, 05:52 PM   #12
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Originally Posted by morrobay View Post
Then with the units of the Poynting vector, S = dU/dtA=1/uo ExB
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.)

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