- #1

fluidistic

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## Homework Statement

For an s-polarized wave (E and B fields are orthogonal to the plane of incidence) passing from medium to medium 2, I'm not understanding a minus sign.

The matching conditions are ##\hat n \times (\vec E_2 - \vec E_1)=\vec 0## and ##\hat n \times (\vec H_2 - \vec H_1 )=\vec 0##, where ##\vec E_1 = \vec E_R + \vec E_I## and ##\vec E_2 = \vec E_T##. So far so good: the transmitted E field is equal to the incident one plus the reflected one, at the interface between the 2 media. The same applies for the H field.

## Homework Equations

Matching conditions.

## The Attempt at a Solution

The idea is that ##\vec E_I## is known and so the 2 matching conditions should allow us to solve for ##\vec E_R## and ##\vec E_T##. We know the relationship between H and E: ##Z_i\vec H_i = \hat k \times \vec E_i##, where Z is the impedance of the medium. So far so good.

Soon comes the problem: using this last relation, I obtain that ##\hat k \times (\vec E_I + \vec E_R)Z_2=\hat k \times \vec E_T Z_1##. So that in terms of magnitude, ##(E_I -E_R)Z_2=E_TZ_1##. That's because ##\vec E_I## and ##\vec E_R## points in opposite directions.

However if I use this same argument then the 1st matching condition becomes ##(E_I-E_R)=E_T## which is wrong. It should be ##(E_I+E_R)=E_T##. I don't understand why.