- #1
fluidistic
Gold Member
- 3,923
- 261
Homework Statement
A monochromatic plane wave with frequency ##\omega## and real amplitude ##E_0## passes from medium 1 to medium 2 orthogonally with the surface between the 2 media. Both media are semi-infinite; the indices of refraction are ##n_1=\sqrt{\mu_0 \varepsilon _0}## and ##n_2=\sqrt{\mu_0 \varepsilon \left ( 1+ \frac{i4\pi \sigma}{\omega \varepsilon} \right ) }## respectively.
1)Find the system of equations that allows to get the value of all the electric fields in both media.
2)Find the transmitted ##\vec E## field in terms of the incident one.
3)Calculate their phase difference.
Homework Equations
##\vec E_I = \vec E_R + \vec E_T##. In words, the incident electric field is equal to the transmitted plus reflected electric fields.
The Attempt at a Solution
I notice that the problem is basically a plane wave passing from vacuum to a metal, with normal incidence.
I must apply the matching conditions for E and H in order to establish the system of equations asked in part 1).
So: ##\hat n \cdot (\vec E_2 - \vec E_1 )=0## and ##\hat n \times (\vec H_2 - \vec H_1)=\vec 0##.
Now, ##\vec E_2 = \vec E_T## and ##\vec E_1 = \vec E_I + \vec E_R##. I could now go on by writing down the H_i's in terms of the E_i's and answer to the question I suppose.
But I have a doubt: are my matching conditions correct? Because if it's a non perfect conductor, there should be some surface charge density and also a surface current or so... And the matching conditions would not be worth 0, but I am not sure.
I'd appreciate any comment.