Finding electric field incident on a medium

[zak8000]

\Gamma

Homework Statement

if an electric field is traveling in air and hits a medium n2. then there will be three fields present:

the incident electric field
the reflected electric field
and the transmitted electric field.

the electric field in medium 1 would be:

E(z,t)=Ei(exp(-jkz)+[itex]\Gamma[/itex]exp(jkz))cos(wt-kz) assuming it is traveling in the z direction

where gamma is the reflection cofficent and Ei is incident amplitude of the field.


and the felid in medium two would be:
E(z,t)=Ei([itex]\tau[/itex]exp(-jkz))cos(wt-kz) where tau is the transmission coffecient

i was wondering if the angle of incidence any affect of the fields. for example if the original e field was incident on the normal angle would it affect the field in medium 2 or the relfected field. if so how?

Homework Equations

The Attempt at a Solution

 

[jmlaniel]

The angle of incidence is actually quite important since the transmission and reflexion coefficient are function of the incidence angle (I think they are usually called Fresnel coefficient; actually the square modulus are the Fresnel coefficient). Furthermore, the transmitted angle is also function of the incident angle (See Snell-Descartes law).

I would also suggest that you don't mix complex wave and cosine wave expression since they complicate a lot any attempt when working with waves.