# Obliquely incident waves on multiple dielectric interfaces

#### DrNick

Joined Dec 13, 2006
110
Does anyone know how to find the effective reflection coefficient for a EM wave hitting a multiple dielectric interface oblequely?

For example:
Rich (BB code):
eps1|   eps2    |   eps3
|           |
|           |
z=0           d
a wave is traveling in medium 1 with epsilon1 hitting at z=0, To find the input impedance at z=0, can i just use this formula:
Rich (BB code):
Zin=eda2 * eda1 - j * eda2 * tan(B*d)
eda2 - j * eda1 * tan(Bd)
?

or do things get skrewed up by the angle of incidence != 0 degrees?

Thanks

#### DrNick

Joined Dec 13, 2006
110

#### Dave

Joined Nov 17, 2003
6,970
For two mediums M1 (e.g air) and M2 (e.g the medium to which you have interacted), isn't the answer to this related to Snell's Law:

Sin ψ = √ε1 Sin θ

You can use Fresnel's Law to deduce the reflection coefficient:

Γ = (√ε2 *Cosθ) - (√ε1 *Cosψ)

For nomal incidence, then Fresnel's Law simplifies to:

Γ = (√ε2) - (√ε1)

Dave