When an

electromagnetic wave encounters an

interface between two

dielectric media with different ε (permittivity) and μ (permeability), the wave undergoes

reflection and

transmission.

The following **Fresnel Coefficients** mathematically describe the reflection and transmission at oblique incidence, assuming the wave is propagating from region 1 to region 2. As the boundary conditions at the interface must be taken into consideration, parallel polarization **E**_{||} (electric field parallel to the plane of incidence) and perpendicular polarization **E**_{⊥} (electric field parallel to the plane of incidence) will be considered separately.

For both polarizations, Snell's Law of reflection and refraction is:

Θ_{i} = Θ_{r} angle of incidence equals angle of reflection, yo

β_{1} sin Θ_{i} = β_{2} sin Θ_{t}

where Θ

_{i} and Θ

_{r} and Θ

_{t} are the angles of incidence, reflection, and transmission, and β

_{1} and β

_{2} are the wavenumbers in dielectric 1 and 2, respectively.

The Reflection coefficients **R**_{⊥} and **T**_{⊥} are:

where η is the characteristic impedance of the dielectric, η = sqrt(μ/ε).

The Reflection coefficients **R**_{||} and **T**_{||} are: