Fresnel Reflectance
Separate s- and p-polarized reflection at an interface and locate Brewster, critical and total-reflection regimes.
Free theory articleSeparate s- and p-polarized reflection at an interface and locate Brewster, critical and total-reflection regimes.
Concept & interpretation
When electromagnetic radiation strikes a planar boundary between two nonabsorbing, nonmagnetic dielectric media with refractive indices n1 and n2, Snell's law n1 sin(θi) = n2 sin(θt) determines the refraction angle θt. Below the critical angle, the Fresnel equations give the power reflectances Rs = ((n1 cos θi − n2 cos θt)/(n1 cos θi + n2 cos θt))2 for perpendicular (s) polarization and Rp = ((n2 cos θi − n1 cos θt)/(n2 cos θi + n1 cos θt))2 for parallel (p) polarization.
Experiment: Exploring Polarized Regimes
Use the Fresnel Reflectance interactive module to compare normal incidence, Brewster polarization, critical boundary, and total internal reflection:
- Set Interface to "Air to glass" and Angle setting to "Normal". Both s and p reflectances equal 0.04 (4%) and transmittance equals 0.96.
- Switch Angle setting to "Brewster" to verify that p reflectance drops to 0 while s reflectance rises to 0.147928994083.
- Change Interface to "Glass to air" and compare "Critical" (θi ≈ 41.81031489578°, θt = 90°) with "60 degrees" (total internal reflection where transmitted angle is unavailable and Rs = Rp = 1).