Analyze polarized reflections across refractive boundaries with confidence. Inspect angle-sensitive transmission and optical turning points. Export clean results, graphs, and comparison-ready values for reporting.
The graph shows s-polarized, p-polarized, and unpolarized average reflectance versus incident angle for the current refractive indices.
| Medium 1 | n₁ | Medium 2 | n₂ | Incident Angle | Transmitted Angle | Rs | Rp | Average Reflectance |
|---|---|---|---|---|---|---|---|---|
| Air | 1.0000 | Glass | 1.5000 | 45.0000° | 28.1255° | 9.2013% | 0.8466% | 5.0240% |
| Glass | 1.5000 | Air | 1.0000 | 50.0000° | Total internal reflection | 100.0000% | 100.0000% | 100.0000% |
Snell’s law: n₁ sin(θᵢ) = n₂ sin(θₜ)
s-polarized amplitude reflection: rₛ = (n₁ cos θᵢ − n₂ cos θₜ) / (n₁ cos θᵢ + n₂ cos θₜ)
p-polarized amplitude reflection: rₚ = (n₂ cos θᵢ − n₁ cos θₜ) / (n₂ cos θᵢ + n₁ cos θₜ)
s-polarized amplitude transmission: tₛ = 2n₁ cos θᵢ / (n₁ cos θᵢ + n₂ cos θₜ)
p-polarized amplitude transmission: tₚ = 2n₁ cos θᵢ / (n₂ cos θᵢ + n₁ cos θₜ)
Power reflectance: Rₛ = |rₛ|² and Rₚ = |rₚ|²
Power transmittance: T = (n₂ cos θₜ / n₁ cos θᵢ) × |t|²
Unpolarized average reflectance: R̄ = (Rₛ + Rₚ) / 2
Brewster angle: θ_B = arctan(n₂ / n₁)
Critical angle: θ_c = arcsin(n₂ / n₁), only when n₁ > n₂
When sin(θₜ) > 1, the interface enters total internal reflection. In that case, real transmitted power becomes zero and reflectance becomes one.
It computes Fresnel reflection and transmission at a flat boundary between two media. It reports s and p polarization behavior, transmitted angle, Brewster angle, critical angle, and average unpolarized reflectance.
s polarization has its electric field perpendicular to the plane of incidence. p polarization has its electric field parallel to that plane. Their reflection behavior generally differs strongly with angle.
At Brewster angle, the p-polarized reflected amplitude becomes zero for ideal non-magnetic media. That means p-polarized light is fully transmitted in power terms at that exact angle.
It occurs when light travels from a higher-index medium to a lower-index medium and the incident angle exceeds the critical angle. The transmitted wave becomes evanescent and reflected power reaches one hundred percent.
No. This version assumes real refractive indices and lossless isotropic media. For metals or absorbing layers, the refractive index becomes complex and the equations require a more advanced model.
For lossless interfaces, energy conservation applies. The reflected and transmitted power fractions add to one, aside from tiny rounding differences caused by decimal formatting in the displayed results.
A negative amplitude reflection coefficient indicates a phase reversal of 180 degrees in that polarization component. This matters in interference, thin films, and polarization-sensitive optical analysis.
It is the arithmetic mean of s and p reflectance. This approximation is commonly used when incident light has no preferred polarization direction at the interface.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.