Calculator inputs
Use the responsive grid below. Large screens show three columns. Smaller screens show two. Mobile screens show one.
Example data table
| Case | n1 | n2 | Angle | Rs | Rp | Unpolarized R | Observation |
|---|---|---|---|---|---|---|---|
| Air to glass | 1.000 | 1.500 | 0° | 0.0400 | 0.0400 | 0.0400 | Normal incidence produces about 4% reflection. |
| Air to water | 1.000 | 1.333 | 45° | 0.0532 | 0.0028 | 0.0280 | P polarization reflects far less near Brewster behavior. |
| Glass to air | 1.500 | 1.000 | 50° | 1.0000 | 1.0000 | 1.0000 | Total internal reflection occurs beyond the critical angle. |
Formula used
This calculator uses the Fresnel equations for two isotropic, nonmagnetic, lossless media. It is ideal for interface studies in introductory and applied optics.
Snell's law
n1 sin(θi) = n2 sin(θt)
S-polarized amplitude reflection coefficient
rs = (n1 cos(θi) - n2 cos(θt)) / (n1 cos(θi) + n2 cos(θt))
P-polarized amplitude reflection coefficient
rp = (n2 cos(θi) - n1 cos(θt)) / (n2 cos(θi) + n1 cos(θt))
Power reflectance
Rs = |rs|², Rp = |rp|², Runpolarized = (Rs + Rp) / 2
The selected transmission estimate uses 1 - R. During total internal reflection, power reflectance becomes 1.0, and amplitude coefficients require complex phase treatment.
How to use this calculator
- Enter the refractive index of the incident medium.
- Enter the refractive index of the transmission medium.
- Set the incident angle in degrees.
- Choose s, p, or unpolarized mode.
- Adjust the graph range and sample points.
- Press Calculate Reflection to view the result above.
- Review the summary tables, notes, and Plotly graph.
- Use the export buttons to save CSV or PDF output.
Frequently asked questions
1. What does the reflection coefficient represent?
It measures the reflected electric field relative to the incident field at a boundary. Its sign or phase shows reversal behavior, while its magnitude helps determine reflected power.
2. Why are s and p results different?
They respond differently to the interface geometry. S polarization is perpendicular to the plane of incidence, while p polarization is parallel. Their boundary conditions produce different reflection strengths.
3. What is the Brewster angle?
It is the incident angle where p-polarized reflectance ideally reaches zero for lossless media. At this angle, reflected and refracted rays become perpendicular.
4. What happens at the critical angle?
When light travels from a higher index medium into a lower one, angles above the critical value cause total internal reflection. The transmitted angle becomes nonreal in simple geometric optics.
5. Why can the amplitude coefficient be negative?
A negative sign indicates a phase reversal of the reflected electric field. Reflectance still stays positive because power depends on the squared magnitude.
6. Does wavelength change the result here?
Not directly in this simplified model. Wavelength matters when refractive indices vary with dispersion, coatings, or material absorption. Enter it as a reference value for your case.
7. Can this calculator model coated optics?
No. Thin-film coatings need multilayer interference equations, not a single-interface Fresnel model. This tool focuses on one boundary between two media.
8. When should I use unpolarized mode?
Use it when the incoming light has no preferred polarization, or when you want an average reflectance estimate for natural or mixed polarization conditions.