Analyze polarized reflection across two engineering media. Enter indices, angle mode, and material assumptions easily. Review outputs, save tables, and validate interface calculations confidently.
| Interface | n1 | n2 | Brewster Angle (deg) |
|---|---|---|---|
| Air to Water | 1.000 | 1.333 | 53.12 |
| Air to Glass | 1.000 | 1.500 | 56.31 |
| Air to Acrylic | 1.000 | 1.490 | 56.13 |
| Water to Glass | 1.333 | 1.500 | 48.37 |
Main relation: tan(θB) = n2 / n1
Brewster angle: θB = arctan(n2 / n1)
Snell's law: n1 sin(θi) = n2 sin(θt)
Material conversion: n = √(εrμr)
Critical angle: θc = arcsin(n2 / n1), when n1 > n2
At Brewster angle, the reflected and refracted rays are perpendicular for the standard lossless case.
Brewster's angle is a key optical design value. It describes the incident angle where p-polarized reflected light drops to zero for an ideal interface. Engineers use it to control glare, improve polarization purity, and reduce reflection losses. This matters in measurement systems, laser benches, protective windows, and precision sensing assemblies.
The calculator helps compare two media quickly. You can solve the angle from refractive indices. You can also reverse the process and estimate an unknown index from a measured Brewster angle. That is useful in optical testing, material inspection, and educational lab work. Material mode also supports relative permittivity and permeability inputs. This is practical when electromagnetic properties are known before the effective refractive index is estimated.
The main output is Brewster's angle in degrees and radians. The tool also gives the transmitted angle at that condition. In the ideal case, the reflected and refracted rays form a right angle. The table also reports the index ratio and critical angle when total internal reflection is possible. These extra values help engineers judge interface behavior, ray geometry, and design limits without repeating manual steps.
This calculation appears in laser optics, camera systems, fiber experiments, display coatings, sensor enclosures, microscopy, and educational instrumentation. It is helpful when selecting glass, polymers, liquids, and dielectric stacks. Teams often use Brewster geometry to reduce unwanted reflected power and improve signal clarity. The result is especially relevant in polarization filters and low-reflection alignment setups.
This page uses the standard lossless relation. Real coatings, absorbing materials, rough surfaces, and wavelength-dependent dispersion can shift measured behavior. Metals and strongly absorbing media need more advanced complex-index models. Even so, this calculator is a strong first-pass engineering tool for clean dielectric interfaces and fast design checks.
It is the incident angle where p-polarized reflected light becomes zero for an ideal, lossless interface between two media.
At that angle, boundary conditions make the p-polarized reflection coefficient equal zero in the standard dielectric model.
Not accurately. Metals usually need complex refractive indices because absorption changes the reflection behavior.
The tool also reports a critical angle. That helps you check whether total internal reflection can occur.
It converts relative permittivity and permeability into refractive index first. That is helpful in electromagnetic and materials work.
For the standard Brewster condition, the reflected ray is perpendicular to the transmitted ray. The calculator confirms that geometry.
Refractive index, relative permittivity, and relative permeability are unitless. Angles are entered and reported in degrees.
It is used in laser alignment, optical coatings, polarization control, sensor windows, glare reduction, and academic experiments.
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.