Brewster's Angle Calculator — Polarisation Angle of Incidence
Find the Brewster angle — the angle of incidence at which the p-polarised component of reflected light vanishes completely — for any pair of optical media. Choose from common materials or enter custom refractive indices.
Medium 1 (incident)
Medium 2 (transmitted)
Angle of incidence at which reflected light is completely polarised (p-polarisation = 0)
- 1
Refractive index ratio n₂ ÷ n₁
1.52 ÷ 1.0003 = 1.5195 - 2
Brewster's angle
arctan(1.5195) × (180 ÷ π) = 56.651At this angle the reflected p-polarised component is exactly zero.
How does this calculator work?
Brewster's angle θ_B = arctan(n₂/n₁) is the angle of incidence at which the p-polarised reflection is zero and the reflected beam is completely s-polarised. At this angle, θ_incident + θ_refracted = 90°. For air-to-glass (n = 1.52) θ_B ≈ 56.7°. Used in laser windows, polarising filters and ellipsometry.
Formula
How this is calculated
When light hits an interface between two media at Brewster's angle (also called the polarisation angle), the reflected beam contains no p-polarised (parallel to plane of incidence) light — only the s-polarised component reflects. This arises because the oscillating dipoles in the transmitted medium, aligned along the refracted-ray direction, cannot radiate in the same direction as the reflected ray when θ_incident + θ_refracted = 90°.
The angle is found simply from the ratio of refractive indices: θ_B = arctan(n₂/n₁). At this angle the refracted ray travels at exactly 90° from the reflected ray — confirming θ_incident + θ_transmitted = 90°. For air–glass (n = 1.52), Brewster's angle is about 56.7°.
The calculator also shows the s-polarisation reflectance Rs at Brewster's angle using the Fresnel equation, and the normal-incidence reflectance for comparison. Refractive index values shown are for the sodium D line (589 nm) at room temperature; they vary with wavelength (dispersion) and temperature. For anisotropic materials (calcite, quartz c-axis) an effective index must be used.
Frequently asked questions
Brewster's angle is exploited in polarising filters, anti-reflection windows for lasers (Brewster windows inside laser cavities eliminate reflection losses for p-polarised beams), photography polarising filters, and glare-reducing sunglasses. It is also used in ellipsometry to measure thin-film thickness and optical constants.
No — Brewster's angle exists for light going from either medium to the other, but total internal reflection (TIR) occurs only when light travels from a denser to a rarer medium (n₁ > n₂) and exceeds the critical angle. The two phenomena are distinct: at Brewster's angle the p-reflectance is zero; at the critical angle all light reflects. Both can be calculated from the same pair of refractive indices.
Because arctan(n₂/n₁) → 90° as n₂/n₁ → ∞. In the limit of a very optically dense medium 2, the transmitted ray bends almost parallel to the interface, so the reflected ray must tilt close to grazing to remain perpendicular to it.
TG we-Calculate Editorial Team. (2026). Brewster's Angle Calculator — Polarisation Angle of Incidence [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/brewster-angle-calculator
TG we-Calculate Editorial Team. "Brewster's Angle Calculator — Polarisation Angle of Incidence." TG we-Calculate. 2026. https://we-calculate.com/calculator/brewster-angle-calculator.
TG we-Calculate Editorial Team, "Brewster's Angle Calculator — Polarisation Angle of Incidence," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/brewster-angle-calculator
@misc{wecalculate_brewster_angle_calculator, title = {Brewster's Angle Calculator — Polarisation Angle of Incidence}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/brewster-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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