Brewster Angle Calculator

At Brewster's angle, the reflected light is perfectly polarized with only the s-component (perpendicular to the plane of incidence). The p-component (parallel) is fully transmitted.

🔍 Optics📐 θᴎ = arctan(n₂/n₁)🎨 Polarization
n₁ (incident medium)
n₂ (transmitted medium)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Brewster AngleθBθB = arctan(n2/n1)deg
n1—Incident medium refractive index—
n2—Refraction medium refractive index—
Property—θB + θrefracted = 90°—

Step-by-Step Examples

Example 1
Air to Glass

Air (n1=1.0) to glass (n2=1.5).

  • theta_B = arctan(1.5/1.0) = arctan(1.5) = 56.3°
✓ 56.3° Brewster angle for common glass
Example 2
Air to Water

n1=1.0, n2=1.333 (water).

  • theta_B = arctan(1.333) = 53.1°
✓ 53.1° — glare at this angle is fully polarized
Example 3
Glass to Air

Internal Brewster angle: n1=1.5 (glass), n2=1.0 (air).

  • theta_B = arctan(1.0/1.5) = arctan(0.667) = 33.7°
✓ 33.7° internal Brewster angle

Real-World Applications

🕶️
Polarized Sunglasses
Glare from roads and water is partially polarized at Brewster angle. Polarized lenses block it.
📷
Photography
Polarizing filters at Brewster angle dramatically reduce reflections from water and glass.
🔬
Laser Windows
Laser tube windows tilted at Brewster angle minimize reflection losses for p-polarization.
🔍
Ellipsometry
Brewster angle measurements characterize thin film thickness and refractive index.

Common Mistakes to Avoid

⚠️
n1 and n2 order matters

Brewster angle from air to glass (arctan(1.5)) differs from glass to air (arctan(1/1.5)).

⚠️
Only p-polarization disappears

S-polarization is still partially reflected at Brewster angle. Complete polarization only in reflected beam.

⚠️
Brewster angle is not critical angle

Brewster angle causes polarization. Critical angle causes total internal reflection. Both use n1, n2 but different formulas.

Frequently Asked Questions

Why is reflected light fully polarized at Brewster angle? ▾
At this angle, the reflected and refracted directions are perpendicular. Dipole oscillators along refracted ray direction cannot radiate back toward reflection direction for p-polarization.
What is the relationship between theta_B and theta_refracted? ▾
At Brewster angle: theta_B + theta_refracted = 90 degrees. This is exact. It means reflected and refracted rays are perpendicular.
How do polarized sunglasses use this? ▾
Road and water reflections are often at near-Brewster angle, making them partially polarized horizontally. Vertical-axis polarized lenses block this horizontally polarized glare.
What are Brewster windows in lasers? ▾
Laser tube ends tilted at Brewster angle. P-polarized light passes through with zero reflection loss. S-polarization reflects out, so laser emits pure p-polarized light.
Can Brewster angle exist for all n2/n1 ratios? ▾
Yes, arctan(n2/n1) is always defined and gives an angle between 0 and 90 degrees. No special conditions required.

Related Physics Calculators

🌈 Malus Law🔍 Critical Angle🔍 Refractive Index🔍 Snell Law🌈 Thin Film

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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