What is the Brewster angle for air to glass?

For light passing from air (n1 = 1.000) into ordinary crown (window) glass (n2 = 1.500), Brewster's angle is arctan(1.500 / 1.000) = arctan(1.5) = approximately 56.31 degrees. This is the angle of incidence measured from the normal to the glass surface. At this angle, all reflected light is s-polarised. Different types of glass have slightly different refractive indices, so the exact Brewster angle varies a little.

Why does Brewster's angle matter in photography and optics?

Brewster's angle is the basis for polarising filters. When a camera's polarising filter is aligned to block s-polarised light, it cuts glare from water, glass, and other non-metallic surfaces most effectively when the camera is aimed at Brewster's angle to that surface (typically around 53 to 57 degrees for glass and water). Polarised sunglasses work on the same principle, cutting horizontal glare from roads and water by absorbing s-polarised light. In laser optics, Brewster windows allow a beam to pass through a glass window with zero reflection loss for p-polarised light.

Brewster's Angle Calculator

Calculate the polarisation angle (Brewster's angle) for light travelling between any two optical media. At Brewster's angle, reflected light is completely s-polarised and no p-polarised component is reflected.

Enter the refractive indices of both media, or choose a common preset, to get the Brewster angle in degrees instantly.

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Formula verified Brewster's Law: tan(θ_B) = n₂ / n₁. Standard optics formula.

1. Media Preset

Common media combination (optional shortcut)

Refractive index of medium 1 (n₁) incident medium

Refractive index of medium 2 (n₂) transmitted medium

2. About the Inputs

The refractive index (n) of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. Air is approximately 1.000, water is 1.333, and common glass ranges from 1.45 to 1.9 depending on type.

Brewster's angle is measured from the normal (perpendicular) to the surface, not from the surface itself.

At Brewster's angle, the refracted and reflected rays are at exactly 90 degrees to each other.

Brewster's Angle Result

Brewster's Angle
-
Degrees from normal

In Radians

rad

Refracted Angle (at Brewster)

Degrees (Snell's Law)

Calculation Breakdown

Medium 1 refractive index (n₁)-

Medium 2 refractive index (n₂)-

Ratio n₂ / n₁-

arctan(n₂ / n₁)-

Brewster's angle-

Geometry at Brewster's Angle

Angle of incidence-

Angle of refraction (Snell's Law)-

Sum (incidence + refraction)-

Reflected ray polarisation100% s-polarised

p-polarised reflected componentZero (0%)

Result: Enter refractive indices above.

What is Brewster's Angle?

Brewster's angle (symbol theta_B, also called the polarisation angle) is named after Scottish physicist Sir David Brewster, who discovered it experimentally in 1815. It is the angle of incidence at which light travelling between two dielectric (non-conducting) media produces a reflected ray that is completely polarised in the s-direction (perpendicular to the plane of incidence). At this angle, no p-polarised (parallel) component appears in the reflected ray; it is entirely transmitted into the second medium.

The physical reason is that p-polarised oscillating dipoles in the second medium, when aligned in the direction of the reflected beam, cannot radiate energy in that direction. This only occurs when the reflected and refracted rays are exactly 90 degrees apart, which is the geometric condition that Brewster's Law captures.

The Formula

Brewster's Law states:

tan(θ_B) = n₂ / n₁

where n₁ is the refractive index of the incident medium (the medium the light is coming from) and n₂ is the refractive index of the transmitted medium (the medium the light is entering). Rearranging gives:

θ_B = arctan(n₂ / n₁)

At Brewster's angle, the refracted angle satisfies Snell's Law (n₁ sin(θ_B) = n₂ sin(θ_r)), and the two angles sum to exactly 90 degrees: theta_B + theta_r = 90 degrees.

Worked Example

For light passing from air (n₁ = 1.000) into ordinary crown (window) glass (n₂ = 1.500):

Ratio: n₂ / n₁ = 1.500 / 1.000 = 1.500
Brewster's angle: arctan(1.500) = 56.31 degrees
Refracted angle (Snell's Law): arcsin(sin(56.31) / 1.500) = 33.69 degrees
Check: 56.31 + 33.69 = 90.00 degrees (confirmed)

This matches the calculator's default output for the air-to-glass preset.

Common Brewster Angles

Media (n₁ to n₂)	n₁	n₂	Brewster's Angle
Air to water	1.000	1.333	53.12 deg
Air to glass (n=1.5)	1.000	1.500	56.31 deg
Air to fused silica	1.000	1.460	55.60 deg
Air to diamond	1.000	2.417	67.52 deg
Water to glass	1.333	1.500	48.37 deg
Glass to air (internal)	1.500	1.000	33.69 deg

Note that the Brewster angle for glass-to-air is exactly 90 minus the air-to-glass Brewster angle (33.69 + 56.31 = 90). This is because n₂/n₁ is the reciprocal in each direction, and arctan(x) + arctan(1/x) = 90 degrees for any positive x.

Practical Applications

Polarising filters (photography): A circular polariser on a camera lens removes glare from non-metallic surfaces (water, glass, wet roads) most effectively when the camera is aimed at about Brewster's angle to the surface.
Polarised sunglasses: Horizontal glare reflected from roads and water is s-polarised. Polarised lenses block s-polarised light, cutting glare without reducing overall brightness as much as tinted lenses.
Brewster windows in lasers: Gas laser tubes often use windows set at Brewster's angle so that p-polarised light passes through with zero reflection loss, improving efficiency and producing a polarised beam.
Ellipsometry: Thin film thickness and optical properties are measured by analysing reflected polarised light near Brewster's angle.
Anti-reflection coatings: Thin film coatings exploit Brewster's angle effects to minimise reflections in camera lenses and glasses.

Related Calculators

Maths and Stats Calculators
Snell's Law Calculator: calculate the angle of refraction at any interface.
Angle of Refraction Calculator: find refracted angle from incidence angle and refractive indices.
Refractive Index Calculator: calculate refractive index from speed or angle data.
Angle of Incidence Calculator: work with incident rays and surface normals.

Method and sources: Formula: theta_B = arctan(n2/n1), from Brewster's Law (1815). Refractive index values from the NIST Handbook of Optical Constants and CRC Handbook of Chemistry and Physics. The relationship theta_B + theta_r = 90 deg follows from Snell's Law and is the geometric basis of complete polarisation at this angle.

This calculator assumes monochromatic light and non-absorbing (dielectric) media. Refractive indices are wavelength-dependent; for precise work use n values at your specific wavelength. Metals and other absorbing media require a complex refractive index treatment and do not produce a simple Brewster angle.