Does Brewster’s angle exist for any pair of media?

Brewster’s angle exists for any interface between two non-absorbing media with real refractive indices n1 and n2. However, if one or both media are strongly absorbing (complex refractive index), the reflectance never reaches exactly zero and the simple Brewster formula is only approximate.

Is Brewster’s angle the same for s- and p-polarization?

No. Brewster’s angle only applies to p-polarized light (electric field in the plane of incidence). For s-polarized light, the reflectance never goes to zero at any angle, so there is no Brewster angle for s-polarization.

How is Brewster’s angle used in practice?

Brewster’s angle is used to design polarizing prisms, anti-reflection geometries, and to minimize reflection losses in laser cavities. By orienting optical surfaces at Brewster’s angle, p-polarized laser modes experience very low reflection losses while s-polarized modes are strongly attenuated.

Brewster’s Angle Calculator

Q: What is Brewster’s angle?

Brewster’s angle is the angle of incidence at which light with p-polarization (electric field in the plane of incidence) is transmitted through a surface with zero reflection. At this angle, the reflected and refracted rays are perpendicular, and the reflected light is perfectly s-polarized.

Q: How do you calculate Brewster’s angle?

For light going from medium 1 with refractive index n1 into medium 2 with refractive index n2, Brewster’s angle θB (measured in medium 1) is given by tan(θB) = n2 / n1. The angle is then θB = arctan(n2 / n1).

Compute Brewster’s angle between any two media, see polarization behavior, and estimate Fresnel reflectance for s- and p-polarized light.

Brewster’s Angle Calculator

Medium 1 (incident) n₁

Refractive index of the incident medium (e.g., air, water, glass).

Medium 2 (transmitted) n₂

Refractive index of the second medium (e.g., glass, water, crystal).

Incidence angle for reflectance θ (deg)

56.0°

Use this to compare Fresnel reflectance at Brewster’s angle vs. other angles.

Brewster’s angle (in medium 1)

53.1° degrees

θ_B = arctan(n₂ / n₁)

At Brewster’s angle, reflected p-polarized light intensity ideally goes to zero (for non-absorbing media).

Geometry

θ_B + θ_t ≈ 90°
θ_t ≈ 36.9°

Reflectance at θ

At θ = 56.0°:

R_p ≈ 0.0%
R_s ≈ 0.0%

Quick presets

What is Brewster’s angle?

When light hits an interface between two transparent media (for example air–glass), part of the light is reflected and part is transmitted. The amount of reflection depends on the angle of incidence and the polarization of the light.

Brewster’s angle (also called the polarizing angle) is the unique angle of incidence at which p-polarized light (electric field in the plane of incidence) is transmitted with zero reflection. At this angle, the reflected light is purely s-polarized.

Brewster’s angle formula

For light going from medium 1 (index \(n_1\)) into medium 2 (index \(n_2\)), Brewster’s angle \(\theta_B\) is:

\[ \tan(\theta_B) = \frac{n_2}{n_1} \quad\Rightarrow\quad \theta_B = \arctan\left(\frac{n_2}{n_1}\right) \]

This assumes both media are non-magnetic and non-absorbing (real refractive indices).

Step-by-step: how this calculator works

Choose the media. Either pick from presets (air, water, glass, fused silica) or enter custom refractive indices \(n_1\) and \(n_2\).
Compute Brewster’s angle. The tool evaluates \(\theta_B = \arctan(n_2/n_1)\) and reports it in degrees.
Find the transmitted angle. Using Snell’s law \(n_1 \sin\theta_i = n_2 \sin\theta_t\) with \(\theta_i = \theta_B\), the calculator finds \(\theta_t\) and checks that \(\theta_B + \theta_t \approx 90^\circ\).
Compare reflectance. With the incidence angle slider you can compute Fresnel reflectance \(R_s\) and \(R_p\) at any angle, including Brewster’s angle.

Fresnel reflectance at and around Brewster’s angle

For an interface between two non-absorbing media, the Fresnel equations give the amplitude reflection coefficients for s- and p-polarizations:

\[ r_s = \frac{n_1 \cos\theta_i - n_2 \cos\theta_t}{n_1 \cos\theta_i + n_2 \cos\theta_t} \quad,\quad r_p = \frac{n_2 \cos\theta_i - n_1 \cos\theta_t}{n_2 \cos\theta_i + n_1 \cos\theta_t} \] \[ R_s = |r_s|^2 \quad,\quad R_p = |r_p|^2 \]

At Brewster’s angle, the reflected and transmitted rays are perpendicular (\(\theta_i + \theta_t = 90^\circ\)), which makes the numerator of \(r_p\) equal to zero, so ideally \(R_p = 0\).

Typical Brewster angles for common interfaces

Interface (n₁ → n₂)	n₁	n₂	Brewster’s angle θ_B
Air → Water	1.0003	1.33	≈ 53.1°
Air → Glass (n ≈ 1.5)	1.0003	1.50	≈ 56.3°
Air → Fused silica (1.46)	1.0003	1.46	≈ 55.4°
Water → Glass (1.33 → 1.5)	1.33	1.50	≈ 48.4°

Practical uses of Brewster’s angle

Polarizing optics: Brewster prisms and Brewster windows transmit p-polarized light with minimal loss while reflecting s-polarized light.
Laser cavities: Orienting windows at Brewster’s angle helps enforce a particular polarization state of the laser mode.
Glare reduction: Many reflections from dielectric surfaces (water, glass) are partially polarized near Brewster’s angle, which is why polarizing sunglasses are effective.

Limitations and edge cases

Absorbing media: If one medium has a complex refractive index (metals, strongly absorbing materials), the simple Brewster formula is only approximate and reflectance never reaches exactly zero.
Total internal reflection: When light goes from higher to lower index (e.g., glass → air) at large angles, total internal reflection can occur. Brewster’s angle may still exist, but only for incidence angles below the critical angle.
Non-planar interfaces: The formula assumes a flat interface and plane waves; rough surfaces or focused beams can deviate from the ideal behavior.

Brewster’s Angle Calculator – FAQ

What is Brewster’s angle?

Brewster’s angle is the angle of incidence at which p-polarized light is transmitted through an interface with zero reflection. At this angle, the reflected and refracted rays are perpendicular, and the reflected light is purely s-polarized.

How do you calculate Brewster’s angle?

For an interface between media with refractive indices \(n_1\) and \(n_2\), Brewster’s angle in medium 1 is \(\theta_B = \arctan(n_2 / n_1)\). Enter \(n_1\) and \(n_2\) in the calculator and it will compute the angle in degrees for you.

Does Brewster’s angle exist for metals?

Metals have complex refractive indices with strong absorption. In that case, the reflectance never goes exactly to zero, so there is no true Brewster angle. The simple \(\tan(\theta_B) = n_2/n_1\) formula applies only to non-absorbing dielectrics.

Is Brewster’s angle the same when light goes from glass to air?

No. Brewster’s angle depends on the ratio \(n_2/n_1\) and is always defined in the incident medium. For air → glass you use \(n_1 \approx 1\), \(n_2 \approx 1.5\); for glass → air you use \(n_1 \approx 1.5\), \(n_2 \approx 1\), which gives a different Brewster angle (and you must also consider the critical angle for total internal reflection).

Why is only p-polarized light fully transmitted at Brewster’s angle?

At Brewster’s angle, the boundary conditions for the electromagnetic fields make the reflected p-polarized component vanish because the reflected and transmitted rays are orthogonal. For s-polarization, the boundary conditions are different and the reflectance never reaches zero, so there is no Brewster angle for s-polarized light.