Brewster's Angle Calculator

Brewster's angle (also known as the polarization angle) is calculated using Snell's law and electromagnetism principles. When unpolarized light hits a boundary between two optical media, the reflected ray is completely polarized parallel to the surface if the angle between the reflected and refracted rays is exactly 90 degrees. The governing formula is:

θ_B = arctan(n₂ / n₁)

Where θ_B is Brewster's angle, n₁ is the refractive index of the incident medium (such as air), and n₂ is the refractive index of the reflecting medium (such as glass or water).

Imagine you are shining a light beam from air into a dense flint glass prism. You want to find the exact angle of incidence that yields total polarization upon reflection. Here are the given variables:

• Incident Medium Refractive Index (n₁): 1.00 (Air)
• Reflecting Medium Refractive Index (n₂): 1.65 (Dense Flint Glass)

Step 1: Divide the refractive index of the second medium by the first medium. 1.65 / 1.00 = 1.65.

Step 2: Take the inverse tangent (arctan) of 1.65. arctan(1.65) ≈ 58.78°.

Thus, Brewster's angle for this interface is approximately 58.78 degrees.

Keep these useful guidelines in mind when working with optical polarization and refractive indices:

• Wavelength Dependency: Refractive indices vary slightly with the wavelength of light due to chromatic dispersion. Ensure your input values match your specific light source (e.g., sodium D-line at 589 nm).
• Medium Order Matters: Always make sure n₁ represents the medium where the light originates and n₂ represents the medium being entered. Swapping them will calculate the complementary angle of refraction.