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Dielectric Brewster Angle & Index Ratio

Calculate Brewster angle or either positive refractive index for an ideal dielectric interface.

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When the transmitted-medium index is √3 times the incident-medium index, the Brewster angle is 60° from the surface normal.

Brewster angle = arctan(n₂/n₁)

Enter these known values and leave the other values blank.

Refractive indices are positive real values for the same wavelength. The angle is strictly between 0° and 90°.
The standard formula assumes a flat interface between nonabsorbing, nonmagnetic isotropic dielectrics. It is not a general formula for metals, complex indices or anisotropic materials.
The angle is measured from the surface normal. At this angle the ideal p-polarized reflection vanishes; s-polarized light can still reflect. Equal indices give the formal 45° result, but an index-matched interface has no reflection at any angle.

It is the medium the incident light travels through before reaching the interface. Swapping the media changes the angle.

For positive real indices in this model, arctan(n₂/n₁) and arctan(n₁/n₂) are complementary.

Bookify requires positive refractive indices and a Brewster angle strictly between 0° and 90°.