Fresnel Equations Calculator (Reflectance and Brewster Angle)

What this tool does

Fresnel's equations, which follow from Maxwell's boundary conditions, say how much light a surface reflects — and the answer depends on the polarisation. Glass reflects about 4 % head-on, but at Brewster's angle (about 56° for glass in air) the p-polarised reflection vanishes completely, which is why glare off water and roads is mostly s-polarised and polarised sunglasses can block it. Going from a denser material into a lighter one, everything beyond the critical angle is reflected: the trick that keeps light inside an optical fibre. A critical angle of 90° means there is none.

Formula

Rs = ((n₁cosθᵢ − n₂cosθₜ) ÷ (n₁cosθᵢ + n₂cosθₜ))² · Rp = ((n₁cosθₜ − n₂cosθᵢ) ÷ (n₁cosθₜ + n₂cosθᵢ))² · θ_B = atan(n₂ ÷ n₁)

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.