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· Last updated：2026-08-29
r_s, r_p, R_s, R_p, T = 1−R, and the Brewster angle for any dielectric interface, with the 4% normal-incidence anchor.
Execution
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Tool usage guide
The Fresnel Equations Calculator computes reflection and transmission coefficients at the planar interface between two dielectric media. It provides exact values for amplitude coefficients (r_s, r_p), power reflectance (R_s, R_p), transmittance (T_s, T_p), Snell's refracted angle, and the Brewster angle based on incident and transmitting refractive indices.
Background
Designing an unpolarized light path striking a standard glass substrate (n = 1.5) from air (n = 1.0) at an oblique angle.
Problem
Calculate the separate reflectance values for s and p polarization states and find the Brewster angle.
How to use
Set n₁ to 1.0, n₂ to 1.5, and angleDeg to 30.
n₁ = 1.0, n₂ = 1.5, θ₁ = 30°Outcome
Yields a refracted angle of 19.47°, R_s of 5.78%, R_p of 2.52%, and a Brewster angle of 56.31°.
Background
Verifying baseline transmission losses for a beam entering perpendicular to an uncoated optic.
Problem
Determine single-surface reflection loss at normal incidence.
How to use
Set n₁ to 1.0, n₂ to 1.5, and angleDeg to 0.
n₁ = 1.0, n₂ = 1.5, θ₁ = 0°They calculate the amplitude and power ratios of reflected and transmitted electromagnetic waves across a boundary between two dielectric materials.
s-polarization has the electric field vector perpendicular to the plane of incidence, whereas p-polarization has the electric field vector parallel to the plane of incidence.
At the Brewster angle θ_B = arctan(n₂/n₁), the reflectance for p-polarized light (R_p) becomes zero, resulting in 100% transmission of the p-polarized component.
At 0° incidence, both polarizations share the same reflectance formula: R = ((n₁ - n₂) / (n₁ + n₂))², which equals 4% at an air-to-glass (1.0 to 1.5) boundary.
For non-absorbing lossless dielectric interfaces, conservation of energy applies such that transmittance is computed directly as T = 1 - R for each polarization state.
Outcome
Yields R_s = R_p = 4.00% and T_s = T_p = 96.00% at θ₂ = 0°.