Single-Layer Anti-Reflection Coating Calculator

Classic Quarter-Wave Coating

A single MgF₂ layer on glass reduces front-surface reflection by controlling the phase of the light reflected from the two film interfaces.

Why This Design Works

An anti-reflection coating cancels the front-surface reflection by combining two normal-incidence conditions at the design wavelength λ₀: a quarter-wave thickness, so the reflections from the two coating interfaces meet 180° out of phase, and an index match \(n_1 = \sqrt{n_0 n_s}\), so they have equal amplitudes. The cosine factor extends the phase thickness rule to oblique incidence via Snell's law.

Quarter-wave thickness gives the cancellation phase; the geometric-mean index gives the normal-incidence amplitude balance. Air on n = 1.52 glass wants \(n_1 \approx 1.23\); MgF₂ at \(\sim\)1.38 is the closest stable practical choice and leaves a small residual.

Interactive design tool

This page includes a live transfer-matrix calculator for this design. Adjust the parameters to recompute spectra, layer stack, and performance figures in the browser, then open the design in the full calculator.