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; at oblique incidence, s and p polarizations have different optimum amplitudes. Air on n = 1.52 glass wants \(n_1 \approx 1.23\) in the visible; MgF2 at \(\sim\)1.38 is the closest stable practical choice and leaves a small residual.