Thin-Film Optics Calculator — Interference & Reflection

Formula

How this is calculated

When light strikes a thin film, a fraction reflects from the top surface and a second fraction transmits into the film, reflects from the bottom, and re-emerges. These two beams travel different distances — their optical path difference (OPD) is 2nt, where t is the physical film thickness and n is the film's refractive index. Depending on how OPD compares to the wavelength, the beams add constructively (enhancing reflection) or destructively (suppressing it).

An additional phase shift of π — equivalent to a half-wavelength delay — occurs whenever light reflects from a surface where the next medium has a higher refractive index. For a soap bubble or oil film floating in air the top-surface reflection acquires this shift while the bottom-surface reflection does not, giving one net phase shift. The constructive condition with one shift becomes 2nt = (m + ½)λ (m = 0, 1, 2…) and the minimum constructive thickness is λ/(4n). With zero or two phase shifts (both reflections shift or neither does) the conditions swap: constructive at 2nt = mλ, minimum λ/(2n).

The calculator normalises the result to a reflection-enhancement percentage using sin²(π·OPD/λ) for one phase shift or cos²(π·OPD/λ) for zero/two shifts — 100 % is fully constructive, 0 % fully destructive. The phasor diagram shows this geometrically: r₁ and r₂ are unit-amplitude phasors for each reflected beam, and the resultant R is their vector sum whose length is proportional to the reflected amplitude. This two-beam model applies to an ideal transparent film; absorption, rough surfaces and multiple internal reflections in real films introduce additional effects.