Thin-Film Interference Calculator
Enter refractive index, wavelength and order to compute constructive thickness t=mλ/(2n) and destructive t=(m+½)λ/(2n). n=1.5, λ=500 nm, m=1 → t_c≈166.7 nm; anti-reflective MgF₂ t≈100 nm.
Input Data
Results
At a glance:Thin-film interference: when light hits a transparent thin film, the reflection from the top surface and the reflection from the bottom surface differ in optical path by Δ=2nt (n film index, t thickness), producing interference fringes. Constructive (bright): 2nt=mλ (m=0,1,2,…); destructive (dark): 2nt=(m+½)λ. If the media on the two sides of the film have different refractive indices, a half-wave loss (π phase jump) must be accounted for. Soap bubbles, oil films and butterfly wings all show these colours. History: Newton studied Newton's rings in 1675; Young's 1801 double-slit established the wave theory; Fresnel completed interference theory around 1820. Classic example: n=1.5, λ=500 nm, m=1 → t_constructive=500/(2×1.5)=166.7 nm; an anti-reflection MgF₂ film (n=1.38) needs thickness λ/(4n)=550/(4×1.38)≈100 nm. Applications: (1) anti-reflection coatings — lenses, glasses; (2) interference filters — narrow-band optical filtering; (3) Newton's rings — lens-curvature measurement; (4) soap bubbles — colour fringes; (5) structural colour — butterfly wings, peacock feathers.
Formula
Constructive: 2·n·t = m·λ (m=0,1,2,…)
Destructive: 2·n·t = (m+½)·λ
Optical path difference: Δ = 2·n·t
Constructive thickness: t_c = m·λ/(2n)
Destructive thickness: t_d = (m+½)·λ/(2n) = (2m+1)·λ/(4n)
$$2nt = m\lambda\ (\text{constructive}), \quad 2nt = \left(m+\tfrac{1}{2}\right)\lambda\ (\text{destructive})$$How to Use
- Enter refractive index n, wavelength λ (m) and order m.
- The tool computes t_constructive=mλ/(2n), t_destructive=(m+½)λ/(2n) and the OPD 2nt.
- Typical: n=1.5, λ=500 nm, m=1 → t_c≈166.7 nm; AR MgF₂ n=1.38, λ=550 nm, m=0 → t_d≈99.6 nm.
Case Studies
Camera anti-reflection coating
A single MgF₂ layer (n=1.38) at t=λ/(4n)=550/(4×1.38)=99.6 nm makes 550 nm reflect destructively, cutting reflectance from 4% to 1.3%.
Multi-layer (7-layer) MgF₂/TiO₂ alternation drops reflectance below 0.5% across 400–700 nm (>99% transmission).
Phone lenses show blue-violet coating, camera lenses green/amber — both are AR designs.
Soap-bubble colour fringes
Soap film n≈1.33, thickness 100–1000 nm flowing under gravity, each thickness picks a different constructive wavelength.
t=200 nm → 2nt=532 nm (green constructive); t=250 nm → 2nt=665 nm (red constructive).
As the film thins below ~100 nm all visible wavelengths interfere destructively (black, about to burst) — butterfly/peacock colour is the same multilayer effect.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.