Thin Film Thickness⚠ unverified
Physics / Optics · Compute the film thickness for constructive interference
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| lambda_ | λ_ | m | 1.0 | Wavelength of the light |
| n | n | — | 1.0 | Refractive index of the film (dimensionless) |
| m | m | — | 1.0 | Interference order (dimensionless integer) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | t | m | Film thickness, in metres (m) |
The science & history
Understanding the Parameters
- $\lambda$, $n$ — optical thickness $nt$ sets the condition; higher $n$ → thinner physical $t$.
- $m$ — successive fringes as thickness increases.
- $t$ — soap bubbles, AR coatings, and oil slicks use related formulas.
Derivation (Approaching a Proof)
Path difference $2 n t$ (normal incidence) plus possible $\pi$ phase shifts from hard reflections yield constructive/destructive conditions. One standard case gives $2nt = (m+1/2)\lambda$ ⇒ the registry form.
History
Thin-film colours were explained in the 19th century; coatings are now a major photonics industry.
Related Concepts: Optical Path Length, Fresnel Reflection, Coherence Length
Notes: Registry calculator thin-film-thickness (unverified). One interference case; phase-shift
details matter for real stacks.