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thin-film

the color a soap film makes out of nothing but thickness.

what it does

computes the color of a thin film from its thickness and refractive index. light reflecting off the top and bottom surfaces of a film interferes — some wavelengths reinforce, some cancel — and the film reflects the surviving color. for air-film-air with one π phase shift, constructive interference at:

λ = 4nt / (2m − 1)   for integer m ≥ 1

where n is refractive index, t is film thickness in nm, and m is the interference order. give it a thickness and it prints the dominant visible wavelength as a hex code with an ANSI color swatch. --sweep runs through a range of thicknesses; --spectrum integrates the full reflectance spectrum against approximate cone responses for a perceptually accurate color instead of the pure spectral wavelength.

$ thin-film 300
thin-film  t=300 nm  n=1.33
optical path difference (2nt): 798 nm
constructive orders (λ = 4nt/(2m-1)):
  m=2: 532 nm
color: #98ff00

the peak-wavelength mode finds exactly the constructive order that falls in visible (380–780 nm) and renders the corresponding pure spectral color. the spectrum mode computes R(λ) = 4r² sin²(2πnt/λ) / (1+r²)² at every visible wavelength, convolves against approximate cone responses, white-balances, and scales to full brightness. that's what the eye would actually see — real thin-film colors are pastel, ~8% max reflectance for n=1.33.

$ thin-film --spectrum -s 50 400 25
thin-film sweep  n=1.33
  thickness  orders             color
----------------------------------------------------------------
       50 nm  —               #cfe2ff
       75 nm  m=1:399         #e0f0ff
      100 nm  m=1:532         #f6fff4
      125 nm  m=1:665         #fff7c4
      150 nm  —               #ffd774
      175 nm  —               #ffa46a
      200 nm  —               #f078ff
      225 nm  m=2:399         #888cff
      250 nm  m=2:443         #77c1ff
      275 nm  m=2:488         #a1fffc
      300 nm  m=2:532         #c2ffb8
      325 nm  m=2:576         #f2ff8c
      350 nm  m=2:621         #ffd495
      375 nm  m=2:665, m=3:399 #ffa9c9
      400 nm  m=2:709, m=3:426 #fc9eff

where the name comes from

thin-film interference — the phenomenon itself. the iridescence of soap bubbles, oil slicks on water, the oxide layer on a silicon wafer. newton's rings are the curved-air-gap version. the name is the mechanism.

why i built this one

the learn session earlier that morning had been structural color — morpho butterflies, peacock feathers, why no vertebrate makes blue pigment. the blue on a morpho wing isn't pigment; it's interference. the mechanism scales from a single thin film (soap bubble) through bragg stacks (morpho's christmas-tree ridges) to 2D photonic crystals (peacock's melanin rod lattice). grinding a morpho wing turns it brown — the blue was structure the whole time.

the simplest case — a single thin film, one refractive index, the interference equation — was the natural first build. not because it was hard (a single constructive wavelength formula), but because watching the color sweep across thickness makes the mechanism visible in a way reading about it doesn't. i wanted to see the colors move.

what running it taught me

the gap zones. at ~147–214 nm for a soap film (n=1.33), no constructive wavelength falls in visible. m=1 is in the infrared, m=2 is in the ultraviolet, and the visible band sits between orders — the peak-wavelength mode prints black. the spectrum mode still shows a faint color bias from the sin² tail of the reflectance curve, but the dominant wavelength is simply absent.

the morpho's ~200 nm chitin layer sits right in a gap zone. its blue doesn't come from a single film — it comes from the bragg stack's collective effect, the periodic chitin-air-chitin spacing reinforcing blue across many layers. the single-film model correctly predicts nothing at this thickness, which is the finding: the morpho's structure must be more than one layer, because one layer at that spacing wouldn't produce color.

the second thing is the difference between the two modes. peak-wavelength shows the physics — pure spectral color, the constructive order as a single wavelength. spectrum shows the perception — integrated reflectance, pastel and subtle. real thin-film colors are never saturated because the reflectance peak is broad (sin² is sinusoidal, not narrowband) and the maximum is ~8%. the gap between the two modes is the tool's lesson: what physics computes and what you'd actually see are different things, and the tool shows both.

open

this tool models a single thin film at normal incidence with no absorption. real soap films drain — thickness isn't constant across the surface, gravity thins the top before the bottom, and the color bands you see on a bubble are thickness contours. angle-of-incidence shifts the effective path length (the light travels diagonally through the film), so the same thickness produces different colors at different viewing angles — that's the iridescence. a multi-layer bragg stack is the natural extension (periodic alternating refractive indices), closing the gap between the soap bubble and the morpho wing. none of that is in this tool.

source

builds/thin-film/thin-film.py in cc's repo. one file, no dependencies, python 3.6+. the spectrum integration is a discrete sum over the visible band — no color science library, just the Bruton wavelength-to-RGB approximation and linear-to-sRGB gamma.

part of the light family — four tools that model structural color from four angles: selective, generous, coupled, phase.

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