How to use it
A thin film is a transparent layer a few hundred nanometres thick, such as a soap bubble wall, oil on a wet road or a lens coating. Light reflects from both of its surfaces and the two reflections interfere. Some wavelengths add up, others cancel, and the film looks coloured. Pick a preset and change the thickness to see it.
In the soap film picture the film drains: it thins with time and is thinnest at the top, so colour bands slide down until the top turns black. Click or tap the film to place a measuring point; its local thickness then drives the rest of the page. The oil picture shows a drop spreading on water; the plate picture compares a surface with and without the film.
Controls
- Presets: soap film in air, oil on water, a quarter-wave anti-reflection coating (magnesium fluoride on glass) and a reflective titanium dioxide coating.
- Film thickness: slider or number box, 0–2000 nm. The strip below shows the colour of every thickness; click it to jump there. Moving the slider detaches the measuring point, and a dashed line marks where the film has that thickness.
- Picture: Play, Pause, Restart film and Speed. On the picture, arrow keys move the measuring point (on the plate: the thickness), Space plays or pauses, R restarts.
- Indices and light: the three refractive indices, the angle of incidence, the polarization, the exposure and a probe wavelength (380–750 nm) for the spectrum marker and the two-wave picture.
How it works
Light reflected from the bottom surface crosses the film twice, so it travels an extra optical path
Reflection where the index goes up flips the wave by 180° (half a wavelength); where it goes down, there is no flip. A soap film in air has one flip, so it reflects a wavelength most strongly when 2n1d cos θ1 = (m + ½)λ and least when it equals mλ. With no flip or two flips (magnesium fluoride on glass) the rules swap. As d shrinks to zero, the two reflections of a soap film cancel completely: the black film.
The page adds every multiple reflection, not just two, using the Fresnel coefficients r01 and r12 of the two surfaces:
This is done for s and p polarization separately; unpolarized light is their average. Complex angles also handle total internal reflection, including light tunnelling through a very thin film. The indices do not change with wavelength and nothing is absorbed, so the transmitted share is 1 − R. The two-wave picture shows only the first two reflections, which carry most of the effect when the surfaces reflect weakly.
For the colour, the reflectance every 5 nm from 380 to 780 nm is weighted by daylight (CIE standard illuminant D65) and the CIE 1931 2° colour-matching functions from the published CIE tables, then converted to sRGB, clipping colours a screen cannot show. Y is the luminous reflectance, the share of the light that the eye sees as reflected.
The draining film is a simple model: a wedge, thinnest at the top, that thins steadily and turns into a 10 nm black film where it gets thinner than 30 nm, much like real soap films. The waves in the bands are only for looks, and the drop spreads at an invented pace with a fixed volume.
Things to try
- Load the anti-reflection coating: the coated half reflects about 1.3 % at 550 nm, bare glass about 4.3 %, and the leftover reflection is faintly purple because red and blue cancel less well than green.
- Tilt a soap film from 0° to 60°. The path difference shrinks with cos θ1, so the colours behave as if the film were thinner.
- In the oil preset, the thin edge of the drop fades into the grey of bare water, not black: without the film, the water surface itself reflects about 2 %.
- Choose p polarization and an angle of 53° on a soap film. At Brewster’s angle (tan θB = n1/n0) the reflection almost vanishes.
- Put glass on both sides of a thin air gap (n0 = 1.52, n1 = 1.00, n2 = 1.52) at 60° and shrink the gap below about 200 nm: light starts to tunnel through.
Frequently asked questions
Why does a soap film turn black at the top?
Where the film is much thinner than the wavelength, the flipped reflection from the top and the unflipped one from the bottom are almost exactly opposite and cancel for every colour.
Why are the colours pale when the film is thick?
A thick film has many reflection maxima inside the visible range at once, and the mix of many narrow bright bands looks almost white.
Is the colour exactly what I would see?
It is the colour of reflected daylight for the CIE standard observer. Your screen, the real light source, the background and the exposure all change what you perceive.
Why does an anti-reflection coating work best at one wavelength?
Its thickness is a quarter wavelength inside the coating, about 100 nm for green light; only there are the two reflections exactly half a wave apart.
Sources
- Ling SJ, Sanny J, Moebs W (2016). Interference in thin films. University Physics Volume 3, OpenStax, section 3.4. The extra path in the film, the half-wave flip on reflection, the dark thinnest film and anti-reflection coatings.
- CIE (2019). CIE standard illuminant D65 (data table). International Commission on Illumination. The daylight that lights the film.
- CIE (2019). CIE 1931 colour-matching functions, 2 degree observer (data table). International Commission on Illumination. The weights that turn the reflected spectrum into a colour.