Classical optics · thin-film interference

Living Rainbow · Thin-Film Interference

White light illuminates a three-dimensional soap bubble as it drains. A gravity-driven thickness gradient, surface flow, and changing incidence angle reinforce different wavelengths into ribbons that drift across the sphere.

Probe thickness

d

$680\,\mathrm{nm}$

Round-trip path

2nd\cos\theta_t

$1750\,\mathrm{nm}$

Strongest visible

\lambda

$550\,\mathrm{nm}$

Selected reflectance

R

$7.7\%$

Optical bench

Paint with thickness

Monochromatic sourceReplace white light with the selected

\lambda

to expose bright and dark orders.Interface ray pairFollow the front reflection and the delayed reflection from inside the film.Thickness contoursMark every

100\,\mathrm{nm}

of local film thickness.Reference thickness

d_0

680\,\mathrm{nm}

Film refractive index

n

1.33

Central incidence

\theta_i

26^{\circ}

Thickness flow

A_d

105\,\mathrm{nm}

Drainage rate

v_d

3.0\,\mathrm{nm\,s^{-1}}

Selected wavelength

\lambda

540\,\mathrm{nm}

Hover over the bubble to move the probe. The readouts and interface rays follow the exact sampled point.

Move the pointer over the sphere to place the nanometre probe, or drag empty space to orbit. Cyan and magenta rays mark reflections from the two interfaces; their phase difference decides whether that point is bright, dark, or colored.

Start with the essentials

Focus question: Why does a colorless transparent soap film develop colored ribbons and then enter a black-film state as it thins?
One-sentence intuition: One thickness gives different phase shifts to different wavelengths. Some parts of white light reinforce while others weaken, turning thickness into color.

Core mathematical model

Phase difference between reflected rays

\Delta\phi=\frac{4\pi nd\cos\theta_t}{\lambda}+\pi

$2nd\cos\theta_t$ is the round-trip optical path inside the film; the extra $\pi$ comes from the air-to-film reflection phase reversal.

Fresnel result including repeated reflections

\tilde r=\frac{r_{01}+r_{12}e^{2i\beta}}{1+r_{01}r_{12}e^{2i\beta}},\qquad \beta=\frac{2\pi nd\cos\theta_t}{\lambda},\qquad R=\lvert\tilde r\rvert^2

The simulation evaluates amplitude reflection for both polarizations and averages their reflectance for unpolarized light.

Common difficulties

One color does not imply one thickness

Typical misconceptionTwo points with the same color must have the same thickness.

Better mental modelApproximate colors repeat after another phase cycle, while incidence angle and refractive index also shift the colors.

A black film is not an absent film

Typical misconceptionA dark region at the top means the soap film has already ruptured.

Better mental modelIn an ultrathin region, visible reflections mostly cancel, so an intact film can look nearly black.

Run the experiment

01
Turn thickness into color
Pause drainage, reduce thickness flow to zero, and slowly sweep reference thickness.
What to observe: Color cycles repeatedly as different wavelengths successively satisfy reinforcement conditions.
02
Keep only one wavelength
Enable the monochromatic source and change the selected wavelength.
What to observe: Colored ribbons become bright and dark orders that expose phase directly.
03
Approach the black film
Choose Black film and move the probe to the top of the bubble.
What to observe: The film remains present while reflections across the visible band mostly cancel.