Classical optics · thin-film interference

Living Rainbow · Thin-Film Interference

Why does a colorless film only hundreds of nanometres thick develop flowing color? Light reflected from the film's front and back surfaces interferes. A given thickness puts a different phase difference on each wavelength, so some colors reinforce and others cancel. As the film drains, its uneven thickness keeps changing, and the color bands flow with it.

White light shines on a three-dimensional soap bubble as it drains. Gravity makes the thickness vary from top to bottom, the surface flows and the angle of incidence keeps changing, so different wavelengths reinforce in different places and form colored bands 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

Film thickness sets the color

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 an empty area to rotate the view. The cyan and magenta rays are the reflections from the two surfaces of the film; their phase difference decides whether that point looks bright, dark or colored.

Physics tutorial

Thin-film interference: read nanometres as color

BackgroundLight reflects from both the front and the back surface of the film, and the two reflections recombine. Two things decide which wavelengths reinforce and which cancel: the extra optical path inside the film, and the phase reversal when light reflects from a higher-index surface on the lower-index side.

Why it mattersSoap bubbles, oil films, antireflection coatings and precision optical coatings all rely on the same phase relation. The color you see is a map of thickness on the nanometre scale.

Start with the essentials

Focus question: Why does a clear, colorless soap film show colored bands, and why does it turn black as it gets thinner?
One-sentence intuition: A given thickness shifts the phase of each wavelength by a different amount, so some colors in white light reinforce, others weaken, and the thickness shows up as a 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 optical path for one round trip through the film. The extra $\pi$ comes from the phase reversal when light reflects off the film from the air side.

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 computes the amplitude reflection for each polarization and averages the two reflectances to get the result 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 modelColors roughly repeat each time the phase goes through another full cycle. The angle of incidence and the refractive index shift the colors too.

A black film is not an absent film

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

Better mental modelWhere the film is ultrathin, the two visible reflections mostly cancel, so an intact film can look nearly black.

Run the experiment

01
Turn thickness into color
Press Pause drainage, set Thickness flow to zero and slowly sweep Reference thickness.
What to observe: The colors cycle again and again as one wavelength after another meets the condition for reinforcement.
02
Keep only one wavelength
Turn on Monochromatic source and change Selected wavelength.
What to observe: The colored bands turn into bright and dark fringes. Each fringe is one interference order, so you can read the 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 is still there, but its two reflections mostly cancel across the whole visible band.

Living Rainbow · Thin-Film Interference

Thin-film interference: read nanometres as color

Core mathematical model

Phase difference between reflected rays

Fresnel result including repeated reflections

Common difficulties

One color does not imply one thickness

A black film is not an absent film

Run the experiment

Turn thickness into color

Keep only one wavelength

Approach the black film

Related experiments and articles

One film, many colours