---
title: "A Rainbow Only Nanometres Thick Interactive Lab | Sandbox Physics"
description: "Why does a colorless film only hundreds of nanometres thick develop flowing color? Light reflected from the film's front and back surfaces interferes."
canonical_url: "https://sandboxphysics.com/labs/thin-film-interference/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/thin-film-interference/"
last_modified: "2026-10-27"
---

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.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

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

**Background** Light 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 matters** Soap 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 misconception** Two points with the same color must have the same thickness.

**Better mental model** Colors 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 misconception** A dark region at the top means the soap film has already ruptured.

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

### Run the experiment

1. 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.

2. 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.

3. 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.

Physical conclusion

The color of a thin film is a thickness reading, set by the optical path, the reflection phase and the Fresnel amplitudes together.

## Related experiments and articles

Continue exploring

### One film, many colours

Separate a changing thickness pattern from the spectrum reflected by one local layer.

1. [You are here **Living Rainbow · Thin-Film Interference** Explore a curved film with changing thickness.](https://sandboxphysics.com/labs/thin-film-interference/)
2. [Lab **Thin-Film Color Studio** Measure spectra and polarization in planar single and multilayer films.](https://sandboxphysics.com/labs/thin-film-color-studio/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)