# Thin-Film Interference & Interferometers - Soap Bubble Colours, AR Coatings, Newton's Rings, Michelson

> Spectrally computed soap bubble and oil film colours, a draining soap film, AR coating designer, Newton's rings radius fit and a Michelson interferometer.

- URL: https://qilingtools.com/en/physics/interference
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

An interactive bench for thin-film interference and interferometers. Film colours are not looked up from a chart: the reflectance at every wavelength comes from the multilayer characteristic-matrix method and is integrated with the D65 illuminant and the CIE colour-matching functions, so you see the true sequence from silvery white through vivid colours to black film. The AR coating, Newton's rings and Michelson tabs let you adjust parameters, take readings and fit results as in a real lab.

## How to use

1. In "Thin-film colours" pick a soap bubble or oil film preset and drag the thickness and viewing angle, or click the colour strip and colour map
2. Open "Draining soap film" and press Play to watch the top of a vertical film thin into coloured bands and then black film; tap the film to read the thickness
3. In "AR coating designer" add or remove layers and set their index and quarter-wave thickness, comparing the reflectance curve with bare glass
4. In "Newton's rings" generate a noisy set of ring diameters and fit D² against order m to get the lens radius of curvature
5. In "Michelson interferometer" move a mirror and count fringes to measure λ, pump out a gas cell to measure its refractive index, or use white light to find zero path difference

## Features

- Exact multilayer reflectance with the transfer-matrix method, including multiple reflections and s/p polarisation
- True interference colours from spectral integration: thickness strip and a thickness × viewing-angle colour map
- Animated draining vertical soap film with an h ∝ √z profile and black-film collapse
- AR coating designer with MgF₂ single layer, V-coat, broadband three-layer and dielectric mirror presets
- Rendered Newton's rings with a least-squares radius fit (the intercept absorbs dust offsets)
- Michelson interferometer: fringe counting, gas-cell refractive index, sodium doublet beats and white-light fringes

## FAQ

### Why does a soap bubble turn black just before it pops?

With air on both sides, the front-surface reflection has a half-wave phase shift and the back-surface reflection does not, so the two reflected beams start half a wavelength apart. When the film is much thinner than λ/4 (below a few tens of nanometres) the path difference is negligible, the beams cancel at every wavelength and the film looks black. This "black film" is typically 5–30 nm thick and very fragile, so black patches usually mean the bubble is about to burst.

### Why do camera lens coatings look purple or green?

A single MgF₂ coating is usually a quarter wave thick at about 550 nm, so reflection is lowest in the green while the red and blue ends still reflect about 1–2%, which mixes to a purple-magenta. Broadband multilayer coatings suppress most of the visible range and the small residue often looks faint green or violet. The "residual reflection colour" in the coating tab shows this directly.

### What is the ideal index for a single-layer AR coating, and why is MgF₂ used?

For a quarter-wave layer, zero reflection needs n₁ = √(n₀nₛ). On glass with nₛ ≈ 1.52 that is about 1.23, but the lowest-index durable coating material is MgF₂ at 1.38, which leaves about 1.3% reflection at λ₀ instead of 4.3% for bare glass. To reach zero you can use a two-layer quarter-wave V-coat with n₂/n₁ = √(nₛ/n₀).

### Why plot diameter squared against order for Newton's rings instead of using one ring?

Ideally the dark rings satisfy r² = mλR/n, but real contacts often have dust or elastic deformation, and it is hard to number the rings exactly from the centre. Fitting D² = 4λR·m/n + c as a straight line makes the slope depend only on λR, while any constant gap offset goes into the intercept c. The result is more robust and comes with an uncertainty.

### Why do I only see a few coloured fringes with white light in a Michelson interferometer?

Fringes are only visible when the path difference is shorter than the coherence length λ²/Δλ. A He-Ne laser has such a narrow line that this is tens of centimetres; a sodium lamp gives a centimetre or two and its doublet makes the fringes beat; white light spans about 300 nm, so its coherence length is only about 1 µm. Coloured fringes therefore appear only near zero path difference, which is exactly how that point is located.

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