Thin Film Interference: Soap Bubbles and Oil Slicks

The iridescent colors of soap bubbles, oil slicks on wet roads, and butterfly wings are all caused by thin film interference — one of the most beautiful phenomena in optics. Light reflecting off the top surface of a thin transparent film interferes with light reflecting off the bottom surface. Depending on the film thickness, wavelength, and refractive indices, certain colors are reinforced and others are suppressed.

How thin film interference works

When light hits a thin film (a soap bubble wall, a layer of oil, an anti-reflection coating), two reflected beams are produced:

1. Beam 1 reflects off the top surface of the film.
2. Beam 2 enters the film, travels through it, reflects off the bottom surface, travels back through the film, and exits through the top.

Beam 2 has traveled an extra distance of $2t$ inside the film (down and back up), where $t$ is the film thickness. But because the film has a different refractive index $n$, the effective optical path difference is $2nt$ (the wavelength inside the film is $\lambda/n$, so the phase accumulates $n$ times faster per unit distance).

These two beams overlap and interfere. If they're in phase, you see a bright reflection of that color (constructive). If they're out of phase, that color is missing from the reflection (destructive).

The phase-change-on-reflection rule

There's a critical subtlety: a phase change of 180° (half a wavelength) occurs when light reflects off an interface where the second medium has a higher refractive index — going from low $n$ to high $n$. No phase change occurs when reflecting from high $n$ to low $n$.

For a soap bubble in air ($n_{\text{air}} = 1$, $n_{\text{film}} = 1.33$, $n_{\text{air}} = 1$):

• Beam 1 reflects at the air→film interface: $n$ increases ($1 \to 1.33$), so there IS a 180° phase change.
• Beam 2 reflects at the film→air interface: $n$ decreases ($1.33 \to 1$), so there is NO phase change.

The net result: Beam 1 has an extra half-wavelength phase shift compared to Beam 2 (from the reflection alone). Combined with the path difference $2nt$, the total phase difference is $2nt + \lambda/2$.

Conditions for constructive and destructive interference

With one phase-inverted reflection (soap bubble), the conditions swap compared to the "no phase change" case:

Constructive (bright — the beams end up in phase): $2nt = \left(m + \dfrac{1}{2}\right)\lambda, \quad m = 0, 1, 2, \ldots$

The extra half-wavelength from the path must compensate for the half-wavelength phase shift from reflection, so they align at half-integer multiples.

Destructive (dark — the beams cancel): $2nt = m\lambda, \quad m = 0, 1, 2, \ldots$

Solving for the soap bubble

$n = 1.33$, $t = 300$ nm.

$2nt = 2 \times 1.33 \times 300 = 798$ nm.

Which wavelengths show constructive interference?

$\lambda = \dfrac{2nt}{m + 1/2} = \dfrac{798}{m + 1/2}$

• $m = 0$: $\lambda = 798/0.5 = 1596$ nm (infrared — not visible)
• $m = 1$: $\lambda = 798/1.5 = 532$ nm (green — visible!)
• $m = 2$: $\lambda = 798/2.5 = 319$ nm (ultraviolet — not visible)

So for a 300 nm soap film, only green light (~532 nm) is strongly reinforced in the visible range. The bubble appears greenish in reflected light.

Which wavelengths are destructively cancelled?

$\lambda = \dfrac{2nt}{m} = \dfrac{798}{m}$

• $m = 1$: $\lambda = 798$ nm (near-infrared)
• $m = 2$: $\lambda = 399$ nm (violet — borderline visible)

So violet is weakly suppressed, and the rest of the visible spectrum is partially reflected. The net color appearance is a blend — dominated by the constructive green.

Why soap bubbles show multiple colors

A real soap bubble isn't a single thickness — it's thinnest at the top (where gravity thins the film) and thickest at the bottom. Different thicknesses reinforce different wavelengths, producing bands of color that slowly shift and swirl as the film drains and changes shape.

Anti-reflection coatings

This same physics is used to eliminate unwanted reflections from camera lenses, eyeglasses, and solar cells. A thin coating (often magnesium fluoride, $n = 1.38$) of thickness $t = \lambda/(4n)$ is applied to the glass surface. At this "quarter-wave" thickness, the two reflected beams are exactly out of phase, and the reflection for that wavelength drops to nearly zero.

For a coating optimized for $\lambda = 550$ nm (green — the eye's most sensitive color): $t = 550/(4 \times 1.38) \approx 100$ nm. The coating appears purple/magenta in reflection because it cancels green but not red or blue.

Oil slick colors

An oil slick on water has two phase-changing reflections (air→oil and oil→water, since $n_{\text{oil}} \approx 1.5 > n_{\text{water}} = 1.33$). With both reflections experiencing a phase change, the net phase shift from reflections is zero (two half-wavelength shifts cancel), so the constructive condition becomes $2nt = m\lambda$ (no extra half-wavelength). The colors are different from a soap bubble of the same thickness because the phase-change rules differ.

Common mistakes

• Forgetting the phase change on reflection. This is the #1 mistake. You must check at each surface whether $n$ increases or decreases. Count the number of phase-reversing reflections (0, 1, or 2) and adjust the constructive/destructive conditions accordingly.
• Using $2t$ instead of $2nt$. The optical path difference is $2nt$, not $2t$. The film's refractive index matters because the wavelength inside the film is shorter.
• Not checking which $m$ values give visible wavelengths. The equations produce wavelengths for all integers $m$, but most will be outside the visible range (380–750 nm). Only report the ones in the visible range.

Try it in the visualization

Drag the thickness slider and watch the reflected color change. Very thin films appear dark (destructive for all visible wavelengths), then cycle through a sequence of colors as thickness increases. Toggle "show spectrum" to see which wavelengths are being reinforced at the current thickness. Switch to "oil on water" mode to see how the different phase-change situation produces a different color sequence.