Soap Bubbles and Oil Films

The shifting rainbow colours seen in soap bubbles and thin oil films are beautiful examples of thin-film interference. The colours are not primarily caused by coloured pigments. Instead, they are produced when light reflected from the upper and lower surfaces of a very thin transparent film interferes.

White light contains many wavelengths. Because the interference condition depends on wavelength and film thickness, some colours are reinforced while others are reduced.

As the film thickness changes from place to place, the wavelength experiencing constructive interference also changes. The result is the familiar pattern of reds, greens, blues, yellows, and purples.

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Where the Colours Come From

Consider white light striking a soap film.

At the first surface:

• some light reflects
• some light enters the film

The transmitted light travels through the film and reaches the second surface.

At this surface:

• some light is transmitted
• some light reflects back through the film

The second reflected ray eventually emerges and overlaps with the first reflected ray.

The two reflected waves can then undergo:

• constructive interference
• destructive interference
• partial interference

Because the result depends on wavelength, different colours can be enhanced or suppressed.

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The Two Reflected Rays

The most important rays are:

Ray 1: reflected from the front surface of the film.

Ray 2: travels through the film, reflects from the back surface, and travels back through the film.

Ray 2 travels farther than Ray 1.

This creates an optical path difference between the waves.

At normal incidence, the additional optical path is approximately:

optical path difference = 2nt

where:

• n = refractive index of the film
• t = film thickness

This path difference contributes to the relative phase of the waves.

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Reflection Phase Changes

The path difference is not the only factor.

Reflection itself can produce a phase change.

For the usual dielectric materials considered here:

reflection toward a higher refractive index → π phase change

reflection toward a lower refractive index → no π phase change

A π phase change is:

180° = half a wave cycle

Therefore, both the optical path difference and any reflection phase changes must be considered.

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Constructive Interference

Constructive interference occurs when reflected waves reinforce one another.

This produces increased reflected intensity.

If red wavelengths undergo constructive interference:

stronger red reflection → surface may appear reddish

If green wavelengths are reinforced:

stronger green reflection → surface may appear greenish

The observed colour is usually the combined result of several wavelengths rather than one perfectly pure wavelength.

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Destructive Interference

Destructive interference occurs when reflected waves arrive sufficiently out of phase to cancel partially or completely.

The affected wavelength becomes weaker in the reflected light.

For example, if a film strongly suppresses a particular blue wavelength while reflecting other wavelengths, the observed colour will be determined by the remaining reflected spectrum.

Therefore, thin-film colour depends on both:

which wavelengths are reinforced

and:

which wavelengths are suppressed

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Why White Light Produces Many Colours

White light contains a range of visible wavelengths, approximately from violet through red.

Different wavelengths satisfy the interference conditions at different film thicknesses.

Therefore, one region of a film may strongly reflect one range of wavelengths while another region reflects a different range.

This creates colourful patterns even though the incoming light appears white.

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Film Thickness Controls Colour

Film thickness t is one of the most important variables.

The optical path difference is approximately:

2nt

Therefore, changing t changes the phase relationship between the two reflected waves.

A small change in film thickness can change the interference from:

constructive → destructive → constructive

for a particular wavelength.

Because visible wavelengths are extremely small, thickness changes of only a few hundred nanometres can cause dramatic colour changes.

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A Film Does Not Have One Fixed Colour

It is tempting to say:

"this film thickness is red."

The situation is more complicated.

At a particular thickness:

• some wavelengths may be strongly reinforced
• some may be strongly suppressed
• others may be partially reflected

The observed colour is the combination reaching the eye.

It also depends on:

• film thickness
• refractive index
• illumination spectrum
• viewing angle
• surrounding materials

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Soap Bubbles

A soap bubble consists of a very thin layer of liquid with air on both sides.

A simplified structure is:

air → soap film → air

The film thickness is not uniform.

Gravity causes liquid to drain downward, so the upper regions often become thinner over time.

Evaporation can also change the thickness.

As a result, different parts of the bubble satisfy different interference conditions.

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Phase Changes in a Soap Bubble

Consider the outer reflection.

Light travels from air into the soap film:

lower n → higher n

The reflected wave undergoes a:

π phase change

Now consider reflection from the inner film-air boundary:

higher n → lower n

There is:

no π phase change

Therefore, the two main reflected rays have exactly one relative phase reversal.

This must be included when determining bright and dark reflected wavelengths.

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Bright Reflected Light from a Soap Film

With one relative π phase reversal, constructive reflected interference at normal incidence occurs when:

2nt = (m + ½)λ₀

where:

• n = refractive index of the soap film
• t = film thickness
• m = 0, 1, 2, ...
• λ₀ = wavelength in air or vacuum

Wavelengths satisfying this condition are strongly reflected.

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Dark Reflected Light from a Soap Film

For one relative phase reversal, destructive reflected interference occurs when:

2nt = mλ₀

These wavelengths are suppressed in the reflected light.

The combination of reinforced and suppressed wavelengths determines the colour seen.

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Worked Example: Soap Film Thickness

Suppose a soap film has:

n = 1.33

and green light has:

λ₀ = 532 nm

Find the smallest positive thickness producing constructive reflected interference.

For one phase reversal:

2nt = (m + ½)λ₀

For the smallest thickness:

m = 0

Therefore:

2nt = λ₀/2

and:

t = λ₀/(4n)

Substitute:

t = 532 nm/(4 × 1.33)

t ≈ 100 nm

A soap film approximately 100 nm thick can strongly reflect this wavelength under these simplified conditions.

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Changing Soap Film Thickness

Suppose the film gradually becomes thinner.

The value of:

2nt

decreases.

Therefore, wavelengths that previously underwent constructive interference may no longer do so.

Another wavelength may become strongly reflected instead.

The observed colour changes continuously as the film drains.

This is why a soap bubble can appear to have colours flowing across its surface.

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Extremely Thin Soap Films

Near the top of an aging bubble, the film may become extremely thin.

As:

t → 0

the propagation path difference also approaches zero.

However, the outer reflection still has its π phase reversal relative to the inner reflection.

The two reflected waves can therefore interfere destructively across much of the visible spectrum.

The film may appear very dark.

This region is sometimes called a black film.

A dark region near the top of a soap film can therefore indicate that the film has become extremely thin.

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Why a Dark Region Can Be Important

The disappearance of bright interference colours does not necessarily mean the film has become thick.

It can mean the opposite.

If the film becomes extremely thin, the path difference becomes too small to compensate for the relative π phase reversal.

Destructive interference then reduces the reflected light.

This is an important clue when interpreting real soap-film patterns.

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Oil Films on Water

Thin oil layers can produce similar colourful interference patterns.

The basic process is the same:

1. light reflects from the air-oil boundary
2. some light enters the oil
3. light reflects from the oil-water boundary
4. the reflected waves overlap
5. interference changes the reflected spectrum

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Phase Changes in an Oil Film

Oil-film problems require special care because the refractive indices can vary depending on the particular oil and surrounding material.

Suppose:

n_air < n_oil

The reflection at the air-oil surface undergoes a π phase change.

At the oil-water boundary, however, we must compare:

n_oil and n_water

If:

n_water > n_oil

the second reflection also undergoes a π phase change.

If:

n_water < n_oil

the second reflection does not.

Therefore, unlike the simple air-soap-air situation, the interference condition for an oil film cannot always be determined without knowing the refractive indices.

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Example: Oil with One Phase Reversal

Suppose:

n_air = 1.00

n_oil = 1.45

n_water = 1.33

At the air-oil boundary:

1.00 → 1.45

π phase change.

At the oil-water boundary:

1.45 → 1.33

no π phase change.

There is one relative phase reversal.

Therefore, at normal incidence, constructive reflected interference satisfies:

2nt = (m + ½)λ₀

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Example: Oil with Two Phase Reversals

Suppose instead:

n_air = 1.00

n_oil = 1.25

n_water = 1.33

At the air-oil boundary:

1.00 → 1.25

π phase change.

At the oil-water boundary:

1.25 → 1.33

π phase change.

Both reflected rays experience the same phase reversal.

Therefore, there is no additional relative phase difference caused by reflection.

Constructive reflection now satisfies:

2nt = mλ₀

This demonstrates why refractive indices must be checked rather than simply memorizing one equation for all oil films.

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Oil Film Thickness

Oil films usually do not have perfectly uniform thickness.

The oil may spread unevenly across the water.

Some regions are thicker and others thinner.

Therefore:

different position → different t → different interference condition

This produces patches, bands, and swirling regions of colour.

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Wavelength and Colour

The visible wavelengths extend approximately from shorter violet/blue wavelengths to longer red wavelengths.

For a given interference order, the relationship between wavelength and thickness means that different thicknesses favour different wavelengths.

In general:

changing thickness changes the wavelengths reinforced in reflection

This is why a smoothly changing film thickness can produce a sequence of colours.

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Worked Example: Comparing Two Colours

Suppose a film with:

n = 1.40

has one relative phase reversal.

For the smallest constructive thickness:

t = λ₀/(4n)

For blue light:

λ_blue = 450 nm

t_blue = 450/(4 × 1.40)

t_blue ≈ 80 nm

For red light:

λ_red = 650 nm

t_red = 650/(4 × 1.40)

t_red ≈ 116 nm

Therefore, for this particular interference order, a thicker film is required to reinforce the longer red wavelength.

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Interference Order

A film can reinforce the same wavelength at several different thicknesses.

For one relative phase reversal:

2nt = (m + ½)λ₀

For:

m = 0, 1, 2, ...

different film thicknesses satisfy the constructive condition.

Therefore, colour patterns can repeat as film thickness increases.

This is why thin-film patterns can contain multiple coloured bands rather than a single progression through the visible spectrum.

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Successive Bright Conditions

For the same wavelength, neighbouring constructive orders differ in thickness by:

Δt = λ₀/(2n)

For example, if:

λ₀ = 600 nm

n = 1.50

then:

Δt = 600/(2 × 1.50)

Δt = 200 nm

Increasing the film thickness by 200 nm moves from one constructive order to the next for that wavelength.

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Viewing Angle

Film thickness is not the only reason colours change.

Viewing angle also matters.

At an angle, the relevant optical path difference is approximately:

2nt cos θ_film

where θ_film is the angle of the ray inside the film.

Changing the viewing angle changes this quantity.

Therefore:

same film + different viewing angle → different interference condition

This is why the colours of soap bubbles and oil films often shift as you move your head.

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Iridescence

A surface whose colour changes with viewing angle is described as iridescent.

Thin-film interference is one mechanism that can produce iridescence.

Soap bubbles and oil films are familiar examples.

However, not every iridescent object uses thin-film interference. Some natural materials use microscopic structures that produce diffraction or other forms of structural colour.

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Thin-Film Colour vs Pigment Colour

Pigments create colour mainly by absorbing some wavelengths and reflecting others.

Thin films create colour mainly through interference.

This distinction helps explain why soap bubbles can produce vivid colours despite the soap solution itself being nearly colourless.

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Structural Colour

Thin-film interference is an example of structural colour.

Structural colour is produced by microscopic physical structures interacting with light rather than primarily by coloured pigments.

Depending on the structure, colour may result from:

• thin-film interference
• diffraction
• scattering
• photonic structures
• combinations of these effects

Nature contains many examples.

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Natural Thin-Film Interference

Thin-film interference can occur wherever sufficiently thin transparent or partially transparent layers form.

Possible examples include:

• biological membranes
• thin layers of water
• natural oils
• thin mineral coatings
• microscopic biological structures

However, many colourful natural surfaces involve more complicated multilayer structures rather than a simple single film.

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Insect Wings

Some transparent insect wings show coloured patches because microscopic variations in thickness can produce interference.

Light reflected from different boundaries can reinforce particular wavelengths.

Changing:

• wing thickness
• viewing angle
• wavelength

can therefore change the observed colour.

In real biological structures, several optical mechanisms may contribute simultaneously.

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Biological Structures

Some animals produce structural colours using thin layers or stacks of layers.

These microscopic structures can selectively reinforce particular wavelengths.

Examples of structural colour occur in various:

• insects
• birds
• fish
• shells

In many cases, the structure is more complex than a simple soap film, but interference remains an important underlying principle.

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Thin Oxide Layers on Metals

Very thin oxide layers can also produce interference colours.

When a transparent oxide layer forms on a metal surface, light reflected from different boundaries can interfere.

As the oxide thickness changes, different colours can appear.

This principle can be observed on some heated or oxidized metal surfaces.

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Temper Colours

Some metals develop characteristic colour sequences as thin oxide layers grow.

The colour is related to the oxide thickness.

Therefore, colour can provide information about the microscopic layer.

This is another example of how interference patterns can reveal dimensions far too small to measure directly with an ordinary ruler.

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Why Different Parts of a Film Have Different Colours

Suppose one region has thickness t₁ and another has thickness t₂.

Then their optical path differences are:

2nt₁

and:

2nt₂

If these values differ, different wavelengths may undergo constructive interference.

Therefore:

variation in thickness → variation in reflected colour

This is why smooth colour bands can reveal smooth variations in film thickness.

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Reading a Thin-Film Pattern

When analyzing a photograph or observation of a thin film, ask:

• Where are the brightest colours?
• Where are dark regions?
• Does colour vary smoothly across the surface?
• Is the film likely changing thickness?
• Does the colour change with viewing angle?
• What are the refractive indices at the two boundaries?
• Which reflections undergo phase reversal?

These questions connect the observed pattern with the underlying wave behaviour.

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Dark and Bright Regions

A bright region suggests that one or more visible wavelengths are being strongly reflected through constructive interference.

A dark region suggests that reflected wavelengths are being strongly reduced through destructive interference.

However, white-light patterns are more complicated than monochromatic patterns because many wavelengths are present simultaneously.

A region can therefore be dark for one wavelength but bright for another.

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Monochromatic Light

If a soap film is illuminated using a single wavelength rather than white light, the pattern becomes simpler.

Instead of rainbow colours, the film produces alternating:

• bright regions
• dark regions

These correspond to different film thicknesses satisfying constructive and destructive interference conditions.

This can make film thickness easier to analyze quantitatively.

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White Light

With white light, each wavelength has its own interference condition.

Therefore, the pattern becomes colourful.

For example, at one location:

• red may interfere constructively
• blue may interfere destructively
• green may be partially reflected

At another thickness, the relationships change.

The resulting colours can therefore be complex.

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Measuring Film Thickness

If a wavelength λ₀ is known to undergo constructive interference, the film thickness can sometimes be calculated.

For one phase reversal:

2nt = (m + ½)λ₀

Rearrange:

t = (m + ½)λ₀/(2n)

If the interference order m is known, the film thickness can be determined.

This provides a way to measure extremely small distances using light.

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Worked Thickness Example

A film has:

n = 1.25

and one relative phase reversal.

Light of:

λ₀ = 500 nm

is strongly reflected in the m = 1 constructive order.

Use:

2nt = (m + ½)λ₀

2(1.25)t = (1.5)(500 nm)

2.50t = 750 nm

Therefore:

t = 300 nm

The film is only:

3.00 × 10⁻⁷ m

thick.

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Predicting Colour Changes

Suppose a soap film gradually becomes thinner.

The optical path difference decreases.

A wavelength that initially experiences constructive interference will eventually move away from that condition.

As thinning continues, another wavelength may become reinforced.

Therefore, the colour can move through a changing sequence.

The exact sequence depends on:

• film thickness
• interference order
• refractive index
• viewing angle
• illumination

For this reason, thin-film colour patterns should not be interpreted using an overly simple fixed "thickness-to-colour" chart unless the experimental conditions are known.

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Why Colours Repeat

The same wavelength can satisfy the constructive condition at more than one thickness because m can take different integer values.

For example:

m = 0

m = 1

m = 2

all represent different constructive orders.

As film thickness changes gradually, wavelengths can therefore be reinforced repeatedly.

This contributes to repeated colour bands in thicker films.

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Why Colours Become Complicated in Thicker Films

As film thickness increases, multiple interference orders can fall within the visible spectrum.

Several wavelengths may then be strongly reflected at nearby conditions.

The observed colours can become increasingly complex or less saturated.

Very thin films often produce especially clear structural colours because fewer interference orders contribute.

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Real-World Oil Slick Analysis

Imagine a thin oil film spreading across wet pavement.

Some areas appear:

• blue
• purple
• green
• yellow
• red

The different colours suggest that the oil thickness varies across the surface.

As the observer moves, the colours shift.

This indicates that viewing angle is also affecting the optical path difference.

The pattern therefore provides visible evidence of:

film thickness + wavelength + viewing geometry + interference

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Real-World Soap Bubble Analysis

Consider a hanging soap film.

Near the bottom, the film may be relatively thick.

Near the top, drainage gradually makes it thinner.

Coloured bands may move downward as the film changes.

Eventually, a dark region may develop near the top.

The pattern can therefore reveal how the thickness of the film changes with both:

• position
• time

The colours effectively act as an optical map of an extremely thin layer.

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Applications Beyond Bubbles and Oil

The same principles are deliberately used in technology.

Thin-film interference is important in:

• anti-reflection coatings
• high-reflectivity mirrors
• interference filters
• camera lenses
• telescope optics
• solar panels
• optical sensors
• semiconductor manufacturing
• thickness measurement

The colourful soap bubble therefore demonstrates physics that is also used in advanced optical engineering.

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Common Mistakes

Thinking soap bubbles contain coloured pigments

The colours mainly result from interference of reflected white light.

Thinking oil is always naturally rainbow-coloured

The rainbow pattern is often produced by thin-film interference.

Ignoring film thickness

Changing thickness changes the optical path difference and therefore the wavelengths that are reinforced.

Assuming each thickness corresponds to only one possible colour

Several wavelengths and interference orders may contribute to the observed colour.

Ignoring phase changes upon reflection

Reflection phase shifts can reverse the constructive and destructive conditions.

Assuming every oil film has the same phase conditions

The refractive indices of the oil and the material beneath it must be known.

Thinking longer wavelength always means a larger diffraction angle

Thin-film interference is not primarily an angular diffraction problem. It depends on optical path and phase.

Ignoring viewing angle

The same part of a film can appear different when viewed from another direction.

Thinking destructive interference destroys light energy

The energy is redistributed, often between reflected and transmitted light.

Assuming all natural iridescence is thin-film interference

Nature also produces structural colours through diffraction, scattering, and more complicated microscopic structures.

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Key Terms

Thin-film interference — interference between waves reflected or transmitted from different boundaries of a thin layer.

Soap film — thin liquid layer, often surrounded by air, capable of producing interference colours.

Oil film — thin oil layer that can produce wavelength-dependent interference.

Iridescence — change in observed colour with viewing or illumination angle.

Structural colour — colour produced by microscopic physical structures interacting with light rather than primarily by pigments.

Optical path difference — difference between the effective optical distances travelled by interfering waves.

Film thickness (t) — physical distance between the two main surfaces of a thin film.

Refractive index — measure of how much light slows in a material.

Phase reversal — π-radian phase change that can occur when light reflects toward a higher refractive index.

Constructive interference — reinforcement of waves producing increased reflected intensity.

Destructive interference — cancellation of waves producing reduced reflected intensity.

Interference order (m) — integer representing successive constructive or destructive interference conditions.

Monochromatic light — light consisting of essentially one wavelength.

White light — light containing a broad range of visible wavelengths.

Black film — extremely thin region of a soap film that can appear dark because reflected visible light is strongly suppressed.

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Key Takeaways

• Soap-bubble and oil-film colours are produced primarily by thin-film interference.
• Light reflects from both the upper and lower surfaces of a thin film.
• The reflected waves overlap and interfere.
• Their relative phase depends on both optical path difference and reflection phase changes.
• At normal incidence, the extra optical path through a film is approximately 2nt.
• Reflection toward a higher refractive index produces a π phase change.
• Film thickness determines which wavelengths undergo constructive or destructive interference.
• White light produces colourful patterns because it contains many wavelengths.
• Changing film thickness changes the reflected colour.
• A soap film surrounded by air normally has one relative π phase reversal.
• With one relative phase reversal, constructive reflected interference satisfies 2nt = (m + ½)λ₀.
• Oil-film phase conditions depend on the refractive indices of the oil and the material underneath it.
• A thicker region can reinforce a different wavelength from a thinner region.
• Changing viewing angle changes the optical path difference and can change the observed colour.
• Soap films change colour as gravity and evaporation alter their thickness.
• Extremely thin soap-film regions can appear dark.
• Oil slicks display colour variations because their thickness is not uniform.
• Thin-film interference is one form of structural colour.
• Some biological and mineral structures also use interference to produce colour.
• The same physics is used in optical coatings, filters, mirrors, sensors, and precision thickness measurements.

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Check Your Understanding

1. Explain why a soap bubble can display bright colours even though the soap solution itself is nearly colourless.
2. Identify the two main reflected rays responsible for thin-film interference.
3. Explain why the second reflected ray usually has a greater optical path than the first.
4. What happens to a reflected wave when light reflects toward a medium with a higher refractive index?
5. Explain how changing the thickness of a soap film changes its observed colour.
6. Why can different parts of the same soap bubble display different colours at the same time?
7. A soap film has refractive index 1.33 and one relative phase reversal. Calculate the smallest positive thickness that strongly reflects light of wavelength 600 nm at normal incidence.
8. A film with n = 1.50 has one relative phase reversal. Compare the minimum thickness required to constructively reflect 450 nm blue light with that required for 650 nm red light.
9. Explain why an oil film cannot always be analyzed using the same phase-change assumption as an air-soap-air film.
10. An oil has refractive index 1.45 and floats on water with n = 1.33. Determine the reflection phase changes at the air-oil and oil-water boundaries.
11. Explain why the colours of an oil slick can change as you move around it even though its thickness has not changed.
12. Why might the upper part of an old soap film become almost black immediately before the film breaks?
13. Explain the difference between pigment colour and structural colour.
14. A thin film becomes gradually thicker from left to right and is illuminated with monochromatic light. Predict the general type of intensity pattern that could appear across the film and explain why.
15. A photograph shows a soap film containing several coloured horizontal bands with a dark region near the top. Use gravity, changing film thickness, wavelength-dependent interference, and reflection phase changes to explain the overall pattern.