Thin-film interference is a natural phenomenon in which
light wave
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ra ...
s reflected by the upper and lower boundaries of a
thin film
A thin film is a layer of materials ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ...
interfere with one another, increasing reflection at some
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
s and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections.
Thin-film interference explains the multiple colors seen in light reflected from
soap bubble
A soap bubble (commonly referred to as simply a bubble) is an extremely thin soap film, film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds b ...
s and oil films on
water
Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
. It is also the mechanism behind the action of
antireflection coatings used on
glasses
Glasses, also known as eyeglasses (American English), spectacles (Commonwealth English), or colloquially as specs, are vision eyewear with clear or tinted lenses mounted in a frame that holds them in front of a person's eyes, typically u ...
and
camera lens
A camera lens, photographic lens or photographic objective is an optical lens (optics), lens or assembly of lenses (compound lens) used in conjunction with a camera body and mechanism to Imaging, make images of objects either on photographic film ...
es. If the thickness of the film is much larger than the
coherence length of the incident light, then the interference pattern will be washed out due to the
linewidth
A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
of the light source.
The reflection from a thin film is typically not individual wavelengths as produced by a
diffraction grating
In optics, a diffraction grating is an optical grating with a periodic structure that diffraction, diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffractio ...
or
prism
PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies. The program is also known by the SIGAD . PRISM collects stored internet ...
, but rather are a mixture of various wavelengths. Therefore, the colors observed are rarely those of the rainbow, but rather browns, golds, turquoises, teals, bright blues, purples, and magentas. Studying the light reflected or transmitted by a thin film can reveal information about the thickness of the film or the effective
refractive index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
of the film medium. Thin films have many commercial applications including
anti-reflection coating
An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the effi ...
s,
mirror
A mirror, also known as a looking glass, is an object that Reflection (physics), reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera ...
s, and
optical filter
An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optic ...
s.
Theory

In optics, a
thin film
A thin film is a layer of materials ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ...
is a layer of material with thickness in the sub-
nanometer
330px, Different lengths as in respect to the Molecule">molecular scale.
The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm), or nanometer (American spelling
Despite the va ...
to
micron
The micrometre (English in the Commonwealth of Nations, Commonwealth English as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American English), also commonly known by the non-SI term micron, is a uni ...
range. As light strikes the surface of a film, it is either transmitted or reflected at the upper surface. Light that is transmitted reaches the bottom surface and may once again be transmitted or reflected. The
Fresnel equations
The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by French engineer and ...
provide a quantitative description of how much of the light will be transmitted or reflected at an interface. The light reflected from the upper and lower surfaces will interfere. The degree of constructive or destructive
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
between the two light waves depends on the difference in their phase. This difference in turn depends on the thickness of the film layer, the refractive index of the film, and the angle of incidence of the original wave on the film. Additionally, a phase shift of 180° or
radians
may be introduced upon reflection at a boundary depending on the refractive indices of the materials on either side of the boundary. This phase shift occurs if the refractive index of the medium the light is travelling through is less than the refractive index of the material it is striking. In other words, if
and the light is travelling from material 1 to material 2, then a phase shift occurs upon reflection. The pattern of light that results from this interference can appear either as light and dark bands or as colorful bands depending upon the source of the incident light.
Consider light incident on a thin film and reflected by both the upper and lower boundaries. The optical path difference (OPD) of the reflected light must be calculated in order to determine the condition for interference. Referring to the ray diagram above, the OPD between the two waves is the following:
:
Where,
:
:
Using
Snell's law
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing th ...
,
:
Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light,
.
:
This condition may change after considering possible phase shifts that occur upon reflection.
Monochromatic source
Where incident light is
monochromatic
A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, mon ...
in nature, interference patterns appear as light and dark bands. Light bands correspond to regions at which constructive interference is occurring between the reflected waves and dark bands correspond to destructive interference regions. As the thickness of the film varies from one location to another, the interference may change from constructive to destructive. A good example of this phenomenon, termed "
Newton's rings
Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces, typically a spherical surface and an adjacent touching flat surface. It is named after Isaac Newton, who investigated th ...
", demonstrates the interference pattern that results when light is reflected from a spherical surface adjacent to a flat surface. Concentric rings are observed when the surface is illuminated with monochromatic light. This phenomenon is used with
optical flat
An optical flat is an Optics, optical-grade piece of glass lapping, lapped and polishing, polished to be extremely flat on one or both sides, usually within a few tens of nanometres (billionths of a metre). They are used with a monochromatic li ...
s to measure the shape and
flatness of surfaces.
Broadband source
If the incident light is broadband, or white, such as light from the sun, interference patterns appear as colorful bands. Different wavelengths of light create constructive interference for different film thicknesses. Different regions of the film appear in different colors depending on the local film thickness.
Phase interaction

The figures show two incident light beams (A and B). Each beam produces a reflected beam (dashed). The reflections of interest are beam A’s reflection off of the lower surface and beam B’s reflection off of the upper surface. These reflected beams combine to produce a resultant beam (C). If the reflected beams are in phase (as in the first figure) the resultant beam is relatively strong. If, on the other hand, the reflected beams have opposite phase, the resulting beam is attenuated (as in the second figure).
The phase relationship of the two reflected beams depends on the relationship between the wavelength of beam A in the film, and the film's thickness. If the total distance beam A travels in the film is an integer multiple of the wavelength of the beam in the film, then the two reflected beams are in phase and constructively interfere (as depicted in the first figure). If the distance traveled by beam A is an odd integer multiple of the half wavelength of light in the film, the beams destructively interfere (as in the second figure). Thus, the film shown in these figures reflects more strongly at the wavelength of the light beam in the first figure, and less strongly at that of the beam in the second figure.
Examples
The type of interference that occurs when light is reflected from a thin film is dependent upon the wavelength and angle of the incident light, the thickness of the film, the refractive indices of the material on either side of the film, and the index of the film medium. Various possible film configurations and the related equations are explained in more detail in the examples below.
Soap bubble

In the case of a
soap bubble
A soap bubble (commonly referred to as simply a bubble) is an extremely thin soap film, film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds b ...
, light travels through air and strikes a soap film. The air has a refractive index of 1 (
) and the film has an index that is larger than 1 (
). The reflection that occurs at the upper boundary of the film (the air-film boundary) will introduce a 180° phase shift in the reflected wave because the refractive index of the air is less than the index of the film (
). Light that is transmitted at the upper air-film interface will continue to the lower film-air interface where it can be reflected or transmitted. The reflection that occurs at this boundary will not change the phase of the reflected wave because
. The condition for interference for a soap bubble is the following:
:
for constructive interference of reflected light
:
for destructive interference of reflected light
Where
is the film thickness,
is the refractive index of the film,
is the angle of incidence of the wave on the lower boundary,
is an integer, and
is the wavelength of light.
Oil film

In the case of a thin oil film, a layer of oil sits on top of a layer of water. The oil may have an index of refraction near 1.5 and the water has an index of 1.33. As in the case of the soap bubble, the materials on either side of the oil film (air and water) both have refractive indices that are less than the index of the film.
. There will be a phase shift upon reflection from the upper boundary because