Thin Film Interference

Thin film interference occurs when incident light waves reflected by the different layers of a thin film interfere and form a new wave.

Learning Objective

Describe process that leads to the thin film interference

Key Points

When the incident light reaches the thin film, it is partially reflected and passed through to the bottom layer of the film. The difference in refractive indices of the air and film causes the light to change direction and interfere with the reflected portion of the ray when it emerges.
This interference can be constructive, producing bright colors, or destructive, producing darker colors.
Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light.

Terms

wavelength
The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
interference
An effect caused by the superposition of two systems of waves, such as a distortion on a broadcast signal due to atmospheric or other effects.
incident ray
The ray of light that strikes the surface.

Full Text

Thin Film Interference

This is a phenomenon that occurs when incident rays reflected by the upper and lower boundaries of a thin film interfere with one another and form a new wave. A material is considered to be a thin film if its thickness is in the sub-nanometer to micron range, e.g. a soap bubble. Studying the new wave can shed light on properties of the film, such as thickness or refractive index. Interference effects are most prominent when the light interacts with something that has a size similar to its own wavelength. The thickness of a thin film is a few times smaller than the wavelength of the light, λ. Color is indirectly associated with wavelength. The interference ratio of wavelength to size of the object causes the appearance of colors.

Thin Film Interference

In this video I continue with my tutorials on Electromagnetism to Optics which is pitched at university undergraduate level. I have intended for a long time to record videos which describe the transition made from classical electromagnetism to optics. In many respects these videos will cover 'wave' optics. I devote much time to discussing the complex exponential representation of waves, Maxwell's Equations, the wave equation etc.Specifically here, I derive the formula for the optical path difference and the phase difference for a 'wave' of light propagating through a thin film. This expression can be used for anti reflective coatings. The phase difference is the product of the optical path differene and the wave vector k.I hope it's of use!! Thank you for watching and I hope that this matches your requirements.

Examples of Thin Film Interference

You have probably witnessed thin film interference in your every day life and just not realized it. Whenever you see the bright, rainbow like colors in oil floating in water, shown in , this is thin film interference. The colors that appear in bubbles that kids play with are also a result of thin film interference. Thin film interference can have commercial applications, such as anti-reflection coatings and optical filters.

Thin Film Interference in Oil

Thin film interference can be seen in this oil slick.

How it Works

shows a diagram of how thin film interference works. 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 light reflected from the upper and lower surfaces will interfere. The degree of constructive or destructive interference between the two light waves is dependent upon the difference in their phase. This difference is dependent upon 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 $\pi$radians may be introduced upon reflection at a boundary depending on the refractive indices of the materials on either side said 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 $n_{1} < n_{2}$and the light is travelling from material 1 to material 2, then a phase shift will occur 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.

Light on a Thin Film

Light incident on a thin film. Demonstration of the optical path length difference for light reflected from the upper and lower boundaries.

Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light:

$2n_{2}dcos (\theta _{2}) =m\lambda$

where $m$ is the integer, $d$ is the thickness of the film, and $\lambda$ is the wavelength of light. However, this condition may change if phase shifts occur upon reflection.

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