Thin-film interference occurs when light waves reflected by the upper and lower boundaries of a thin film interfere with one another, increasing reflection at some wavelengths 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 bubbles and oil films on water and also many colors found in nature. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses. 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 of the light source. The reflection from a thin film is typically not individual wavelengths as produced by a diffraction grating or prism, 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 of the film medium. Thin films have many commercial applications including anti-reflection coatings, mirrors, and optical filters.
Theory
In optics, a thin film is a layer of material with thickness in the sub-nanometer to micron 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 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 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 π {\displaystyle \pi } 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 n 1 < n 2 {\displaystyle n_{1}<n_{2}} 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:
O P D = n 2 ( A B ¯ + B C ¯ ) − n 1 ( A D ¯ ) {\displaystyle OPD=n_{2}({\overline {AB}}+{\overline {BC}})-n_{1}({\overline {AD}})}
Where,
A B ¯ = B C ¯ = d cos ( θ 2 ) {\displaystyle {\overline {AB}}={\overline {BC}}={\frac {d}{\cos(\theta _{2})}}}
A D ¯ = 2 d tan ( θ 2 ) sin ( θ 1 ) {\displaystyle {\overline {AD}}=2d\tan(\theta _{2})\sin(\theta _{1})}
Using Snell's law, n 1 sin ( θ 1 ) = n 2 sin ( θ 2 ) {\displaystyle n_{1}\sin(\theta _{1})=n_{2}\sin(\theta _{2})}
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