<P> Thin - film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light . When the thickness of the film is an odd multiple of one quarter - wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other . Since the wave cannot be reflected, it is completely transmitted instead . When the thickness is a multiple of a half - wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission . Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are attenuated . Thin - film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water . It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses . </P> <P> 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 . </P> <P> 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 . </P> <P> 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: </P>

A thin layer of oil with index of refraction