(Figure) shows how light reflected from the top and bottom surfaces of a film can interfere. Strategy Use (Figure) to visualize the bubble, which acts as a thin film between two layers of air. Phase changes occur upon reflection at the top of glass cover and the top of glass slide only. (b) What is unreasonable about this result? What color is most strongly reflected if it is illuminated perpendicular to its surface? Why? The refracted ray is partially reflected at the bottom surface and emerges as ray 2. 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. For light incident perpendicular to the surface, ray 2 travels a distance approximately 2t farther than ray 1. (c) If the air wedge is illuminated with monochromatic light, bright and dark bands are obtained rather than repeating rainbow colors. Light waves produce the same effect, but the deciding parameter for light is the index of refraction. Solution a. (Figure) illustrates the phenomenon called Newton’s rings, which occurs when the plane surfaces of two lenses are placed together. In addition to pigmentation, the wing’s color is affected greatly by constructive interference of certain wavelengths reflected from its film-coated surface. How is the difference in paths taken by two originally in-phase light waves related to whether they interfere constructively or destructively? Check Your Understanding Going further with (Figure), what are the next two thicknesses of soap bubble that would lead to (a) constructive interference, and (b) destructive interference? For example, a traveling wave on a string is inverted (i.e., a phase change) upon reflection at a boundary to which a heavier string is tied. No phase change takes place when reflecting from a medium of lower refractive index (). Thin Film Interference-One phase change. University Physics Volume 3 by cnxuniphysics is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. When this distance is an integral or half-integral multiple of the wavelength in the medium , where is the wavelength in vacuum and n is the index of refraction), constructive or destructive interference occurs, depending also on whether there is a phase change in either ray. That is, what limits would there be on the index of refraction and thickness of the coating? New Resources. The index of refraction of the lens is about 1.5, and its top surface is dry. To get constructive interference, then, the path length difference (2t) must be a half-integral multiple of the wavelength—the first three being , and . A soap bubble is 100 nm thick and illuminated by white light incident perpendicular to its surface. If the wedge angle is too large, fringes are not observed. Thus, Solving for t and entering known values yields. It is too thick, and the plane would be too heavy. Reflection can cause a phase change, which also affects how waves interfere. Light waves undergo a or radians phase change upon reflection at an interface beyond which is a medium of higher index of refraction. These rays interfere in a way that depends on the thickness of the film and the indices of refraction of the various media. Light incident from above can reflect from the top and bottom of the glass cover and from the glass slide below the water drop. Another example of thin-film interference can be seen when microscope slides are separated (see (Figure)). No phase change takes place when reflecting from a medium of lower refractive index ((Figure)). A film of soapy water () on top of a plastic cutting board has a thickness of 233 nm. For an incidence angle , the path length inside the coating will be increased by a factor so the new condition for destructive interference becomes . At which surfaces will there be a phase change in the reflected light? As the film gets thinner, most of the phase difference between the two reflected rays is due to π radians phase shift during the reflection off the air-film interface. • The phase difference is due to two factors: – Path difference through the film (corrected for the change in speed of light in the material) Reflection at an interface for light traveling from a medium with index of refraction. Thin film interference thus depends on film thickness, the wavelength of light, and the refractive indices. As the layer of air increases, the bands become more difficult to see, because slight changes in incident angle have greater effects on path length differences. Thus, to obtain destructive interference, ray 2 needs to travel a half wavelength farther than ray 1. Determine the phase difference due to reflection between the portion of the wave reflected at the upper surface and the portion reflected at the lower surface. Thus, when the film is very thin and the path length difference between the two rays is negligible, they are exactly out of phase, and destructive interference occurs at all wavelengths. Because of the periodic nature of waves, this phase change or inversion is equivalent to in distance travelled, or path length. This phase shift is the same for all wavelengths, and results in destructive interference. Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. The index of refraction of soap is taken to be the same as that of water. Furthermore, if you observe a soap bubble carefully, you will note it gets dark at the point where it breaks.