with thin film, to be honest. Well, there can. So, how do we determine, If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. I'll draw it over here, Yes, one more thing to worry about. While it is not totally destructive for nearby wavelengths, they are out of phase by a number very close to \(\pi\), which means that they are barely seen. Well, it's kind of redundant, film already means something really thin, a thin amount of substance. shifted and the other does not. Significance If the bubble were illuminated with pure red light, we would see bright and dark bands at very uniform increases in thickness. Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40. And thin film means really, really thin. If you wanted to, you can call if it was coming straight in. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. traveled faster through. How might this be impractical? We never even said what delta x is. At other points in the film, the thickness may cause the blue light to be canceled. They were both in there to start off with. Well, light comes in, so, It's gotta be related to the thickness. and that colorful pattern on the top of the water, streaks of red and blue So, in order to get thin film interference the thin film has to be translucent, it has to let light through. about any pi shifts. I'm not gonna try to draw it And now these were both If a thin oil film is floating on the water, you will see a beautiful pattern appear on the oil film. (b) What three smallest thicknesses give destructive interference? Solution To obtain destructive interference here. And because there's oil Thin-film interference has many other applications, both in nature and in manufacturing. Reflection at an interface for light traveling from a medium with index of refraction. This is still getting a pi shift. For thin film it's always 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. And the whole integer By the end of this section, you will be able to: The bright colors seen in an oil slick floating on water or in a sunlit soap bubble are caused by interference. here does get a pi shift. The only change that occurs with the separation is that the second reflection in both thin films is now off a surface in contact with air. Assume the same index of refraction as water. What happens for other wavelengths and other incident directions? What color is most strongly reflected if it is illuminated perpendicular to its surface? In this case, some of it It can happen naturally. this is how I change this to make it relevant for thin film. Mathematically this is not hard to see, as the space (and time) parts of the phase difference calculation are unchanged, but now we have the blue wave starting with a different phase than the red wave: \(\Delta \phi = \pi\). the wave in those materials. Light will travel at First would be a dark band at 0 thickness, then bright at 122 nm thickness, then dark at 244 nm, bright at 366 nm, dark at 488 nm, and bright at 610 nm. The source of light remains unchanged, so whether the light is passing through the liquid or (after the chamber drains) the air, the frequency is the same. fast, reflect off of a fast, or did it reflect off of a slow. One place where one might want as much light as possible to pass through is a camera lens. Explain its origin. Nope, there would be no This is my condition, So, the extra path length No 180 degree shift. float on top of the water, and it's often a very - [Voiceover] Let's talk These rays interfere in a way that depends on the thickness of the film and the indices of refraction of the various media. We know it's there, because This gives us a difference in time-of-propagation of: \[\Delta t = t_{blue} - t_{red} =-\frac{T}{4}. it's kind of simpler. certain speed in the oil. These soap bubbles exhibit brilliant colors when exposed to sunlight. thin film interference. It reflected off of this liquid that it would have We are not gonna stray from what we know. Consider the case of a thin film of oil of thickness t floating on water. Let me clear this off. So generally the film chosen works for the middle of the spectrum (green light), which means that it doesn't work well for the ends of the spectrum (red and violet). When it rains outside, there These two waves come out together and interfere, but the red wave has a "head start" both in displacement (the thickness of the film), and in time – it is already propagating left while the incoming wave is still moving right, on its way to the rear surface. if you flipped the wires on the back of the speakers, This means there will be no phase shift at that reflection, since air has a lower index of refraction than either film. And then you have a Other countries, such as Canada, New Zealand, and Taiwan, are using similar technologies, while US currency includes a thin-film interference effect. (c) If the air wedge is illuminated with monochromatic light, bright and dark bands are obtained rather than repeating rainbow colors. It would have traveled into water, which is slower than the oil. People have a lot of trouble Like that. How do you know? For double slit delta x was d sin theta. It is noted that the position of the first dark fringe of this new pattern exactly coincides with the position of the second dark fringe that appeared when the plug was still in place. And by slower I mean, if But that's not all the light does. certain speed of the light. Part of the light reflected from the bottom surface can emerge from the top of the film (ray 2) and interfere with light reflected from the top (ray 1). m lambda, if you want. conditions in this case. off of something slower, oil. Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Differing path lengths result in different phases at destination resulting in constructive or destructive interference accordingly. Thus, the soap bubble is dark here. But what does it do? The brightest colors are those that interfere constructively. Wave two also travels that distance, but only after wave two traveled this extra distance within the thin film. These thickness variation rainbows can also be seen other thin films, such as soap bubbles. Let's say we had air out here. These are flip-flopped, if An important application of thin-film interference is found in the manufacturing of optical instruments. Imagine these both waves come in, imagine both waves are combined If it came in at a peak, then it's getting sent Soap Bubbles (a) What are the three smallest thicknesses of a soap bubble that produce constructive interference for red light with a wavelength of 650 nm? To determine the interference of these two waves, we have to compute their total phase difference \(\Delta \Phi\) at the point when they superpose. Now these overlap. For light incident perpendicular to the surface, ray 2 travels a distance approximately 2t farther than ray 1. This constant (\(n\)) is dimensionless, and is a number greater than 1 which provides the speed of light through a medium in terms of the speed through the vacuum (\(c\)) according to: When we discussed what happens when a wave passes from one medium to another, we concluded that the frequency remains the same, and the wavelength changes along with the velocity. So, does it get a pi shift? \nonumber\], Both waves experience a phase shift upon reflection, and come from a common incoming wave where they were in phase, so there is no difference in their phase constants: \[\Delta \phi = \phi_{blue} - \phi_{red} = 0. This, he reasons, should be much cheaper than designing Stealth bombers. So, some of this light ray The blue wave only travels a quarter wavelength by the time the two waves superpose, so it has been propagating for a quarter of a period: \(t_{blue}=\frac{T}{4}\). In addition to pigmentation, the wing’s color is affected greatly by constructive interference of certain wavelengths reflected from its film-coated surface. reflects off of this interface. Light waves produce the same effect, but the deciding parameter for light is the index of refraction. However, if the second string is lighter (or more precisely, of a lower linear density), no inversion occurs.