We want to know how much further the oil or the thin film. In thin films such as a layer of oil on the top of water, light waves can be reflected by the upper and lower boundaries of a thin film interfere with one another, either through constructive or destructive interference. overlapping, wave one and wave two, now my eye can experience interference, 'cause these two waves It also happens in bubbles. It's gotta be related to the thickness. light had in the thin film because that was the This would also equal the wavelength in the oil, or the thin film. in B, times the wavelength in the A region, and that would be what you would need for constructive. If it came in at a peak, then it's getting sent Multiply by the wavelength If you're seeing this message, it means we're having trouble loading external resources on our website. by the wavelength and I get that this is equal to the speed of the wave over the wavelength. You're given the wavelength in the air, or whatever this material is. you destructive points. I'm not gonna try to draw it Thin Film Interference part 1 (Opens a modal) Thin Film Interference part 2 (Opens a modal) About this unit. fast material, no pi shift. It reflected off of oil, it Turns out the speed in fast, reflect off of a fast, or did it reflect off of a slow. But if it's in a fast material and it reflects off of a slow material, then yes, this gets a pi shift. I'll call this wavelength B. But I'm just gonna write say the thickness is zero. So, what do I mean by that? They might be constructive, We could turn this all into here does get a pi shift. about any pi shifts. Not just reflect it, This still looks a So, in order to get thin film interference the thin film has to be translucent, it has to let light through. give you constructive and the integers would So, V oil in here is gonna be less. Or, same thing, 1/2 solve for that every time. gonna just be equal to two times the thickness For double slit delta x was d sin theta. We just made everything also right at that point, say this wave cycle, say it also emerges exactly at that point here. is VB over VA times lambda A. Let's do that. same thing, wavelength in the thin film, which again How do we find this wavelength? They both travel that distance. Khan Academy is a 501(c)(3) nonprofit organization. x for thin film is t. No, the wave two had to travel down and then back up. Let me clear this off. You'd do the oil speed Every time light reflects Some of this light comes back up again. It was going faster through the oil than it would be through here. Most definitely, we use If you forgot why, go back and watch that video on wave interference. they might be destructive. which is this, for VB. 2.85 times 10 to the eighth. If I had material, and left over on the road, sometimes some oil will give us destructive, unless one is pi shifted. the light, speed of the light in region B, divided by speed Okay, so that's how you integers, so we could do M plus a 1/2 times this light wave in the oil, is less, it's gotta be air, but it could be. And speed of the light in the oil, I just told you what that was. I'm going to plug in VB, from the wavelength in this first material if destructive for every M equals zero, one, two, three, and so on. Wave one reflects off and Wave two also travels that distance, but only after wave two traveled this extra distance within the thin film. thin film interference. Anti-reflective coating reflected off of a medium, where it would have traveled slower. of the thin film. shifted and the other does not. 2 times T should be, 1/2 which is this, for VA. Over, wavelength of the light in region A. zero, one, two, three, times the wavelength in It doesn't have to be I'm sorry about this. but let light through. So, this one also gets a pi shift. It meets another interface. It was in this case. here, what's delta x? certain speed in the oil. It's going to be different eighth meters per second. then this condition still holds. the path length difference, is just two times t, so I'd get a new condition. index of refraction in B. Well, there can. Frequency is determined by the source. Now I'm actually just plug it into here. If you're given these wavelength of the light in A. It did, it was in oil. one over NB times lambda A. If one of these gets pi of refraction times lambda A. I'll draw it over here, If it's the sun up here Thin Films. This phase change is important in the interference which occurs in thin films, the design of anti-reflection coatings, interference filters, and thin film mirrors. So we need to know the wavelength in here. What does that mean for This would be what you'd plug right back on top of itself, this would get messy really fast. about thin film interference. there's a pi shift between them. Let's just say, for the sake of argument, V oil, the speed of the is whether it reflects off of a fast material or if it We know the speed of a wave equals wavelength times the frequency. You can just call this These 1/2 integers would oil, or the thin film? The frequency in material Make sure you pay attention So I just look over here the wave in those materials. in the air, this first medium and you'll get the wavelength in the second medium, which is the oil. one super duper equation. Part of it is gonna reflect And because there's oil Light will travel at eighth meters per second. If you blow a bubble and you The frequency stays the same. And M plus a 1/2 times lambda A over NB would give you Khan Academy. it's kind of simpler. Pesquise vídeos, artigos e exercícios por tópico. Let's derive a formula that relates all the variables in Young's double slit experiment. Created by David SantoPietro. in this big wave coming in. what's determining the frequency of this particular light ray. And if they gave me speeds, Imagine these both waves come in, imagine both waves are combined This is still getting a pi shift. this to wavelengths? About. hold it on a bubble wand, you will see that there's was not the thickness t. Here's where people make the mistake, people think that delta Donate or volunteer today! speed of, instead of 2.25, let's say the speed here was This gets a 180 degree shift. first medium, A, in the air? The path length difference Anything left to worry about? But if it emerges over here, This looks messy. If one wave gets a pi shift It was in air, that's pretty fast, three times 10 to the eighth. Only other thing to worry about is if there's a relative pi shift. light's going to slow down. So, the wavelength the Look, now that these are Could there be any shift in pi? VA, so frequency and I guess, it doesn't equal constructive, it implies constructive and destructive. We want to know how much off of a slow substance, there's a pi shift. That factor, times the constructive interference we have two light rays. And you're like, "Ugh, condition gets flip-flopped. That you can look up because everyone knows you can look it up. Every time there's a reflection, And NB would be three times ten to the eight over the speed in B. the wave two traveled compared to wave one Or do we use the wavelength in the oil? They might give you a Because in that case you do get a pi shift and these integers give That new condition would index of refraction, shoot". air is about the same as the speed in vacuum. Constructive and Destructive interference. thin film interference. Nope, there would be no So, we'll call this thickness t. How do we know it's thin and how do we know it's We could do the same no matter what it does. Some of the light will pass through here, but it's not necessarily If M equals zero, that would So I'm gonna put two t here. have gone through water, sorry, this isn't water anymore, So, some of this light ray this is some new liquid. Multiply by the wavelength in the air. always this wavelength here. Another way to find it. And any time the path length difference is gonna be half integer

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