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Current time:0:00Total duration:12:03

let's talk about thin-film interference what does this mean well it's kind of redundant film already means something really thin a thin amount of substance and thin film means really really thin so how does this happen it can happen naturally when it rains outside there will be puddles of water and because there's oil leftover on the road sometimes some oil will float on top of the water and it's often a very thin small amount of oil in other words the thickness of the oil floating on the water is extremely thin so we'll call this thickness T how do we know it's thin and how do we know it's there if we can't see it we know it's there because if you look down at it if you look down at the water you'll sometimes see a colorful pattern in here and that colorful pattern on the top of the water streaks of red and blue and orange and green happen because of thin film interference it also happens in bubbles people a bubble and then you hold that on the bubble wand you'll see that there's these colors in there and those are coming from thin film interference how does it happen well light comes in so this might be from the Sun or whatever some source of light comes in here that's only one light ray we need multiple light rays to get interference so what happens when it hits the oil part of it is going to reflect off the top of the oil so it's going to reflect right back on top of itself but if I were to draw it right back on top of itself this would get messy really fast so I'm going to draw it over here but no this light really reflects right back on top of itself if it was coming straight in we'll call that light ray one but that's not all the light does part of it reflects but part of it continues through the oil so in order to get thin film interference there has to be some trick the oil the thin the thin film has to be translucent has to let light through not just reflected but let light through so some of this light ray is going to continue on through like that but what does it do it meets another interface and every time light meets an interface between two medium well it's going to reflect on some of its good pass through refract so in this case some of it reflects off of this interface so we had a reflection here and we had a reflection up here both of these were reflections and so some of this light comes back up again I'm not going to try to draw it right back on top of itself I'll draw it over here so that we can see them so it comes up now these overlap look at now that these are overlapping wave one and wave two now my eye can experience interference because these two waves are going to hit my eye they might be constructive there might be destructive and I might see different colors in here depending on the wavelength that's what we want to try to figure out how does the thickness of this oil and the wavelength of the light determine whether this is going to be constructive destructive or neither here's what we're going to do we know we're not going to stray from what we know what we know is that to get constructive interference we have two light rays what matters is the path length difference so if the path length difference is zero lambda right any integer lambda you can just call this M lambda if you want that's going to be constructive and any time the path length difference is going to be half integer lambdas so half lambda 3 halves lambda and so on if you wanted to you can call this M plus 1/2 lambda these are going to be destructive I guess that doesn't equal constructive it implies and constructive and destructive but remember there's a there's a got to be careful it can be weird here these are flip-flopped if if there's a PI shift between them if one of these gets PI shifted and the other does not if one of the way waves is PI shifted and the other is not remember if this was the thing with the back of the speaker's if you flip the wires on the back of the speakers now instead of the speaker wave coming out like that speaker wave comes out like this now if you overlap these this condition gets flip-flopped if you forgot why go back and watch that video on wave interference so this is the condition integer wavelengths give us constructive half integer wavelengths give us destructive unless one is PI shifted if they're both PI shifted then this condition still holds but if only one is PI shifted you flip-flop these relations and the half integer wavelengths get you constructive and the whole integer wavelengths give you destructive so does that happen here do we have to worry about PI shifts we didn't with the thin or we didn't with double slit remember with double slit shoot we didn't worry about any pi shifts that was because one way it came in and now these were both from the exact same wave so we know they started off in phase how about these waves for thin film could there be any shift in PI well there can every time there's a reflection there can be a PI shift I repeat every time light reflects there may be a PI shift how do you know it depends on the speed of the wave in those materials so let's say we had air out here so light has some speed in the air turns out the speed in air is about the same as the speed in vacuum three times 10 to the 8 meters per second but I'm just going to write it as V air out here and then you have a certain speed of the light light will travel a certain speed in the oil so the oil in here this is going to be less let's just say for the sake of argument the oil the speed of the light wave and the oil is less it's got to be less let's just say it's two point seven times ten to the eighth meters per second and in water again it's going to have a speed of light in the water let's say the speed of light in the water well we don't have to say we know that's about two point two five times ten to the eighth meters per second so how do we determine knowing these speeds whether there's going to be a PI shift or not here's how we tell every time light reflects off of a slow substance there's a pie shift so what do I mean by that well the light here started off in this material and did it reflect off of a slow substance it was in air that's pretty fast three times ten to the eighth it reflected off of oil it reflected off of a medium where it would have traveled slower so this reflection right here does get a PI shift there is a PI shift for this reflection the light wave that came in if it came in at a peak then it's getting sent back out as a valley and if it came in as this point going up it'll leave as this point going down it's going to get shifted by 180 degrees or PI how about this one down here did it reflect off of a slow medium it did it was in oil it would have traveled into water which is slower than the oil and so this one also gets a PI shift and same thing if it came in as a peak and will leave as a valley what does that mean for this condition up here well if both are PI shifted it's as if neither of them get shifted if we flip both of them upside down well everything's cool again you just made everything back to where it was so we would not swap these conditions in this case if for some reason we use something besides water we use some other liquid here and this liquid had a speed of instead of 2.25 let's say the speed here was 2.8 five times ten to the eighth now that doesn't change anything up here this is still getting a PI shift it was in air and reflected off of something slower oil and so and by slower I mean if the light traveled into it it would travel slower so that gets a PI shift but now this one down here this light ray that was in the oil would have gone through water it reflected off of oh sorry this isn't water anymore there's some new liquid it reflected off of this liquid that it would have traveled faster through so does it get a PI shift nope there'd be no more pi shift down here only one of these reflected light rays get a PI shift and if that ever happens if one of the light rays gets PI shifted and the other does not then we would swap these conditions and be the half integer wavelengths that would give us constructive and the whole integer wavelengths that would give us destructive so I'm going to just be clear here let me show you what I'm talking about if let me clear this off if I had material and right here it's slow compared to this one if it reflects off of a fast material no PI shift no 180 degree shift but if it's in a fast material and it reflects off of a slow material then yes this gets a PI shift so this gets a hundred and eighty degree shift that's how you determine it is whether it reflects off of a fast material or for if it reflects off of a slow material for both sides the top two up here got to ask the same question did it go from slow to fast reflect off of a fast or did it reflect off of a slow that's how you determine if it reflects off of a fast no pot shift if it reflects off of a slow material then it does get a PI shift okay so that's how you deal with PI shifts let's go back to this one there's a few more details here people have a lot of trouble with thin film to be honest that's one problem is they don't like figuring out whether it was PI shifted or not it's actually not that hard once you know the rule but there's another problem here what's Delta X we never even set with Delta X's well it's got to be related to the thickness so imagine this both waves come in imagine both waves are combined in this big wave coming in they were both in there to start off with so they both travel that distance wave one reflects off and just travels this distance wave two also travels that distance but only after wave two traveled this extra distance within the thin film so the extra path length wave to travel compared to wave one was not the thickness T here's where people make the mistake people think that delta x for a thin film is t know the wave two had to travel down and then back up so it's two T so this is the key for thin film interference the path length difference will always be 2t so I shoot I just have to come up here I know what Delta X is for thin film it's always going to just be equal to two times the thickness of what the thickness of the thin film so I'm going to put two t here this is my condition this is how I change this and to make it relevant for thin film for a double slit Delta X was d sine-theta for the thin film Delta X the path length difference is just two times T so it's kind of simpler you got these PI chefs to worry about but the Delta X is simpler alright so that's not too bad anything left to worry about yes one more thing to worry about