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# Young's double slit introduction

## Video transcript

young's double slit experiment looked a little something like this you've got a barrier with two holes in it but these holes are so small and so close together we characterize them as slits and double because there's two of them Young was the English physicist who first did an experiment of this kind and what we do nowadays is we take a laser we shine this laser at the double slit now the laser has to be wide enough that it hits both holes and you might think oh my god you need a big laser no you make these holes very close together that's why you make them really close together or at least one reason the other reason is the distance between these holes has to be comparable doesn't have to be the same size or smaller but it has to be all round it can't be a trillion times bigger than the wavelength of this laser light you're sending in here it's got to be around the same size or what we're going to talk about here you won't see you won't see the interesting pattern that's going to emerge you might wonder what I've drawn here what is this this isn't a wave that's not this is a wave right here I thought these were waves what are we doing now why we got this different representation and the reason is when I draw this this pretty much just lets me show a wave in one dimension but that's not good enough this process is going to be fundamentally two-dimensional this wave is going to sprout in two dimensions so I can't draw like this I have to draw like this now this whole line here what is this represent this represents a peak everywhere along here is a peak of the waves you've got this wave filling up this entire region these lines represent lines where every point along there is a peak of the wave what's in the middle yeah in the middle would be the trough of the wave over the valley so that's what I'm going to use I'm going to use this representation for the wave this will let me show this wave spreading out in two dimensions better than this one could I couldn't draw very well with this one so what happens this wave comes in here this laser light comes in here well that part hits that barrier it doesn't get through this part is that barrier doesn't get through this part hits the barrier doesn't get through the only portion that's going to get through is basically this portion here and this portion here these are going to be the ones that make it through and so what happens what do you see on the wall over here if this was a screen that you could project the light on what would you see naively what I would have thought have been like up a shoe light comes through here bright spot light comes through here bright spot you just get two bright spots right well no that's not what you get that's why this experiment is interesting because you don't just get two bright spots you get a pattern over here because waves don't just travel straight through this hole when a wave encounters a hole or a corner it spreads out and that's spreading out we call diffraction so you're going to get a wave spreading out from down here so this is not going to go in a straight line it spreads out in two dimensions that's why I had to use this wave drawing representation it's going to spread out from the top one two oh look what's going to happen you have two waves overlapping these two waves going to start overlapping and where they overlap constructively you'd get a bright spot where they overlap destructively you'd get a dark spot where it's sort of half constructive half destructive you might get a medium ly bright spot how do we figure out what's going to be well I can't draw this precise enough to show you that so let me get rid of all of this mess real quick get rid of that out of the bottom hole what would you get you'd get this a nice spherical pattern coming out of here now it might not exactly be the same intensity throughout here but I can't draw it with the exact right intensity up here this intensity of this portion would be smaller than this portion here the degree to which it's spreading but this will help me visualize it you've got this wave spreading out out of the bottom hole you also have a wave spreading out of the top hole and now these are going to overlap let's draw them both both waves overlapping in the same region you're going to have constructive and destructive interference and if you look remember these lines represent Peaks so every time a peak lines up right over a peak or in the middle of valley over a valley every time the wave is exactly in phase when it gets to the same point these are all constructive points so right in the middle you'd get a big bright spot that's kind of weird right in between these holes there'd be a big bright spot where else well look at this right this is constructive constructive all constructive they form a line they get these lines of constructive interference same with this line constructive constructive all the way over to here so on the wall you'd see multiple bright spots down here these are all constructed because Peaks are lining up perfectly and I'd get another one here you keep getting these bright spots on the wall they wouldn't last forever I mean at some point it start to die off and be hard to see but you'd be getting these bright spots continuing on at some point they're so dim you can't see them and in the middle well wherever let's see what's a good point to look at wherever a peak lines up with a valley so this wave is a peak right here but for the other wave look it we're in between the two green lines so and that's one you have destructive because the peak is matching up with the valley and this would be destructive and this would be destructive so in between here you get a destructive point the same is true in between each of these perfectly constructive points you get a perfectly destructive point in between those it'd be kind of half constructive half destructive and merge into each other and what you get sometimes physicists draw a little graph to represent this you get a bright spot in the middle this is sort of representing a graph of the intensity zero and then another bright spot and it goes down to zero again another bright spot they get weaker and weaker as you go out at some point it's hard to see same on this side zero bright spot zero bright spot this is the classic double slit pattern you'll see on the wall and it's caused by wave interference in two dimensions and what's the rule for wave interference in two dimensions is the same rolls the wave interference for one dimension it was this remember for one dimension Delta X the path length difference had to be 0 lambda 2 lambda 3 lambda so on would give us constructive interference and now if you're paying close attention you might say hold on there was a condition remember this was only true if there was no funny switcheroo business with the back of the speaker we had to make sure that these two sources were in phase to start off with is that true of these light waves it is the fact that's why we do it double-slit like this that's why we take one wave we let one wave come through here that way we break it up into two pieces why because we know if a peak was going into the top hole well the same wave was going into the bottom hole that's also a peak this is a tricky way a quick easy way to make sure your two sources coming out of these two holes are exactly in phase you don't have to worry about any phase difference caused by the source you just have to worry about a phase difference caused by the fact these waves are going to travel different distances to different points and what do I mean by this what is path length difference mean here well if I look it from this top line for this top hole this is basically like our speaker one source here one source here but it's light instead of sound waves from here to the center bright spot the wave from the top hole had to travel a certain distance and from the bottom hole to that spot wave had to travel a certain distance so basically this we can call X 1 this length X 2 and the path length difference would be X 1 minus X 2 the difference in these and you can just make it the absolute value if you want but the size of the difference between these two path lengths what is that going to be 4 right in the center well that one's just Delta x equals 0 because the waves are traveling the same distance to get to that point and that makes sense that's a constructive point because 0 gives you a constructive point where the path length difference is 0 how about the next point well the way from the bottom has to travel this far the way from the top hole has to travel this far this time they're not traveling the same distance the way from the bottom holes traveling farther how much farther well it's got to be the next one's got to be lambda so this way is going to be traveling the bottom wave would travel one wavelength further to get to this point then the way from the top hole because that's the next possibility for constructive interference nope it's not from here to there that's one wavelength this is a common misconception this distance on the wall between constructive points is not one wavelength the difference than path like that one wave travels to get there compared to the other wave is one wavelength and I bet you can guess the next one that x1 Delta X would just be two wavelength and you can keep going how about the destructive points shoot you know how to do that these are going to be the half wavelengths lambda over two this one's going to be three lambda over two and so on and down here what would you get well if you got rid of the absolute value sign and you want it to you can start talking about this Delta X would be negative one lambda this one would be negative two lambda and so on so you can have negative values if you wanted to note the fact that might be lower or higher depending on where you were in this interference pattern