If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Diffraction grating

## Video transcript

double slits are cool because they show definitively that light can't have wave-like interference patterns and if you shine a green laser through here what you'd see on the screen would be something like this you'd have these bright spots but they kind of blend into dark spots which blend into bright spots which is why when we draw a graphical representation of this it kinda looks like this where these spots are blending into each other which is cool but it also kind of sucks because if you go actually try to do this experiment you'd want to measure some angles and that means you have to measure some distances that measured distance from the screen to the wall that would give me this side of the triangle and then I'd also probably want to measure distance between two of these bright spots because that's what I can see but because they're smudgy it's like is that the center is this the center sometimes the lights not so strong and it's hard to tell and what's worse is these kind of die off and so there's another problem these die off pretty quick sometimes you're lucky to even see the fifth or sixth bright spot down the line so my question is is there a better way is there a way to make these spots more defined and so you can see more of them so they're brighter and the answer is definitively yes and we figured out how to do it the way you do it is you just make more holes so you come over here and if these are spaced to distance D I'm just going to make another hole distance D and then I'm going to make another hole at distance D and then I'm going to make another hole a distance DL makes hundred thousands of these holes extremely close together as long as they're all a distance D apart something magical happens so if these are all D apart what happens is on the wall over here instead of getting this smudgy pattern you'll get you Lily will just get a dot right it there and then darkness and then another dot and then darkness and another dot and you'll see this continue out much further than you could previously why well let's talk about why so let's talk about this how come you see this pattern over here like this so the first wave from this first hole let's imagine this first wave from this first hole it's going to travel a certain distance to the wall let's say we look at a point over here where it is constructive let's say we just have these two holes to start off with right two holes double slit disregard all this stuff for a minute two waves coming in from two holes get over to here let's say this is a bright spot let's say it's the bright spot that corresponds to Delta x equals one wavelength in other words this would be the constructive point where the second wave from the second hole travels one wavelength further than the way from the first hole and again what that means is if I were to carefully draw a line from here at a right angle right there that means that this way from the second hole this is the extra part so that would be one extra wavelength and because this second wave is traveling one extra wavelength going to be constructive because if I draw my wave they're going to match up perfectly there so if I draw my wave let's say the wave from the first hole happen to be at this particular point on its cycle it doesn't have to be but let's just say it was there the first wave hit that point at this point in its cycle well the second wave since it's traveling one wavelength further is going to hit at this point in its cycle so it'd be here now these are both hitting there at the same point so the first wave gets their hitting right here the second wave guess they're hitting right here these overlap because these are two different waves overlapping at this point it's going to be constructive because if a peak matches a peak constructive if a valley matches Valley constructive how about the third hole here's where it gets interesting this third hole the way from the third hole is going to have to travel this far to get there well let's see for them the second how much further does it travel compared to the second hole I'm going to do the same game I did just a minute ago it travels this much further which again since these are the same angle this is going to be the same distance here this is also going to be one wavelength remember we derive this that D sine theta is the path length difference and the theta is the same for all of them and so I could just look at these to consider these two is the double slit this one travels one wavelength further than the second how much further does it travel them the first I'm going to continue that line down it's just going to travel two wavelengths farther than the first so the wave coming out of the third hole travels two wavelengths further than the first hole the second and the third are going to be constructive because they're one wavelength apart and the third and the first are going to be constructive because there are two wavelengths apart that's okay two wavelengths doesn't matter look it if the first one is here away from the second one's here away from the third hole travels two extra wavelengths when that third wave that gets to this point it'll be at this point on its cycle they're all going to be overlapping at the same point on their cycle it's going to be constructive you can keep doing this you can come down to this hole and it will also be constructive interference in other words this fourth hole travels one wavelength further than the third two wavelengths further than the second hole three wavelengths further than the first hole but they're still all going to overlap perfectly you will get an extremely bright spot here because now you have even more light overlapping and it's all perfectly constructive bright spot now here's where it gets strange so you got to be careful this is the part of the explanation I hated as a student I thought this made no sense whatsoever so pay close attention at this point here's the weird thing if you deviate slightly from this constructive point if I go up just a little bit over here to some point right here let's just see what happens this way from this first hole would travel that far to get there okay and the way from the second hole travels that far to get there the path length difference isn't going to be one wavelength let's say the pathway the path length different happens to be 1.1 wavelengths so let's say the wave from the second hole happen to be traveling not one wavelength further anymore it's not travelling one wavelength further it's going to be traveling 1 and 0.1 wavelengths further and so if the first wave happened to hit at this point the second wave would be hitting at not exactly one wavelength but one point one now if I keep drawing them over here I'm going to run out of room so since they're all the same points on the cycle the cycles the same over and over one wavelength point one I'm just going to draw that right here so the second wave would hit right there those would overlap you know it's partially constructive I mean you're going to get a just looking at these you think you'd get a bright spot but if you keep going let's see what happens wave from the third hole also travels to get there how much farther does it travel well it travels 1.1 wavelengths further than the second hole but it travels 1.1 plus 1.1 wavelengths further than the first hole so it travels 2.2 wavelengths further than the first hole so to make this clear let me just be clear here so if I do the same trick right I draw this down to a right angle it's a little farther so I've to draw the line a little further out first wave travels one wavelength and point one wavelength further how about this one here well the way from the third hole travels one wavelength 0.1 1.1 wavelengths further than the wave from the second hole but it's going to travel 1.1 plus 1.1 wavelengths further than the first hole so it's going to be 2 point 2 this way from the third hole is going to travel to point 2 wavelengths further than the way from the first hole where would that be so 1/2 wavelengths point 2 would be even further down the line here not pleaded at the bottom but further down the line so it would be at this point over here and you can keep doing this and let's just see what happens it should do a couple more this wavelength has to travel this far so now you can probably see the pattern this wave through the fourth hole has to travel 1.1 wavelengths further than the wave from the third it travels 2.2 wavelengths further than the way from the second it travels 3.3 wavelengths further than the wave from the first so if I compare this wavelength where this wave is on its cycle compared to the first then I'm going to be 3.3 wavelengths so if I go 1 2 3 and then 0.3 I'd be down here somewhere I'd get one that's at point 4 I get one that's at point five and get one that's at 0.6 0.7 1.8 1.9 one it.well point 10 which is back to a whole wave like then wavelength again a whole wavelength difference what is this going to be if all these waves are overlapping like this at this point it's only slightly deviated from this other point what am I going to see there well this look at you could pair these off this point and this point are going to interfere completely destructively ones at a maximum ones at a minimum ones at the peak ones at the trough and so you get zero and you can keep pairing these off this one here and that one there completely do completely annihilate each other completely destructive and you can keep doing this this one here and this one there completely destructive you can keep finding points that completely destruct each other and that means you're going to get no intensity at all even slightly off from this magical point this magical integer wavelength point what that means is instead of getting a blur instead of getting this instead of getting this smudgy pattern you're going to get at the bright spots a dot and then another dot at the bright spot in between these bright spots you will get darkness which is great it's great because it's easier to measure so that's one good thing and it relies on this fact that if you've got multiple holes hundreds thousands of holes if you go off even slightly because this isn't going to always match up perfectly you keep going down the line one of these are going to interfere constructively with another and you can keep pairing these off and then the second would interfere constructively with a different one and the third with a different one and the fourth with a different one and they're always going to match up so that you can destroy them all and you get destructive points in between that's why it's dark now at first I didn't like that argument I I had to go back over that make sure that made sense to me so if it doesn't make sense do you go through you got to hammer it out try it out draw it out I've tried my best to explain it here but I have to admit it's a difficult one to sort of comprehend but that's that's the idea and so this is great actually these multiple holes here giving us points that are points that are spaced out and clearly delineated now I can clearly see okay if I wanted to measure this distance I'll have to guess there's no guesswork one dots here on dots they're bright bright no smudge enos so that's one great thing about this the other great thing is because I've got more holes this brightness lasts longer these bright spots will keep going further I can see this travel further down the line than I would with this smudge enos because I've got multiple holes interacting I'll have more intense dots it's brighter the dots are more delineated and they're typically brighter more intense and so we give this a special name because this is so useful these multiple holes instead of a double slit these multiple holes are more useful we call this a diffraction grading so this is a diffraction grading and it's more useful than a double slit in many ways because it gives you clearly delineated dots and it lets you see them more clearly and how many holes are there in a diffraction grading will typically these are measured these are rated in lines per centimeter in other words if took a diffraction grading asked how many holes are there the lines are the holes how many holes are there per centimeter well the lines could be the blocked parts and the holes can be the parts where there's no block part but regardless there'll be as many lines as there are holes how many holes are there per centimeter there's typically thousands of lines per centimeter in a diffraction grating that's how small these are spaced together you might worry though isin the math going to be complicated here we've got all these holes here turns out no this is the best part by far the best part this relationship still holds all that math we did still fine and because these all line up for the for the good points the magic points these points where they all overlap in such a way that they're one wavelength further those line up perfectly so that no matter how many holes you go down the line they're all perfectly constructively interfering and so you get this equation you get the same equation it's the same equation we had before where D sine theta equals M lambda gives you the constructive points for a diffraction grading interference pattern on the wall