Hey, guys, in this video, we wanna look into more detail as to why exactly diffraction happens, and we're gonna analyze why diffraction happens by exploiting Hagen's principle for light. Okay, let's get to it. Remember, guys, what Hagen's principal says is two things about how a new way front is gonna appear after an old way front. Okay, the first thing that Hagen's principal says is that the old way front is going to produce these little spherical wave lits at every point along the way front. Okay, so if I consider this an old way front, then I have a point here where I'm considering these spherical wave. Let's to be produced. I have a point here where I'm considering these spherical wave leads to be produced, and I have a point here where these spherical way leads are being produced. Okay, now, this actually happens along the entire length of the wavefront instead of at the specific points that have indicated. But just for clarity's sake, I'm only showing you three points. If I were to show you every single point which is a new infinite number, it would look crazy. You wouldn't be able to tell anything that was going on. Okay, So for the sake of clarity, I only showed three points. Now, considering this old way front right here, I can choose a point here and look at the spherical wave. Let's going out. I can choose a point here of the apex and draw spherical wave. Let's going out or I can choose the point down here and draw spherical wave. Let's going out. The point is that no matter the shape of the old way front, the new wave front is sorry. No matter the shape of the old way front, Every point on the old Wavefront is producing these spherical wave. Let's that air emanating from it. The second point of Higgins principle is that the new wave front is a tangent line that crosses the apex is off each of the wave. Let's Okay, so each of these wave lits has a new apex. Anay packs here hopes the throng color on Apex here and in Apex here. Okay. And then the new wave front is just gonna be drawn tangent through those apex is so I'm just going to draw a line straight through and you see that drawing a line straight through here means that the new wave front is parallel to the old way front. Okay, Now, for this circular wave, I have an apex here. I have an apex here, Niven Apex here and drawing a line tangent through all those means. Another circular wavefront. This new wave front is also circular. If we wanna look at what those light rays would look like, just remember that light rays are perpendicular toe every point on the weight fronts. This light Ray is gonna look like this column ated light. This light ray is gonna look like this is a tropic the same in all directions. Okay, so that's just a refresher on Hagen's principle, and it's important to understand it toe understand exactly how diffraction occurs now, the important key for diffraction toe understand is that the smaller the slit what do you mean smaller relative to, I mean smaller, relative to a constant wavelength. So let me remind myself for this I have three figures, each of them showing wave fronts with identical wavelengths, right? The distance between two wave fronts is, by definition, the wavelength, so three waves with identical wave fronts. But the slit width is changing in each picture. Initially, we have a length much with much larger than the wavelength. Then we have one near the size of the wavelength. Maybe the wavelength is one millimeter. Maybe the width is three millimeters. It doesn't have to be identical. It just has to be on the same order of magnitude. And then I have a length much smaller with much smaller than the wavelength. Okay. And the important thing to see here is that essentially, the way to think about this is as that which gets smaller and smaller and smaller as the slit gets smaller with number of wave lits that can pass through the slit decreases. So you see, in the first picture we have a ton of wave. Let's then when the slick it's smaller, we don't have as many wavelengths that can pass through. And then when this let's really, really, really small, we say essentially, on Lee, a single wave lit can pass through. So what are the new? What wave fronts gonna look like on the opposite side off the slip? Well, remember, we have to draw a line through the apex is off each of these new wave. Let's so here. I'm just gonna draw a line straight down. So this line is parallel toe all the wave fronts before, So it's just going to continue being parallel And what we had initially, which was this column mated light. We also have passing through the slit. Okay, we have culminated. Like entering. We have colonnaded like leaving. There is clearly no diffraction here. All right, now, what are the wave fronts gonna look like here in the second image? The thing to consider here is that these wavelengths are small. They're less wave. Let's Okay. So the effect that each wavelet has on the other is less here in this image, we said they're essentially so many that the line is basically straight. But now, because there are fewer, the line actually curves a little bit at the edges, and then it curves a little bit at the edges, but it's still basically parallel in the center. So what are these? Ray's gonna look like? Well, these rays air clearly column mated. But what are the rays gonna look like coming out well near the center? They're basically still gonna be column mated. Right column a did at the center. But what about the edges where those wave fronts get distorted a little bit? Well, then they aren't culminated anymore. They actually spread out a little bit, so we have spread, uh, edges. What this means is that for light passing through the center of this slit, it's essentially passing through London. Diffraction did. It's entering column aided, and it's leaving colonnaded for light, passing through near the edges of the slit, its diffraction as it passes through. Now what does the wave fronts look like when we Onley? Consider a single wave lit, as shown in the figure on the right? Well, since it's only a single wave lit, it's gonna have to continue being spherical. There are no other wave. Let's to distort the wave front. It's going to continue being spherical. And now, if we look at what happens to the light rays as it passes through the slit, thes new light rates have to be perpendicular to the way fronts at all points. The Onley way for that to be true, is it? The light spreads out Aissa tropically so it enters. Column aided and it leaves ice a tropic so there's definitely diffraction here. Okay, so on the left, we have no diffraction on the right. We have full diffraction or a lot of diffraction. And in the middle, we have some diffraction. We have diffraction at the edges, but not really at the center. Okay, So this process of diffraction is explained entirely using Hagen's principle, okay. And a few consequences of this are important. All right, if you're looking at a single slip, as I showed in the above figures, you can never really make the slit so small that Onley a single wave lit is produced. Okay, I approximated that, but in reality wave, it's occur everywhere on old way from's. Since they occur everywhere, you can never make a slit so small that you're gonna isolate a single wave lit. Okay, so in reality, there will always be multiple level. It's passing through a slip, no matter how small the slip is light, then comes out at different angles from two different parts of the slip. Okay, so if we look at near the top of the slit, we actually have light coming out at multiple angles, and we look at the bottom of the slit we actually have light coming out at multiple angles, right? This is exactly what I said. Happens when you have a feel wave lits, but not one. You have diffraction at the edges. That means that there's no guarantee that a light ray coming out of the top part of the slit is going to be the same angle as light coming out of the bottom of the slit. Okay. And what this means is, when you have all this light at different angles relative to one another, these air actually waves. Don't forget that. So you're gonna have, let's say a maximum here and then over here, maybe you have a minimum. And when you have a maximum and a minimum at the same place interacting with one another, you have destructive interference. So the light passing through the slit is going to interfere. Okay with itself. Okay. Now, if you have two slits, you can then assume you can approximate that. Basically, the light comes through the slit fully distracted that you only have a single wavelet passing through. And so you have basically Aisa Tropic Light coming out of here. And the reason we can assume that is because we want to consider the actual size of the slit to be very, very, very small compared to how far apart the slits are. Okay, so compared to how far apart this actual length right here, how far apart those two slits are? We want to consider that bigger than the width of the split itself. Okay, now, once again, because light is coming out of all these different angles, the light child is a different distance. So maybe this top light has no displacement when it reaches there. And then this bottom light has a maximum displacement when it reaches there, and then the light is going to constructively interfere. The point is that as the light passes through these two slits, which is called the double slit, each light ray will interfere with each other. Okay? And I'm sorry I put a condition here that I did not address that distance deed. Is this with this separation distance between the two slits and the length l that I indicated there is different than the length l that I indicated in the figures above. That's actually the distance from the screen to the slits. Okay. So as long as the slit width. The distance between those two slits is very, very small. That split separation is very small compared to how far apart the screen is. You will get light coming out of those slits. Aisa, tropically and each light right coming out of the slip will interfere with one another. All right. And this produces a very, very important pattern that we're gonna look at here, which is called a diffraction pattern. Okay, this is what the light looks like when you assume diffraction occurs. All right, so maybe light coming out of this slit at this point and like coming out of this split at this point, if we look right here, this is dark, right? The brightness is very, very low. This means that there has to be destructive interference. If it's destructive, you're going to reduce the brightness of the light. And then if I consider another point over here, where now we have a peek? This is bright. That means that the two light rays reaching that point have toe have constructive interference. All right. And we get a similar brightness pattern in a single slip. The only real difference between the double slit and the single slit is how bright the sorry, how wide the central bright spot is. Alright guys. So that wraps up our discussion on diffraction specifically using Hagen's principal. Thanks for watching.
