Refraction of Light

by Patrick Ford
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Hey, guys. In this video, we're gonna talk about something called The Refraction of Light, which is the change in the lights angle as it passes from one boundary to another. All right, let's get to it. Remember, guys that at a boundary Lykken do two things it can reflect off of that boundary, or it can transmit. It can transmit through the boundary and make it into the new medium. And remember, that light in general does a combination of the two. Okay. When light crosses a boundary into a new medium, it turns out that it will change its direction. Remember that at a boundary, we always measure angles from the normal to that boundary. So if this is state a one, then the light is gonna come out at some new angle. Fate of two and data one is not necessarily going to equal data to In general, they will not. Okay, remember that in each medium, light still travels in a straight line. Those lines just aren't parallel because the ray has changed direction. Okay, Now, the reason that the light changes it's direction is due to one thing and one thing alone. Light travels at different speeds in different media. Okay, in a vacuum, light travels the fastest it will ever travel. The speed of light in a vacuum is a fundamental constant of the universe. But in a medium light will always travel more slowly than in a vacuum. Okay, remember that a fundamental fact about waves in general, all waves is that their speeds air determined by properties of the medium and the type of wave in this case, since they're all light, is electromagnetic waves. The speed is determined simply by the properties of the medium, the property of the medium that tells us how fast light is going to travel in it is known as the index of refraction. Okay, this is a very important word. Sometimes it's called the refractive index, just so you don't have to call it the index of refraction. Okay. And the index of refraction off any medium is always defined the same way. It's defined as the speed of light in a vacuum divided by the speed of light in that medium. Okay, Now, remember, because light always travels slower in a medium than it does in a vacuum, the index of refraction is always going to be bigger than one. The speed of light in a vacuum is always gonna be larger than the speed of light in any medium. So the index of refraction is always gonna be bigger than one. The two indices of refraction that you need to remember are the index of refraction for a vacuum, which is obviously one right. How fast does light travel in a vacuum? C C, divided by C is one. But for air, the index of refraction is 1.29 It's so so close toe one that we always just say it's simply one. Okay, so the index of refraction of air is the same as the refractive index off vacuum, Which is what? Okay, now I'm going to talk about an analogy to explain why refraction occurs. Okay, I'm gonna minimize myself so we can all see this figure. You can think about refraction like a barrel rolling on a smooth surface to rough surface. So imagine this barrel right here is rolling on smooth, fresh pavement, okay, and it's rolling very, very quickly. And then it encounters some grass, which is rough, and it slows the barrel down when the barrel is rolling entirely on the smooth surface, all of the points along the barrel are moving at the same speed, so the barrel rolls in a straight line. But once the edge of the barrel hits the grass, that edge is now moving more slowly than the opposite edge. Okay, now that this is rotating more slowly than this edge is, it hooks the barrel right. This barrel hooks inward, and it causes it to change direction once the barrel is entirely on the rough surface. Once again, all points on that barrel are moving at the same speed, so it moves in the straight in a single direction. Again, it moves straight again. But since it hooked when it transitioned from the pavement to the grass, it is now moving in a new direction. Okay, this is the idea with refraction. It's due solely to the fact that as you transition from one boundary to another, the speed that you're traveling with changes okay and the speed in the case of the barrel change once the barrel hit the rougher grass and that caused it tow hook inwards and move along the grass at a different angle. Okay, let's do an example to further illustrate this. We want to explain refraction using Hagen's principle. Okay, Before I do refraction, though, I want to talk about what Hagen's principal says about a single ray of light moving through a vacuum. So imagine that that boundary wasn't there. Let me minimize myself for this because I'm going to be drawing over where I am right now. All right, so this Ray is coming in and there's a boundary right here that separates the media on the left side. On the right side, I'm still indicating where the boundary is, but I'm not sorry. Let me redraw that really quickly. I wanted to end at where the imaginary bounder is. I've indicated where the boundary is, but I don't actually have a boundary here. In reality, we're still looking at this light ray without changing the media that it's in. So remember how to do these problems. We're going to draw wave fronts as they approach the boundary. So there's a way front at one time, after a certain amount of time, There it is, right after another amount of time. There it is, and there it is and then it hits the imaginary boundary, and then it hits it again, and then it hits it again. And remember that this was the first time that it hit that boundary. Okay, actually, let me write that over here. This is the first time that it hit that boundary right here. This is the second time that it hit that boundary. And right here, this is the third time that it hit that boundary. So that third point was the most recent time hit. So it produces the smallest Ray. I'm sorry. The smallest wave lit the green dot is the second time that it hits. So it produces the second smallest or the second largest wave lit Because there's only three of them. The blue is the most recent Sorry, the earliest time that it hit. So it's had the longest time to propagate the wave lit. So it has the largest wave lit. And what ends up happening is that this wave front is gonna be parallel to all of those other wave fronts. And this ray is going to go through undisturbed, right? That's exactly what we expect. Because as it passes through no boundary right This is no boundary right here. I drew it as an imaginary boundary, but in fact it's traveling in the same medium because there's no boundary. It shouldn't change direction. It should absolutely move in the same direction. Now let's see what happens when we encounter a boundary where the speed of the light does change. So once again, here's away front. Then a little time later, another way front, little time after that, another way front, then away from hits the boundary. Then time after that, another way front hits and then it hits again. Okay, so it hits at those three places the first places here. The second place is here, and the third place that hit is here. So the most recent encounter is at the third point. The earliest encounters that the first point This is no different than every time we've applied Hagen's principle. Now what's the difference between the situation on the left with the boundary and the situation right here with no boundary on the left side. In the new medium, light travels more slowly than when you don't change media. Okay, because light travels more slowly. These wave let's don't travel as far. So that third wave lit the red one is gonna be smaller over here than it waas right here. The green wave lit is also gonna be smaller over on the left. Then it was here. And finally the BlueWave lit too, is gonna be smaller on the left than it is on the right. And that's simply due to the fact that light travels more slowly in this new medium. So what happens? The new wave front is at a different angle, then the old wavefront, because it's at a different angle. Now, when I draw my ray, my ray is moving at a new angle. Okay, remember that this process, which is called refraction, is due solely solely to the fact that the speed of light is different between these two boundaries. Okay, that wraps up our discussion on refraction. Thanks for watching guys.