Okay, so that was the first observation, the first experimental evidence for a finite speed of light. Now, later on, experiments got much more sophisticated and they came up with some new ways to measure the speed of light. Okay, and I'm going to tell you about one of these ways, who co was a famous French experimental scientist in the 1800s. He did a lot of very interesting experiments, actually. So, I'm going to tell you about this one. This is one you did measuring the speed of light and you got a very accurate value of 298000. Okay, so about 1% less than 1% error. And the idea is quite nice. You have a light source here and then very far away from each other. You have two mirrors. I think in the original experiment it was about 10 kilometers distance between these two mirrors. And the light goes from the source. It's not really a light bulb. It needs to be a focused source of light. Right? So, the focus source of light. So, in the modern sense, we'd use a laser. He didn't have lasers, so he used the optical tricks to get a focus beam of light. But anyway, the light source, the light goes to the first mirror. It's then reflected to the second mirror, reflected back to the first mirror, and then you observe it. So, this is somebody measuring the light. Okay. Okay, so I'm going to try and explain how the experiment works using this bulb. It needs you to be good at catching it. Okay, so in the original experiment, I'll give you the bulb. Okay, right? So, you are the light source. Okay, I am the mirror, and then I'm the first mirror, and then let's say yes or you can be the second mirror. Okay, so the light comes to the first mirror. Okay, it then goes to the second mirror, and then it comes back. Now, if I am stationary, then I just throw the light back straight back at you. Right? But the first mirror, that's me, is not stationary. The first mirror is made to rotate. So, as time goes on, I go round and round. Right? So, if we do the same thing again, I get the light here, and I'm like this, so I pass it to you, then you pass it back to me. But in that time, when the light goes between you and me, I've rotated about this much. Right? And that means instead of throwing the light back over here, I throw the light back at a slightly different angle. Right? Like that. Okay. Now, if the speed of light is slow, then I turn through a big angle. Right? So, therefore, there's a big change in the direction of the light. If the speed of light is fast, then I turn through a small angle. So, therefore, there's a small change in the angle of light. Right? So, by measuring the change in the angle, you can calculate the speed of light. Okay. That's the idea of the experiment. Okay. So, okay. So, in the next slide, I draw a picture of this. So, here's the light source. The light hits the first mirror here, goes to the second mirror, and it comes back. But once it's come back, the first mirror has rotated through an angle of theta. That means the light is reflected by an angle of two theta. Yeah. Okay? So, if you measure the angle of two theta here, you can calculate the speed of light. The formula is there. We're going to derive this formula now. So, this is question two on the works. Okay. So, this is the full-core experiment. So, you have in the full-core experiment two mirrors, like this, one is rotating. Okay. Let's say that the speed, the distance between the mirrors is L. L on the worksheet. Okay. And the worksheet tells you that L is 30 kilometres. I don't think this is the actual experimental value. I think I just made this up. Okay. Okay. Then you have a light source here. Here's a source of light. Okay. And the light comes in. It's reflected off the first mirror, goes to the second mirror, comes back to the first mirror. But in the time it takes to come back, the first mirror has rotated through an angle of theta. Like this. Okay. So, therefore, the light is not reflected exactly where it was originally, but it's reflected at a different angle here. It's angle 2p. Okay. And what you do is you observe the light here and you measure the angle. Okay. So, the key thing in this experiment is how much time does it take for the light to go from here to there? Does that determine how much the mirror rotates, which determines the angle you measure here? So, that's part A of the question. Find the time that it takes for the light to go here and back. Okay. And that's very easy, right? Because it's just time is distance divided by speed. The distance is 2L. Speed of light. See. Okay. That's easy. Right. So, let's suppose that the mirror rotates at a certain rate. Oh, my God. Okay. So, oh, my God, is the rate of rotation of the mirror. Okay. Which we know. Then, using that, you can find the angle at the mirror turn. This is part B of the question. So, the mirror turns through an angle. Theta, which is just the vote of rotation, times the time. Okay. But from part A, the time is 2L over C. And in this experiment, you know everything, right? So, you measure the angle theta, you know the rate of rotation, you know the distance between the mirrors. So, therefore, you can calculate the speed of light. That's the way it works. So, just rearranging, then you get the speed of light equal to 2L over theta. So, that's it. So, that's the equation that was on this light here. Except, omega is d theta by dt. And H, I've called L. It's the same formula. Okay. Finally, I put some values in the Nassiu to calculate. So, actually, in part C, I give you the speed of light. I do it backwards. I give you the speed of light. And I ask you to calculate the angle theta. So, I tell you that the speed of light is 3 times 10 to the 8 meters. Second. Okay. And I tell you that omega is one revolution. Second. Okay. And I ask you to find theta. Okay. So, theta, then, is 2 omega L. C. And then, you know all this. So, you just calculate it. And if you do so correctly. You get an answer of 0.072 degrees. So, the point of this question was to show you that this is really, really small. Right? And even though the distance between the mirrors in this hypothetical experiment was 30 kilometers. So, it's a very long way. The angle you have to measure is still very, very small. So, what this shows is it's a really difficult experiment to do. Right? First of all, sending light over such a distance and being able to exactly hit the mirror. And then, having enough light to come back and hit the other mirror, that's not easy. Right? The further light goes, it gets weaker and weaker. Right? Because it scatters off the air and all other things. Right? And you have to send it exactly the right angle to hit this mirror. And then, even if you achieve that, the angle you have to measure is still incredibly small. So, it's really, you know, Foucault is a genius experimentalist to be able to pull this off. Right? In fact, last year, a group of students at this university tried to do the Foucault experiment using modern equipment. Okay? So, we've got some equipment in this university. There's a laser we can use. And then, there's a rotating mirror, which it's a very small mirror, but it can rotate a thousand times a second. So, it can rotate very, very fast. Okay? And because the mirror rotates very fast, the distance doesn't have to be so large. Okay? So, when the students did it last semester, the distance was only about 20 meters. Okay? But still, it was a really, really hard experiment to do. And still, actually, the answer that my group of students got was worse than the answer Foucault got. So, even all that time ago, he got a much more accurate answer than we were able to get using modern equipment. So, this is very impressive. This is result. Okay?