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MITOCW | Lec 2 | MIT 2.71 Optics, Spring 2009 the Following Content Is Provided Under a Creative Commons License MITOCW | Lec 2 | MIT 2.71 Optics, Spring 2009 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. GEORGE So does anybody have questions from the last lecture? After some time to wake up, anybody still have BARBASTATHIS:questions? So I will start, and if you remember of a question that you had, please interrupt. I think if you push the button the button, I will hear a sound over here. So we will know that there's a question. So I'd like to pick up the thread from where I left last time. We covered fairly quickly because we ran out of time. But we covered that the law of reflection and the law of refraction. So I'd like to go back to the low of reflection, and remind you that it is a very simple, very simple result. The minimum path requirement for the light rays force those reflections to be symmetric. So this has a strange consequence that we're unfamiliar with from when we look in the mirror daily. And that is the fact that our left and right locations in our body. They flip when we look at the mirror. So we'd like to make that a little bit more quantitative by looking at this diagram. So to understand this, suppose that I am-- I have an object that is oriented. You can think of it as perhaps two pencils that are sort of following the ray paths and then they get reflected from the mirror. So, for example, if you look at the central ray, it will be reflected symmetrically. So, again, what you see here is the front view of the mirror. And then I will draw a few ray a paths in perspective. So this is the ray paths that start from the object. I don't know if you can see me over there, but I'm trying to show what will happen with an actual pencil. So if this was a pencil that is coming towards the mirror, and this is the surface of the mirror. The pencil will go like this. And then law of reflection says that it will also come out like this again. This follows very easily if you simply trace the rays. In the next step in my animation here, it paints the sort of positions of the pencils and their tops as they get reflected from the mirror. So what happened here is the following. As you can see, the pencil did not actually change orientation. This is a strange thing about mirrors. But what did change is the following. Imagine that you are walking together with this pair of pencils. As you are walking this way, you will see that the one that is horizontally oriented. The top of it is pointing to your right. But if you walk all the way to the mirror. Go to the center of the ray, and start going backwards the other way around. Then all of a sudden, the top of the pencil appeared on your left. This is a simple consequence of the law of reflection. The way we interpret it in everyday life when we see through a mirror is the following. Of course, in everyday life, we don't talk about left handed and right handed triads. But the way we interpret it is because normally when we look at a good quality mirror, we do not know that there is a mirror there. We actually see a continuation of that are being reflected behind, back behind the mirror. So what you're seeing then if we look behind the mirror is actually this triad, with the pencils oriented as shown here. And if we interpret it as being seen from behind, then, of course, left has become right, and vice versa. So another way to think about it is that when we look through a mirror, it is as if we're looking from the image from the back. So a better way to think about it is if you're looking at something that is written on my t-shirt. If you look at it from the mirror, it would appear as if I were hollow, and you would see the back of the writing on my t- shirt. And you all know that if you look at the ambulance sign in ambulance trucks, ambulance whatever you call them, cars. Because it is meant to be visible through the mirror of a driver, they actually write the sign backwards. So when you look at it, it is as if you saw a transparency of it from the back. So this is a simple consequence of the law of reflection. This is a very simple silly question that sometimes is asked. And it actually takes quite a long explanation to answer. And that question goes like this. If you look at the mirror, yes, we know that left and right flip, but up and down do not flip, right? You don't see yourself upside down in a flat mirror. You see yourself flipped from left to right. What is the reason? The reason is shown here. The reason is because of the flipping of the relationship between the left and right in the object side, as you interpret the projection of the rays that are coming from the opposite side of the mirror. So this requires a little bit of thinking, so I'll let you think about it. Unless you have a question now, please ask it. If not, you can think about it and come back with more questions on Wednesday. Is there any immediate question about this? That's kind of a subtle and elegant point. I should have brought a mirror with me. Piper, do you have a mirror over there? AUDIENCE: No, I don't have a mirror here. GEORGE No mirrors, OK. But everybody has access to mirrors, right? It's the one optical element that we can find very BARBASTATHIS:easily. So I'll let you practice with your mirror in your bathroom, and then come back and ask me questions. OK. AUDIENCE: I'm lying down. You're horizontal. GEORGE That's right. Our producer like this. The other thing I wanted to talk about is expand a little bit on the law of BARBASTATHIS:reflection. Oh, I'm sorry, the law of refraction that we derived last time. So the law of refraction is the last equation shown on this line. It says that this quantity, the index of refraction multiplied by the sign of the angle of incidence, where the angle of incidence is defined with respect to the normal to the surface. It is preserved. So as you go through multiple surfaces, the law of refraction says that this quantity must be preserved. So there is a common problem that I have posted just a couple of hours ago that asks you to make an analogy between the law of refraction, and the problem of a lifeguard who has to save a person in the water. So recall the reason the law of refraction happens is because the light must minimize its path between two points, P and P prime. So a very similar problem is if you have a trajectory that you're trying to design in a way that you minimize the time that you will spend going on this trajectory. So here, you have a swimmer who is sitting on the beach. I'm sorry, not a swimmer. You have a lifeguard sitting on the beach. And the lifeguard sees a person drowning in water farther behind. The lifeguard can run on the beach at some velocity, v sub r. They can also swim in water at some velocity v sub s. Most people swim slower than they run, so we can assume here that the running speed is faster than the swimming speed. And the question is how should the swimmer plan his path so that he can reach the drowning person as fast as possible? Again, you can think that, for example, the straight path is not the best because he's spending too much time in water. I mean, water, he's slower. So he may want to spend a little bit extra time in the fast middle, and a little bit less time in the slow medium. But, again, he cannot overdo it. If he goes a really crazy path, then, again, he will end up with a longer time. So light is trying to do a similar thing. It is time to optimize the obstacle path length, or equivalently, the time that it takes for the light ray to reach from a starting point to an ending point. And, again, remember this is almost an exact analogy here. The speed of light is faster in air, and slower in a dielectric medium. So if you had the air and glass here, that would be a very similar situation. I'm going to skip the next line. And I'm going to go to this one, to number 34. So what I'm trying to say here is to point out two cases. They're not really different. They're just two cases of the same situation. In one, you are going from a medium of lower index to a medium of hire index.
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