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Anderson Video - Image Formation with Spherical Mirrors

Professor Anderson
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 So let's draw an optic axis. And let's put our spherical mirror right there. And now let's take an object and we'll put the object right there. The spherical mirror, of course, has a focal point. If the center is there for the spherical mirror, then the focal point is somewhere around there. We'll label that F. When we think about the rays coming off of our object we know that rays come off in all directions. But there's a few that we're very interested in. One of those is the following. There will be a ray of light from the object that goes parallel to the optical axis. Okay, it's going to come towards the mirror parallel. When it bounces off the mirror it's going to go through the focal point. Okay, and it'll just keep going on out. Alright, so that's a very important one. The second one is rays going through that focus are going to come out parallel. And there's one more point, which is the following. If the center is there then rays that come through the center just keep going, bounce off the mirror, and come back on themselves. Okay, let's label those three rays. This is ray number one. This is ray number two. And this is ray number three. And let's see if we can identify the rules that we just wrote down for those three rays. So ray number one is the following. Parallel ray goes through the focus. And that's exactly what we drew. There was a ray that came in parallel it bounced off the mirror, and it went through the focus. What about number two? Number two is really just number one in reverse. Rays through the focus go parallel. Alright, number two was this one that came right here. It went through the focal point, bounced off the mirror, and then went parallel back. And the final rule is this ray number three. Rays through the center do not bend. Okay, this is image formation. And these three rules are important to understand because they not only apply to mirrors they are going to apply to lenses, once we start talking about lenses. So, where is the image in this picture? The image is where the rays all meet. They started there at the tip of the object they went out in all these different directions and then they came back together right there. So that's where the tip of the object is. The base of the object is on the optic axis. Okay, so this is a nice way to draw it. When you draw the object and you put it on the base of the optic axis, its image still has its base on the optic axis. And so all you really need to figure out is, "where's the tip of the image?" Okay? And so this is the final point. Image is where they meet. Now, when we have image formation like this you have to classify it as either a real image or an imaginary image, a virtual image. Images are real when real rays meet up. Okay? In other words, could I put a piece of paper there and form an image on it because real rays are coming to meet up with it? Yes. Those three converging rays all meet right there. Virtual image is when the dashed line rays meet up. And that means you can't form that image on a piece of paper. So when we were doing the flat mirror we said where's the image? It's on the other side, but remember those dashed lines that went to form that image? That means it's a virtual image. There's no real light that got there. All the real lights stayed on this side of the mirror. In this case, there is real light that went to form the tip of that image. It said the following. an object is placed two meters away from a concave mirror of focal length 1 meter. So mirror to focus is 1 meter. But the object is placed 2 meters away. Which is interesting. That would put us right at the position C. Remember, F is half of the radius of curvature. C is the full radius of curvature. So that's where the object would be. Where is the image? Okay, and is it bigger? Smaller? Real? Virtual? Let's see if we can follow our lens rules and figure out exactly where it should be. All right, rule number one. Parallel rays go through the focus. Okay, here comes a parallel ray. It goes through the focus. Okay? Rule number two. Rays through the focus go parallel. All right? And rule number three is rays through the center don't bend. Well,I guess a ray through the center would be straight down on itself. That would be ray number three. So let's label those and make sure everybody's on the same page. This is ray number one. This is ray number two. And this is ray number three. And now where is the image? It's where they meet. That's where they meet. The image looks to be exactly the same size as the object. Here's our object, here's our image. Okay, so it's also real because there are real rays coming to form it. And it is inverted, which just means upside down. And so the answer is C, of course. Real and same size. Okay. Excellent