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Ray Diagrams for Concave Mirrors

Patrick Ford
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Hey, guys, in this video, we're gonna talk about Ray diagrams for con cave mirrors. Okay, let's get to it. You can see what happens toe light when it reflects off of a mirror by drawing what we refer to as ray diagrams, ray diagrams or diagrams that simply follow the law of reflection, which we've talked about before to show the path of these light rays as they reflect off the surface of these mirrors. Okay, before you can draw any ray diagrams, there's one important point on a raid diagram that you always need to find, which is known as the focus. It's the point where initially column mated Light converges after reflecting off of the mirror. So these blue light rays this is like coming in from the left that's column mated. Remember column Mated means all of the light rays are parallel. Okay, this column aided light then encounters the surface of this con cave mirror and that causes all of the light to bounce closer towards what we would call the central axis, which goes through the apex of our mirror, sometimes called the Vertex. Okay, now this light gets reflected towards the central access and it converges on a point right here, which we call the focus the point where the light is focused the distance from the apex, too. This point of focus is known as the focal length and is given by the letter F. Okay, now that we know what a focuses, when you are given the position of the focus, it's very easy to draw Ray diagrams to draw diagrams for con cave mirrors. You need to draw two of the following lines. Okay, one is a line parallel to the central axis that, when reflected off of the mirror passes through the focus. Okay, and that's exactly what we just saw. A line parallel to the central access by definition is reflected through the focus. If you draw a line through the focus, then it's when it's reflected off the mirror. It's parallel to the central access. Okay, this is also just geometry. If I scroll back up really quickly, just like we can follow a line this way and then end up going through the focus. If we follow a line through the focus, we end up reflecting off parallel to the central axis. Okay? It works. Both ways. Lastly, if you draw a line to the apex of the mirror, it reflects at the same incidents angle. And this is just the law of reflection, right? That if no matter where you are in relation to the mirror, you draw the line straight to the apex, it bounces off at the same incident angle. That's just the law of reflection. Okay, let's see this in action. When light comes off oven object. In this case, I drew a person. A mirror conform an image. This is something that we all know, right? You can look in the mirror. You could look in the spoon and a reflective surface, and you will see a reflection of yourself. That reflection is an image formed by the mirror. What we want to talk about is how this image is formed by the mirror. Okay. An image, by definition is a convergence of light. In order to find where light converges, we need to draw two lines two of those three possible ray diagram lines and find the point where they intersect. That will be the point where all of the light converges. Okay, so I'm going to use a protractor because I don't have a ruler and I need to draw these lines straight. So just bear with me, because this is going to take a moment. All right, so I have a ray coming off the head of the person and is going to be reflected off of the surface of this mirror. Whoops. This protractor is not working great for the position that it's in. So I'm gonna scroll up just a little bit, okay? And it hits the surface. Once it hits the surface. It is then reflected through the focus. Okay, That's the first of our three types of rays. Next, I'm just gonna draw the second one, which is through the focus to the edge of the mirror. Okay, straight through the focus to the edge and then parallel to the central axis. Coming off. Whoa. That was weird. That it changed at the end. You can see right here there is a convergence of light. Okay, that convergence of life is going to be an image. What's the image of the top of the head of this guy that I drew? I want to draw the image of a second part of this guy I want to do it for his hand. Right. So I'm gonna draw up the first line, which is going to be parallel to the central axis and then through the focus, All right. And then I'm gonna draw the second Ray, which is going to be through the focus and then parallel something like that. Okay, this is not exact, because I'm literally just using a protractor to draw straight lines on the screen. In order for rate diagrams to work, you would need graphing paper. Ah, protractor that you could actually use to find angles, rulers, etcetera. But basically, what's happening is right here is the image formed of his hand. And right here is the image formed of his head. So we can clearly see that the full image of the person is going to be upside down. In this case, the images inverted. Okay, the central axis for these ray diagrams, right? This right here provides that information really, really easily. If the convergence of the light is below the central axis, your image is going to be inverted. If the convergence of light is above the central axis, your image is gonna be upright. That way you don't have toe. Look, every time at two individual points on an object, you can look at one point and see. Does the light converge above the central axis or below the central axis? Okay, let's do an example. Where would an image be formed for an object at the focal point off a convict? Sorry. Concave mirror. So this guy sitting right on the focal point, we can still draw our same lines parallel to the central axis, then through the focus. Okay, the second line that I'm going to draw is going to be to the apex. Okay? The reason is is because I can't draw through the focus that would be straight down. So I'm gonna do the third line. Now I'm gonna draw through. Sorry to the apex. And then when it comes off the apex, it's gonna come off at the same angle that it entered something like this. Okay, now look, those to raise don't converge anywhere in this image so clearly, if they converge, it's gonna be way, way, way behind the guy. I want to see if they actually do ever converge. In order to test that, I have to compare these two angles, right? If Fada is larger than Fi, that means the blue line will be moving towards the red line and they'll converge eventually. But if I is the bigger angle, that means the red line is always moving away from the blue line and they never converge. So no image will be formed in order to test this or in order to find the relationship between those angles, I'm going to draw this as one triangle, and I'm going to draw this as another triangle. Okay, let me minimize myself for this. First of all, this angle right here is fine, right? That's the whole point off that third line. Whatever the incident angle is, that's the same as the reflected angle. So this is fine. But notice What's this leg right here? That's just f the focal length. How tall is this triangle H. What about for the Blue Triangle? How tall is it? H. However tall the guy is. What's this edge length Also the focal length. Look at this. These two triangles are identical, so theta equals five. This means no convergence, no intersection of the light anywhere, which means no image is formed. Okay, So if you have an object on the focal point for a con cave mirror, no image will ever be formed because the lines coming off the mirror, the rays coming off the mirror will always be parallel thes two angles. They're going to be equal. And those rays will always be parallel. So no image. Alright, guys, that wraps this up. Thanks for watching.