Hey guys, in this video we're going to talk about ray diagrams for concave mirrors. Okay, let's get to it. You can see what happens to light when it reflects off of a mirror by drawing what we refer to as ray diagrams. Ray diagrams are 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 ray diagram that you always need to find which is known as the focus. It's the point where initially collimated light converges after reflecting off the mirror. So these blue light rays, this is light coming in from the left that is collimated. Remember, collimated means all of the light rays are parallel. Okay? This collimated light then encounters the surface of this concave 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 axis and it converges on a point right here which we call the focus, the point where the light is focused. The distance is the focal length and is given by the letter f. Okay? Now that we know what a focus is, when you are given the position of the focus, it's very easy to draw ray diagrams. To draw ray diagrams for concave mirrors, you need to draw 2 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 axis 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 axis. 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 incident 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 an object, in this case I drew a person, a mirror can form an image. This is something that we all know. Right? You can look in a mirror, you can look in the spoon, any 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 2 lines, 2 of those 3 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 gonna 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 gonna take a moment. Alright, 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. This protractor is not working great for the position that it's in so I'm going to 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. Wow. That was weird that it changed at the end. Okay. You can see right here there is a convergence of light. Okay? That convergence of light 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 out the first line, which is going to be parallel to the central axis and then through the focus. Alright? 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 actually used to find angles, rulers, etc. 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 image is inverted. Okay? The central axis for these ray diagrams, right, this right here, provides that information really easily. If the convergence of the light is below the central axis your image is gonna be inverted. If the convergence of light is above the central axis your image is gonna be upright. That way you don't have to look every time at 2 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 of a concave mirror? So this guy is 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 3rd line now and I'm gonna draw through, sorry, to the apex. And then when it comes off the apex it's going to come off at the same angle that it entered. Something like this. Okay? Now look, those 2 rays don't converge anywhere in this image. So clearly if they converge it's going to be way way way behind the guy. I want to see if they actually do ever converge. Order to test that I have to compare these two angles. Right? If theta is larger than phi, that means the blue line will be moving towards the red line and they'll converge eventually. But if phi 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 gonna draw this as one triangle, And I'm gonna draw this as another triangle. Okay, let me minimize myself for this. First of all, this angle right here is phi, right? That's the whole point of that third line. Whatever the incident angle is that's the same as the reflected angle so this is phi. But notice what's this angle? This is theta. 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 phi. 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 concave mirror, no image will ever be formed because the lines coming off the mirror, the rays coming off the mirror, will always be parallel. These two angles are going to be equal and those rays will always be parallel, so no image. Alright guys. That wraps this up. Thanks for watching.