Ray Diagrams For Mirrors

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.

Hey, guys, In this video, we're gonna talk about Ray diagrams for convex mirrors. We already saw them for con cave mirrors. Now we want to see what they look like for the opposite shaped mirrors. All right, let's get to it. While a con cave mirror converges light as we saw when initially column ated light enters a con cave mirror It all comes closer together. Ah, convex mirror will diverge light When light reflects off of a convex mirror, it spreads apart. It doesn't come closer together. That means that the light will never focus. Okay, I cannot emphasize this enough off of a convex mirror. You will never, ever get convergence of light. It will always be divergent. However, if you were looking at this light because your brain is stupid for some reason, you on li see lines. You only see light as traveling in a straight line. So to your brains this line this ray and this ray and this ray this ray this ray and this ray all appear toe have come from a point where they focused. This is known as an apparent focus. There is an apparent focusing of light or an apparent convergence and your brain cannot tell the difference. Okay, so when you look at light coming off of this convex mirror, it appears tohave focused at this point. Okay, this focus, while it's not riel, is often simply referred to as the focus anyway, even though it's technically an apparent focus. And we can define a focal length just like we did before, which is the distance from the apex, too. The apparent focus. Okay, now, to draw Ray diagrams for convex mirrors once again, you need to draw two of the three lines. Thes rules are basically the same, but slightly different because the focus is on the other side of the mirror. So a lot a lion draw a parallel to the axis is then reflected off of the mirror away from the focus. Okay. Ah, line towards the focus is it reflects off of the mirror, parallel to the central axis and finally aligned to the apex of the mirror is reflected at the same incident angle. So the third line is the same. The third rule for Ray diagrams is the same. The first two are very similar, but slightly different in how you apply them because the focus is on the opposite side of the mirror. Let's see what I mean. I'm gonna minimize myself. So we have an unobstructed view of this image when light comes off oven object a convex American also form an image, which is what we're about to see. I cannot stress this enough, Though this image is not actually a really image. It's not really, because light never convergence. Let's see what I mean by this. I'm gonna draw the first type of Ray, which is gonna be parallel to the central axis and then reflected off of the mirror in the direction away from the focus. So you see that green line? The reflected Ray follows that green line as if it was leaving the focus. Okay, now the second line goes towards the focus. Okay, If I were to continue this, it would look like it was going towards the focus. I don't wanna have that right now. Okay? But that's what I mean by towards the focus. And then it's reflected off of the mirror parallel to the central axis. But notice something when you see this Ray, it appears tohave come straight across from the other side of the mirror, right? So there appears to be a focus. There is an apparent image. This image is not riel. This image is not there because the light never actually converge, is there? But it sure does appear to our brains like it's there now. I'm going to draw how we always draw images as just being an arrow that points from the central access to the focus. So this would be upright because it's above the horizontal axis. Okay, since this light appears to converge to our brains, this looks identical to any other image. This is known as a virtual image or an apparent image. It's not riel. It's just virtual. And in this case, the images upright right, The apparent focus point. The apparent convergence of light occurs above the central axis. So the images upright. OK, but these images air. Not really. They are virtual images, but to our eyes they appear to be riel. Okay, let's do a quick example. Where would the image reformed for an object of focal length away from the surface of a convex mirror? So I'm just gonna use the first Ray diagram. The first Ray which is parallel to the central axis. Okay? And then directed away from the focus. Okay, lets whenever you are drawing these lines, you need to continue them on the other side like this. So you know where the light appears to have intersected. The second one is towards the focus and then off of the mirror, parallel to the central axis. So that's towards the focus and then off of the mirror, parallel to the central axis. Whoops. I need to complete this. So you see, right here we have an A parents convergence of light, which is known as a virtual image, and it will appear inside off the focus of the convex mirror. Okay, that wraps up this discussion on ray diagrams for convex mirrors. Thanks for watching guys.

Hey, guys. So far we've done convex mirrors and we've done concave mirrors. But now the final type of mirror plane mirrors, not plane, is in simple but P L. A. And E plane is in flat. Okay, these are the types of mirrors that you would hang on your wall. These are your bathroom mirrors, etcetera. So, by far the most popular kind of mirror. All right, let's get to it. Column mated. Light coming off of a plane mirror doesn't converge or diverge, right? The law of Reflection says that if you're hitting a flat surface perpendicular to that surface, you bounce off at the same angle. Right? So all the blue raise those initially column mated. Rays of light all bounce off colonnaded. Okay, the light doesn't converge or diverge. That means that there's no focus for a plane mirror, not on the front side of it, and not an apparent focus on the back side of it. Sometimes just for equations, which will cover in the future just to make those equations work, the focal length of a plane mirror is said to be infinity. It said that infinitely far away hypothetically, those lines could converge okay. It's just a mathematical tool to make equations that we'll see in a little bit work better. Okay. To draw raise diagrams for plain mirrors, we need to draw two of the following lines. Okay, there are two types of line, but the second line is actually a new infinite number. Now get to that in a second number one, a line parallel to the central axis, then reflected off of the mirror parallel to the central axis. Right. And that's exactly what I showed in the image above. If you come in parallel to the central axis, you leave parallel to the central axis, and then any line from anywhere to any points on the mirror that's reflected at the same incidents angle okay for convex and concave mirrors. The second point was on Lee, true for lines that went to the apex, but for plain mirrors because they're flat everywhere, not just at the apex. This applies to any line drawn at any point on the surface. Let's do an example. A 1.6 m tall person stands 0.7 m away from a plane mirror. How tall does the person appear in the mirror? How far from the mirror. Does the image appear? Is this image really or virtual so just a whole bunch of information about the image that they want to know. So let's draw our lines first. Parallel, and this is gonna return parallel. So this one is a rounded trip. It goes both ways. What this also means, though, is when it's coming back to you, it appears as if it came off the other side of the mirror parallel. Right now, what I'm gonna do next is I'm going to draw a line from the head toe halfway down the body, because then it's gonna reflect at a 45 degree angle and reach the feet. Okay, so from the head, I could choose any point on the mirror, and it will reflect at the same angle that it hits. But I'm strategically choosing toe. Have it reflect at a point halfway down the person's body. Okay, okay. And so I need to draw where this line appears to come from and you can see right away there is an apparent convergence of light. So there is an image here, right? What type of image is it? A real image Or is it a virtual image? This is absolutely a virtual image. Okay, this is not really because light is not actually converging on that point. It only appears to converge on that point. Furthermore, the Onley types of mirrors that can produce riel images are mirrors that can actually converge light, which air con cave mirrors. Convex mirrors diverge light so they can never form a real image. And plain mirrors don't converge or diverge. But since they don't converge, they cannot form a real image either. What's the height of this image? Well, look at this particular green line. It's at the same height as the person. So the height of the image is just 16 m. Now, the question is, how far away is this? Well, this angle is actually going to be the same as this angle. Okay, These two triangles are identical triangles. That means that this distance has to be the same. Okay, so you're gonna find that whenever a knob jek tis in front of the plane mirror, that mirror produces a virtual image off the same height as the object upright and the same distance behind the mirror that the object exists in front of the mirror. Okay, This wraps up our discussion on Ray diagrams for playing mirrors. Thanks for watching guys.