 Welcome. I wanted to go through the ray diagrams that we can make with a curved mirror and we're going to take a look at every scenario we can get with a concave or a convex mirror here today. You can make any ray diagram basically out of just two rays for a concave or a convex mirror. The first ray I'm going to do in red today and it is always going to start off from my object, in this case my object is an arrow, parallel to this line called the principal axis that's running along here. And then after it hits the mirror, it's going to go back through the focal point. The focal point is the point where all the light converges in one of these mirrors and it's half of the distance from the center of curvature, which is like the center of the circle this mirror would make if you were to go and extend it into a circle, from the center of curvature to the mirror, half that distance is the focal point. These are my first ray, my second ray I'm going to do in blue, first goes through the focal point, then it hits the mirror, and then it comes back parallel. So it looks a little something like that. Now where's your image? Your image is formed where the two rays overlap and so there it is. It is smaller, so we say it's diminished. It's upside down, so we say it's inverted. It's position is between C and F. It's between C, center of curvature and F, the focal point, and we call this a real image. And you're going to see why we call it a real image in a moment when we see the opposite of a real image, a virtual image. That was so much fun, let's try it again. Now I've moved my object so it was right at the center of curvature. Let's see what happens now. Parallel through the focal point, through the focal point, parallel. Look at that, I think it's going to line right up. It does. What we get here is an image which is inverted, but it is exactly the same size as the object, and it is at the same position as the object at the center of curvature. It's also a real image. That's basically the same as the last one we did, it just happened to be at C. Why don't we take a look at the next one. What if we put the image or the object between C and F? Now we're going to notice a little difference, although it's pretty much the same. Parallel through the focal point, and the blue one goes through the focal point first, and then runs parallel. Now you're noticing here that we're going to get our image way to the left here, somewhere past C is what the position is. It is inverted upside down, it is enlarged, I think it's a little higher in terms of its height, it's a little bigger than the original was, and it's a real image as well. Now we get to one I think that is quite interesting. What if we put it right on the focal point? What if we put the object right in the focal point? Well the first ray you do wouldn't really look any different, same as we've always done. The second one though would give you some trouble. You want to go from the top of the arrow through the focal point and then hit the mirror. I'm sorry that ain't going to happen, it's not possible. And so you don't get an image when the object is at the focal point of a concave mirror. It just doesn't work out. If you look at the math you notice you're going to get an asymptote or an undefined value at this point in the math as well. Okay so that's kind of neat. What if we put it in front of the focal point? That's our last scenario for concave mirrors. So this is going to be a little interesting too. We're going to go parallel and then we're going to go through the focal point. Okay that wasn't interesting, that's the same as we've always done. Now the next one is going to try to go through the focal point and then it's going to go parallel. Okay so that's, that was a horrible one. Let's see if I can do that a little better. Okay that's not bad. Now problem, these two rays that I drew, they're never going to touch. They're diverging, they're moving apart, they're not coming together. So what we need to do is we need to extend these as virtual rays. What we're going to do is we're going to take the reflected rays and then just keep drawing them back on the other side of the mirror. So for my red one, this was the reflected ray right here. I'm going to keep the same angle and I'm going to just extend it back. And for my blue one, I went through the focal point, the parallel one was the reflected one. I'm just going to extend that back. And the point where those two reflected virtual extended rays meet is where your image is going to be. This image is erect, it's right side up, it's enlarged, it's a little bigger than the original one. It's behind the mirror and that makes it virtual. In a mirror any time you have the image formed behind the mirror, it's virtual. And also you have it formed as a virtual image because it's made of these virtual extended rays. Now one last scenario we need to look at and that scenario is for our convex mirror. In your convex mirror, your focal point, your center of curvature is on the other side of the mirror, like the not shiny side of the mirror. And our image is on the shiny side of the mirror. Now how are these rays going to go? Pretty much the same. It's going to start off going parallel, parallel. And then it is going to reflect in a way so that it would go through the focal point if that mirror wasn't there. So it's going to reflect back like that. So it would go through the focal point if the mirror wasn't there. The second one is going to aim at the focal point. So it's going to sort of try to go to the focal point. But unfortunately that mirror is going to be in the way and then it will go back parallel like that. Now again you probably know what's going to happen here. Those two rays I drew, the real ones are never going to meet. So I'm going to have to go through and extend those as virtual rays. I'll do the blue one first because I got blue out. So the reflected one is the one I extend. And I'm going to extend this reflected one as well. Alright, kind of looks like that about the same angle. It actually should have, I can do a little better than that. I should have tried to go through that focal point. There we go. And here is my image. It is diminished, it's erect, it's behind the mirror, and of course that's going to make it virtual. And that's every scenario you can see with a curved mirror. For more information on this topic, for questions to practice, information on the math that goes along with this, you can visit my website, ldindustries.ca.