 So let's explore the laws of reflection. The first law says that the incident ray, which is the ray that strikes the mirror, the normal, which is an imaginary perpendicular that you draw at that point, and the reflected ray. All three rays lie in the same plane. In this example, the plane is that of the blackboard. Now this rule is only useful if you're dealing in three dimensions, but we're not dealing in three dimensions, so it's not useful for us, so don't worry too much about this law. But the second rule, the second law, which is going to be important for us, that rule states that the angle of incidence, which is the angle between the incident ray and the normal, not this angle, but this angle, that will always equal the angle of reflection, the angle between the reflected ray and the normal. And what this means is that if you have a larger angle of reflection, angle of incidence, you will have a long, larger angle of reflection. If you have a smaller angle of incidence, smaller angle of reflection. And if the angle of incidence is zero, which means the ray of light is along the normal, then the angle of reflection will also be zero, the ray of light will go back along the normal, retracing its original path. Now let's apply this to carmeters to find the size, nature, and position of the image. So for example, imagine we have an object which is outside the center of curvature for a convex concave mirror. Where will its image be? How do we figure this out? Well, we can draw a few specific rays of light to help us out. The first ray of light we can draw is parallel to the principal axis. We know that this ray of light after reflection has to go through focus. Why? Because that's a definition of focus. It's the point through which all parallel rays of light after reflection goes through. So that's the first ray of light I can draw. Then I can draw a ray of light that goes through the focus. If parallel rays of light goes through the focus after reflection, then a ray of light goes through the focus after reflection will go parallel. It's just the opposite of that. And now by looking at these two reflected rays, you can see that these two reflected rays meet at these point. And so I know that the tip of the object's image has to be formed here. And I can draw the image. But before I do that, let me draw, let me show you a few other rays I can draw as well, a couple of more. Another ray I can draw is through the center of curvature. Now if a ray of light goes through the center of curvature, it is going along the normal. Remember that normal for a spherical mirror passes through the center of curvature. So this ray is along the normal. And we just saw that any ray of light goes in going along the normal gets reflected straight back. It retraces the path. And so now this itself becomes the reflected ray. And finally the fourth ray that we can draw is we can shoot a ray of light right at the pole. And then we know that the principal axis this time, which is passing through the center of curvature, that acts as the normal. And then we can ensure that the reflected angle has the same as the incident angle. And we can draw a reflected ray like this. And now you can see all the four reflected ray pass through the common point. They all meet at one single point. And that is where our image is going to be. And so we know now that the images between C and F, it's going to be diminished inverted. And inverted images are always real images. These can be captured on a screen. So we have solved our problem. Okay, consider a case where the object is kept between P and F. Why don't you pause and see if you can solve and figure out where the image is going to be. Okay, now I'm not going to draw all four rays. That's not necessary. Okay, again, one ray of light parallel to the principal axis goes through the focus. Now the second ray of light, where will I draw? I can't draw through the focus because I know it's not going to hit the mirror. I can't draw through the center of curvature because that's also not going to hit the mirror. So I'm going to directly draw the fourth ray, which is I'm going to shoot it right at the pole. This there becomes a normal. This is the angle of incidence and the angle of reflection has to be equal to the angle of reflection incidence. And then this becomes the reflected ray. And now these are the two reflected rays. Where do they meet? Notice they will not meet anywhere, which means I will not get an image on this side. So if I don't see them meeting this side, I will retrace them back and notice they do meet here, which means it appears that these two rays are coming from here. They're not really, but it appears like that. And so now the tip of the object's image is going to be over here. And so this is where the image is going to be. It's inside the mirror. The image is bigger than the object. And you can see the image is erect, which means it's a virtual image. Virtual meaning you cannot capture it on a screen. All erect images are virtual images. You can't capture them on a screen. Okay, one last case. You have an object in front of a convex mirror. Where will the image be? Again, try to draw all the four rays of light that we saw, which we drew for the concave mirror. Okay, let's do this. This might sound a little tricky, but let's do this. First way of light, I'm going to pass parallel to the principal axis. Where does it go? It doesn't go through the focus because this is a mirror and it can't go inside the mirror. Instead, it reflects as if it appears to come from the focus. Can you see that? It's very similar to what we drew earlier. Parallel rays of light reflects appearing to come from the focus. That's the first way. Next, I'm going to draw a ray of light that is aimed at the focus. If a ray of light is aimed at the focus, after reflection, it'll go parallel to the principal axis. Just like before, parallel goes just like before. If the incident ray is parallel, the reflected ray appears to come from the focus. And so if the incident ray is towards the focus, the reflected ray becomes parallel to the principal axis. These two rays are enough for me to figure out where the image is going to be, but I'm going to draw a few more rays. The next ray I'm going to draw is aiming at the center of curvature. Now I know that this is along the normal, which means the reflected ray will retrace its path. It'll go along the same path. And the fourth ray of light I can hit at the pole, making sure that the angle of incidence and the angle of reflection is exactly equal, and that gives me the reflected ray. And again, I have these four rays of light. And where will the image be? Notice all the four rays of light appear to be going away from each other, which means they're not going to meet anywhere. So I have to retrace them back. And if I retrace all of them back, look, they appear to be coming from one single point. So I know that the tip of this object's image is going to be somewhere over here. And therefore I'm going to get the image here. Notice it's inside the mirror between P and F. It is diminished smaller than the object and it is erect, which means it's a virtual image. It cannot be captured on a screen.