Virtual objects and virtual images are one of the concepts that always cause students trouble. They're actually quite simple, and once you get used to them, they won't cause you any problem at all. We're going to go through it fairly carefully here to make sure that you have this very important concept. Let's imagine that we have a positive lens, again, shown as our little double headed arrow. And let's place our object, less than one focal length away from that lens. So here is my object shown as a single headed arrow. And from the tip of this object, I'm going to launch a spherical wave. It's my field point. I'm going to use the same three rays that we just described with graphical ray tracing, again, illustrating why graphical ray tracing is a great thing. I'm going to shoot one ray right through the center of the lens. I'm going to shoot one ray parallel to the axis. It will go through a back focal point of the lens. And I'm going to shoot one ray that goes through the front focal point. And I actually have to go backwards to find that front focal point, but that's okay. And now, I just take my rule and I put it on this point, and the tip of my object and that's now the ray that comes out parallel to the axis. This concept of, we just shoot the rays backwards and forwards and we project them as needed, is part of the concept of virtual objects and images. So, what do I see over here on the image side of the lens now? I see a set of diverging rays, so those are never going to intersect. My object apparently, that's shown in my image, apparently, doesn't exist over here in image space. But if l was to look, if l put an eye ball over here, and looked back these way, l would see what apparently are a set up of rays emanating from right here. I project each of these rays backwards into object space, that's the dotted lines. These are not real light, there's not really light here, that's why I've dotted them. But it would appear to be the case if I looked from over here, that I'm seeing a spherical wave emanating from right here. So this is a virtual image. There's not actual light here, that's why it's virtual. And one of the ways to think about it as I put a piece of paper up, and I try to focus our camera piece of film. And I try to get all the photons to make a spot on that film, I can't do that, they're not actually here. I would actually have to put a second lens system, grab these rays, bend them back and re-focus them, and then I could put my film on my camera. So that's why it's virtual. Notice that my object distance is negative, and so I would, in this case, if I label the distance to the image, T prime, I would also label that as a negative number. This is going to be something we'll jump out of our simple equations for imaging, is that when we get a negative distance, we know that the image is to the left of the lens. And, therefore, it must be virtual because, again, I can't put a piece of film over here to left of the lens. So, in this case, I have a real object forming a virtual image from a positive lens. And I can do this with both positive and negative lenses. And you're going to want to understand, and we will in the homework, what lenses in what object configurations give you a virtual image. All right, let's flip it around. Now, I'm going to try to have a virtual object. So, what does a virtual object mean? It means it's on the wrong side. Instead of being over here in object space where any proper object would be, a real object, and now my object is in the image space. It's on the image side of the lens. What does that mean? Well, it simply means instead of there's a set of rays diverging from my object, there's a set of rays converging to my object. Which rays would I choose? Well, I am now a master of graphical ray tracing. I would chose rays one, two, and three. I would shoot one ray right through the center of the lens to this object point that I want to use. I would shoot a second ray through the front focal point of the lens, that's ray number two. Now, if I'm putting a ruler on here and imagine you just got a straight edge, I know now one of the points of my line, the other point. It's the top of my object that's why I have this little pointy bit, this little arrow on my objects, so I draw a ray right through here. Now, I know once that ray hits the lens, rule number two, it bends and goes parallel to the axis. So I draw on the list of the ray as dotted here. In the this rule, remember, is a ray that starts parallel to the axis, remember, that's ray number two. I can't remember, but rules two and three are pretty much the same. If we have a ray that's parallel to the axes upfront, when it hits the lens, it bends and goes through the back focal point. So, what ray I want to draw? It would be the one that would be parallel to the axis. And if the lens wasn't there, it wouldn't intersected the top of my object. That's why I'm drawing this part dotted because instead, it actually bends and goes down through back focal point. Notice the magical thing that happens is those three rays converge and make a real image. So another way of saying this, is if I built a converging spherical wave that's converging to this point here. And then I drop this lens in the way, the converging spherical wave converges even faster, more strongly. And instead of coming to a focus, all the rays coming together at this object point, they come together even faster, even shorter distance away, and they come together all here at this image point. So this is an imaging system, just like we had before. But now, the object is virtual and we make a real image. And you might guess, you can make all possible combinations of this. This is an example of how you'll actually use this things. There might have been an earlier system up here, some lens system. And it was creating, from the perspective of that earlier lens system, an image here. But now, we've dropped one more lens here, like your eyeball, for example, and this is your cornea. And that takes this what was going to be an image of the earlier system. And now, it treats that as a virtual object and re-images the light to somewhere else. So this is the concept of cascading optical systems. And it tells you how you can generate these virtual objects, or why virtual images can be useful. So to summarize, Images and objects can be either real or virtual. You can easily tell if either one of them are virtual, is if you can't put a screen or a piece of film at that plane, and have photons actually show up there and going backwards, again. Once I put this lens in the system, I can no longer put some film here and find photons converging, because they're here now, right? So they're not really there, they just appear to be converging towards that point. Another way of thinking about what makes an image virtual is if you need another lens to once again make the image real. Here, we have something that we can think of is a virtual object, and I use this lens to make a real image of it. Equivalently, virtual objects and virtual images are on the wrong side of the lens. Objects are to the right of the lens, images are to the left of the lens if they're virtual and, again, you can see that here. This object is on the improper side, it's object on the image side of a lens. So think about this carefully, this is a super important concept. Because it turns out, as we trace through complex lens systems, we can have virtual and real images and objects all the time.