As engineers, we want to be able to do more than just do calculations to design a lens, to calculate where an image or an object needs to be in a system. We need to have some intuition in order to be able to design more complicated systems. Ultimately, we'd like to be able to draw basic design on a piece of paper before we do in-depth calculations. We'd like to be able to go to a meeting and approve or reject ideas based on what we know about how lenses form images and affect light as they travel through them, instead of spending a week on calculations to discover an idea that's not going to work. So, one way we can do this is to play around a little bit with these online simulations from PhET. And since this is interactive video, so go ahead and open up the phet.colorado.edu website and we'll go ahead and play around with some of the things we can do on it. So, once we're on the PhET website, we want to play with the simulations. And there's a large number of different simulations here. We're going to choose Physics, Light and Radiation and the Geometric Optics simulation. And I'm going to go ahead and play that. So, this simulation has a lens, it has an object. It says move me, so I can know I can move that up and down. And I can move that around. It also has options for looking at rays. I can take all the rays out. I can sort of guess what's going to happen here. I can use the marginal rays. Those are the rays that go through the edges of the lens and the center of the lens. I can use the principal rays. Those are the rays that we talk about with our ray diagrams. This is a ray that travels parallel to the optical axis. A ray that travels through the center of the lens and another ray that travels through the front focal plane of the lens. I can use many rays and I can see which ones are captured by the lens.Let me use the principal rays for right now. I can also look at a second point on my object and look at how two different things form images. I can change the properties of the lens itself, the refractive index, the radius of curvature and the diameter. And there are some other things over here, you can change the object, use smiley face for fun. I can make it so that it'll show me when I have a virtual image. If you want to switch from object to a light source with the screen, now you can move the screen as well. There's a couple of different things that you can play around with here. You can use a ruler if you want to do some measurements. Obviously I'd like you to do is to just move things around. You can move the lens itself, you can move the object. So, move this around then look at what happens when we move the object closer to the focal plane, farther away, and see if you can figure out if there's any circumstances under which I get a virtual image with this positive focal length lens. Okay, now that we've played around a little bit, I see that if I take my object and I move it farther away from the lens, that my image becomes smaller and moves closer to the back focal plane. As I move towards the focus, the focal plane, the front focus of the lens, my image gets larger and gets further and further away. Now it's moving off the screen. If I get right at focal plane, I get the computer to get a little confused. But if I come inside the focal plane, I now have a virtual image. And these green lines here are showing, I have light over here that does not form an image on the back side of the lens, but I have a virtual image. We can see if we follow these rays back, and I have this back here. So I can form a virtual image with this positive lens. And as I move this around, I can see what happens to the image. I now have an upright image. Now I have it flipped, negative magnification on this side of the focal length. So, you can play around and get some ideas. I move this up, the image goes in the opposite direction on the other side of the lens. Next thing that I want to take a look at, is what happens when we change the lens properties themselves. So, go on and play around that a little bit. What happens when you change the curvature radius, the radius of curvature of this glass, the refractive index of the glass and the diameter of the lens? All right, let's see what happens when we do that. I'm going to move this in a little bit, out a little bit sorry. I'm going to move my image in a little bit. I'm going to take my radius of curvature and make it very small. So, my focal length becomes shorter and shorter and shorter and that correspondingly affects my image formation. As I make the radius of curvature of that lens larger, so not as curved, my focal point goes out, focal length, and my image is formed accordingly with that new focal point, the new focal length. So this changes the focal length of my lens. How about the refractive index, does that make the refractive index really, really small? My focal length becomes very, very large. As I make the refractive index very, very large, my focal length becomes much, much smaller. So, higher refractive index and lower radius of curvature decrease my focal length. And as I make a large radius of curvature or a lower refractive index, we're getting a much larger focal length. Let's put those above average again, we're about where we started. Now, what happens when I change the diameter of my lens? The image is still in the same place. I haven't changed the focal length of this lens. What is happening to the image? The image here as I make the diameter of the lens smaller. Let's look at many rays now just for fun. As I make it smaller, this becomes pale, less of an image. There's is less light being used to form that image. And as I make the diameter larger, I get more of the light from the object is used in forming the image and so it becomes brighter. And so that's going to affect, the diameter of my lens is not going to affect where the image forms, but it is going to affect how much light is used to form the image, assuming that everything else remains constant. So here's another test. What if I wanted to use my positive lens as a magnifying glass? Where should I put the object and what is my image going to look like? All right, if I want a magnifying glass, I want my image to be larger than my object. So, here it's larger than my object, and I've got an image out here that I could put on the screen and I can look at that with my eye though it's upside down. Often time with the magnifying glass I'd like the image to be right side up. So, what if I keep moving this in closer to the lens? Well, now I have a virtual image that's much larger than my object was originally. But there's no actual image over here. I just have rays coming up. Well, my eye which is a fabulous lens, will take these rays and form an image. So I do have another lens in my optical system when I am using a magnifying glass. I have my eye. And so if I put an object inside the focal length of a positive lens, I will see a magnification of the object on the other side of the lens, because my eye will form an image so that I can see that. Then I will get an image that looks upright of a positive magnification and it'll be having magnification of greater than one. It will be larger than the original object. This is how we use a magnifying glass. And depending on where I put the object, and here normally when I'm doing it, I move the lens depending on where I move the lens with respect to that object, I can change the magnification of that object that I'm looking at. So, this is just a way to play around with things a little bit in a quick way and get some intuition on how images are being formed with objects, and how rays travel through lenses, and what types of things in my system, my object distance, my image distance, my lens characteristics, how those affect how my image is going to be formed. So, play around a little bit more and see what other things you can make happen with this. This will help you develop some intuition as then we move on to more complicated systems with more lenses and mirrors in the future.