PhD., University of Maryland
Jonathan is a published author and recently completed a book on physics and applied mathematics.
Lenses are curved glasses or transparent materials. The focus of convex lenses is where rays parallel to principal axis go. The focus of the concave lenses is where rays parallel to principal come from. A converging lens looks fat in the middle. A diverging lens looks thin in the middle.
So let's talk about lenses, a lens is a curved piece of glass or some other transparent material that we're going to use to focus light and generate some images. So let's see how it goes, suppose that I've got an object out here in air and then I've got a piece of glass that's curved outward like this in a convex way. Alright we always with a lens have a principle axis if light comes in exactly along the principle axis it goes straight through the lens with no deflection whatsoever so that's the principle axis but most of the times if it's a lens it'll have 2 sides the principle axis needs to be perpendicular to both because light needs to go all the way through without being deflected. Alright let's see what some light rays coming from this object do. So we come in like that alright, now at the glass the light is going to refract in order to determine how it's going to refract we have to give ourselves a normal and then we say well this is a more crowded hallway than that so that means that the light is going to bend toward the normal.
Alright so that's fine, what about one that comes let's see what about one that comes down like this, well down here our normal looks like this. Remember the normal has to be perpendicular to the lens. So the light is going to bend toward the normal notice what happens the light beams are coming together so this is going to give us light rays that come together and hit somewhere along the principal axis it seems like. So the focus is the place where rays that come in parallel to the principal axis go. So this focus will be right over here, where this hits the principal axis. Alright so this is called converging, when I have convex glass light ray converge after they go through. Alright what happens if I've got a piece of glass that's like this concave well in this case we're going to do the same thing so let's go ahead and draw some light rays. Here's one it's going to come down like this alright and then again we need our normal. Our normal is that way and again we bend toward the normal just like this. Alright now notice this light ray is not going towards the principal axis so something different is going on.
Let's give ourselves a light ray that's parallel to the principal axis again I need a normal and I need to bend toward the normal like that so this guy is causing the light rays to diverge. So concave glass is called diverging alright because light rays come in and then they split apart. Alright now notice that this light ray appears to be coming from somewhere like there, that's called the focus of a diverging lens. So for convex the focus is the place where rays parallel to the principal go. For concave the focus is the place where rays parallel to the principal axis appear to be coming from. If I was looking on this side I would see the light coming like that and I would just continue that line straight back and that would be where the focus is. Alright, alright now let's say that we've got some real lenses and that mean they got to have 2 sides to them, right you're not just going to have a lens which consist of a piece of glass that goes on forever you just don't.
Alright so let's say that I've got a glass like this well the glass is convex on both sides. So that means that this side is converging, this side is converging and therefore this glass will be a converging lens alright. Well on this side the glass is concave and on the other side it's concave too. So both sides are concave that means that it's diverging on both sides, so this is a diverging lens alright what about here? So this were easy because there was convex, convex, concave, concave. What about here? On this side it's convex but on this side it's concave. I don't know so we've got convex or and then on this side concave so we need to know whether this lens will ultimately converge or diverge light. Here's the idea, this side is more curvy, this side is flatter it doesn't curve as much. Now if they would be completely flat then it wouldn't converge or diverge. So that means that in this case the concave side is not as strong as the convex side. So the 2 together are going to combine to make a converging lens. Alright and then let's look at the last one, the last again we've got converging and on this side we've got diverging or concave but which one is more curvy? Well in this one it's more curvy on the diverging side and that means that diverging wins and this will be a diverging lens.
Alright now it's really, really easy once we've seen these examples to do one in general because all we need to say is, is it converging or diverging? Well jeez is it fat in the middle or fat at the top? Fat in the middle or thin in the middle? If it's fat in the middle then it'll be a converging lens alright and what that will mean is that light converges at focus. Alright what about diverging? Well if it's thin in the middle then it's going to be a diverging lens and it's going to diverge the light. Alright now remember that with a diverging lens light that comes in parallel is going to come out and it's going to appear to come from the focus. And that's lenses.