13.7 Lenses

Ok, today we're gonna look at how to do lens questions. The good news with lenses is that the formulas still work the exact same way, and the concepts of drawing them in and figuring out how to solve lens questions work exactly the same as with mirrors. Just with a few slight tweaks and tips that you need to remember. So, keep in mind that a lens basically is just some sort of clear glass or plastic (or something) that has a higher index of refraction. What that means is, instead of reflecting like a concave mirror, where the light ray comes in and reflects outwards at the same angle, with lenses it works differently. It's refraction. The light ray comes in and then it's going to refract through the lens, instead of reflecting off the mirror. But, other than that, it works pretty much the same way. The first thing you have to understand is what type of lens are we dealing with. So, a converging lens then is a lens that bulges outwards on both sides, so it's a convex lens. So, a double convex is the one that we typically draw and use, but you can see that we could have it just flat on one side or it could even be slightly curved as long as the inside is thicker than the outside. Then we'd say it would be a convex lens. So, a convex lens is converging. If you remember, for a convex lens, converging Mir was a concave mirror. So, a concave mirror and a convex lens basically do the same thing - they both converge. And then the reverse is also true. If we have a diverging lens, which would be a concave lens where the inside is thinner than the outside, that would do the exact same thing as a convex NIR, so a diverging lens is concave and a convex mirror. Those two sort of work the same. And concave and convex lenses work the same. So that's the first thing you need to remember, is sort of keep track that they work. And the way I usually remember is if I look at a backside. So let's suppose we have some sort of object and it's in front of a concave lens. What I do is I think of it as what is the back side of the lens. So the back side of the lens, compared to the object, is convex. So the back side of the lens works just like the same type of mirror. So what we're drawing, these in terms of drawing the diagrams, would basically do the exact same thing. And what we do is we only worry about the center of the lens. We don't have to worry about the actual rest of it, so we basically do the same thing. So, if we have our object, let's see if our object is there. Rule one: we went for mirrors, we went through the focus and it bounced back parallel. So, we go through the focus again, but now instead of bouncing back, it's going to refract through the lens. It goes through the lens parallel, through the focus, and then through the lens parallel. Rule two is the opposite: if we go parallel to the lens, it'll refract and go through the focus point. And then you can see where these two lines intersect, that is where our image is. Rule number three for mirrors: if I went through the center of the curvature of the mirror. So, in this case, what we do is we go through the center of the mirror, our center belen. If we go right through the very center of a lens, the line will just keep going straight because we won't get any kind of refraction. So, you can see all three of those lines, all three the rules line. Up to the same place, and we get our image. So, in this case, we would say that because of the lens, we want the light to go through and refract through. So we'd still call this a real image, even though it went through the lens. So that's different, remember with a mirror it's on the front side of the mirror, it's real. If it's on the back side, it's virtual. So that's opposite. Through the lens would be real, and we say it's still inverted. And in this case, it's larger. Now let's look at a diverging lens. So, in this case, our object is in front again. So we're gonna do the parallel rule first. So parallel, and it's gonna diverge or spread out. So we extend that back with a dotted line through the focus to those the line up. And then if we do the center rule, that's part of the next best one. So if we do it where it goes through the center, straight through, I'm a little bit off but you get the idea. So, our image would end up ready to vote there. With this diagram, there's the center one. You can see our little image shows up right there. So, in this case, because it didn't go through the lens, we'd say it's a virtual image and it's right side up or erect. In this case, it is smaller. Okay, so this is how typical glasses work. Most people that are nearsighted have glasses that are like this. So, what it does is the image that's formed is a virtual image, right-side up, but a little bit smaller. When we're using formulas, we do the exact same thing. The only difference is we just have to be careful of the positive or the negatives again. So, a converging lens, remember, is a convex lens. So, we say our F is positive, and things that are on the other sides. Our object is in front, our image is on the other side. We call that... [Music] Positive, so you want to think of it as if it goes through the lens. That's positive. So our diverging lens was a concave one, and this is one where our object stayed on the front side. So we'd say it has a negative focus. So once again, feeding back to the back side, it's the back side of this one. Would it be a positive focus? The back side of this one would have our negative focus. And then the same thing, our image doesn't go through the lens, so we call it the virtual, which would be negative. So that's the only thing that's different from yours. So let's do this question. We have 1/f = 1/do + 1/di. They tell us it's a converging lens, so that's going to be good. So that means we have a positive F. We have 1/0.22 and the object is 0.41 in front, so that'll be... 0.41, and if we're asking what the distance is going to be after it goes refracted through the lens, we would have 1 over di. So in our calculator, all we have to do is go 1 divided by 0.22 and minus 1 divided by 0.41. That gives us 2.1. And if we go 1 divided by that answer to get the reciprocal, we get a di of 0.47. Because it's positive, remember it's going to be on the other side of the lens. 0.47 meters would be our final answer characteristics. Because I went through the lens, we'd say real. And we could figure out the height, and they would end up giving us a negative. So we could do that second part of the calculation if... We want the high hole over Dido, and we could plug that in if we knew what the original height was. But we don't. What we do know is that it's going to be a real image, and it can likely be upside down and bigger or smaller depending on the distances involved. That's it. So you can see that pretty much the same thing happens as with mirrors; you just have to remember a few differences. I think of it as the backside of the lens, and I think of it being upside down, right side up, and so on. And that's all.