# Lenses

by Jared Rovny

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00:01 Now we’re ready to discuss lenses. Lenses will follow many of the same properties or the same logic that we had when we were discussing mirrors. For a lens, again you can have something that is concave or convex but there’s actually a different sort of terminology. Sometimes we call this concave lens a diverging lens because as the light goes into it, it gets dispersed in many different directions. Then we call the convex lens, the outward lens, the converging lens because as light goes into it, it converges towards some point. We could think of a lens as being again, part of a circle where instead of just one circle, we have a circle for each side of the lens. Each lens also has a focal point.

00:43 We’ll be considering thin lenses so that we don’t have to worry about the effects of the light as it goes through the lens and bends with refraction each time. For a thin lens like this one, again, we also have a focal point which we’ll discuss more in a moment. We also have a center of the curvature, if we again drew for ourselves that circle that we already showed.

01:03 Then, we could follow the same logic for putting some object again just some arrows, so that we have some orientation to talk about on one side of the lens and seeing where the corresponding image would appear on the other side of the lens. The two rays we’ll draw from the arrow, in this case are very similar to the ones from the mirror. We have one going right through the focal point.

01:22 That one, after hitting the lens will leave parallel to the lens. The other ray that we’ve drawn will be parallel to the axis. Then on the other side of the lens, rather than reflecting, it will go through the lens and pass through the focal point on the opposite side of the lens. The second ray after it’s gone through the lens itself and passing the second focal point will meet up with the first ray that we drew which went through the focal point and then left parallel. Then we have the new image distance that we perceived for this particular lens. Again, this follows the same logic.

01:57 If I were on the other side of this lens where I would see the two rays coming out from this whole procedure, I would think that those two rays were coming from some point that they weren’t actually coming from because I wouldn’t be able to process that they might have bent on their way to my eyes.

02:11 So, I would perceive this image, this image that’s on the right of the lens. For a diverging lens, we have something slightly different. We first draw a parallel ray to the axis and then say that that ray diverges directly away from the near focal point. For the other ray, we would draw towards the far focal point. It would refract to be parallel to the axis. You can see in this case, we’re always following the same sort of logic. We have a first ray and a second ray, one of which is trying to be parallel to the axis and the other one is trying to go towards a focus.

02:45 We can always see how the focus and the parallel nature of the rays is playing back and forth to find where the rays will go. Again, we’ll do the same logic for finding the image, where the image would be and what the image would look like. We take the final point of those two rays. We ask ourselves the one question that we keep bringing up which is where would my eye perceive these rays to have come from? We just trace those two rays back until they finally meet. In this case, we can see that the image which is where the rays will meet is going to be found on the near side of this lens. We would perceive a smaller image of our object. As a summary for what we’ve talked about with lenses, if we have parallel rays coming in from an object that is sort of at an infinite distance, if you will, the rays will all converge to some focal point. If we have an object that is near the lens but still outside of the focal point, we end up with an inverted real object. If our object is on the focal point, we’ll have the same problem of each beam leaving at a parallel, in a parallel path so they’ll never meet. Then finally, for an object inside the focal point, we could trace our rays in the same way that we’ve been doing, one going straight towards the lens, parallel, and then going through the final focal point, the other one going directly away from the near focal point and leaving parallel. Then, we could trace these two rays back. Again, we would find an upright, virtual image. For diverging lens, we have the same sort of idea that we had for a convex mirror which is that the rays impinging from an object for a diverging lens are always going to cause the same sort of thing to occur rather than having many options. For any object anywhere near a diverging lens, we can draw one ray parallel which will leave away from the focal point, one directly towards the opposite focal point which will leave parallel. Then all of these cases will always end up with an upright, virtual image. For the locations of the objects that we’ve discussed, we’re going to go back to this little letter o and try to figure out some things about the locations.

04:54 Again, for lenses just as for mirrors, we can define a location o for our object, a location i for our image, and then a location for our focus. Again, we’ll call that f. We have the exact same equation that we had for mirrors as we will have for lenses. The thing to worry about or the thing to be concerned about here is that the conventions can be a little bit different. We have the same lens equation for how the object, image, and focal distances are related but our conventions are slightly different because of course, for lenses, the rays can go through the lens rather than bouncing off as they did for a mirror. The conventions for a lens are that the focal point is positive for a converging lens and negative for a diverging lens. The object distance is again always going to be positive.

05:42 This is sort of by convention. If we try to put the object on the other side of the lens, we could always just turn ourselves around and look at it from the other point of view. We’ll always sort of consider the object distance itself to be a positive number. Finally, the image distance is going to be a positive number for real images but a negative number for virtual images no matter where those are.

06:05 This concludes our lecture on mirrors and lenses. There’s a lot of material in this lecture with regard to the distances of the image, and the object, and the focus as well as how to treat both mirrors and lenses. So, I definitely recommend that you would go back over it and maybe try some practice problems. As you sort of let it sit for a while and maybe go over it a few more times, hopefully it becomes more comfortable because again, this procedure that we introduced for this parallel rays and then the rays going to the focus, these procedures are just used over and over again.

06:34 Once you sort of get an intuition for when should I use parallel rays, when should I use rays towards the focus, when will they leave and go away from the focus, for example, how can I use my lens and mirror equation, these things will all become more and more intuitive with even a few practice problems. I highly recommend you do that. We have one more section on optics which is coming up next. Thanks for listening.

The lecture Lenses by Jared Rovny is from the course Geometrical Optics.

### Included Quiz Questions

1. Parallel rays will pass through the focal point on the opposite side of the lens.
2. Rays through the focal point will reflect parallel to the lens axis.
3. Parallel rays will reflect through the focal point.
4. Rays towards the focal point on the opposite side will reflect through the focal point on the near side.
5. Rays through the focal point on the near side pass through the focal point on the far side.
1. Parallel rays will diverge directly away from the focal point on the near side.
2. Parallel rays will diverge directly away from the focal point on the opposite side.
3. Parallel rays will diverge directly towards the focal point on the near side.
4. Parallel rays will diverge directly towards the focal point on the far side.
5. Parallel rays will diverge parallel to the lens axis on the opposite side.
1. At 20 cm distance from the lens on the same side as the object. The image is a virtual image.
2. At 20 cm distance from the lens on the other side of the lens. The image is a virtual image.
3. At 20 cm distance from the lens on the other side of the lens. The image is a real image.
4. At 20/3 cm distance from the lens on the same side as the object. The image is a virtual image.
5. At 20/3 cm distance from the lens on the other side of the lens. The image is a real image.
1. The image is always virtual.
2. The image is always smaller than the original.
3. The image is only formed on the opposite side since light passes through the lens.
4. The image is always inverted.
5. The image is always real.

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