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Physics

Learn the toughest concepts covered in Physics with step-by-step video tutorials and practice problems by world-class tutors

33. Geometric Optics

Ray Diagrams For Lenses

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concept

Ray Diagrams for Converging Lenses

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Hey, guys. Now what? We're gonna talk about our ray diagrams for converging lenses. Okay, We talked about Ray diagrams for converging mirrors, but a mirrors job is to reflect light and produce an image in front of it. Ah, lenses job is to transmit light and produce an image behind it. So we're gonna see how that works now, conceptually with ray diagrams. All right, let's get to it. When light strikes the surface of a mirror, it reflects, right? This is already something we talked about a bunch. But when light strikes the surface of a lens, it transmits lenses. You're gonna be made out of transparent material that allows the passage of light through it. The transmitted light undergoes refraction, just like the reflected light off of a mirror obeys the law of reflection. Okay, converging lenses, right. As the name implies, our lenses that allow the convergence of light when you have initially column ated light like you do here. When it passes through the lens, those light rays all bend towards the central axis and therefore they converge on a points. This is a point of convergence. The point on the opposite side of the lens where the light converges is known as what guys? We know it as the focus, same as we had four mirrors. The thing about lenses, though, is that in order to draw diagrams properly, we have to represent focuses on both sides of the lens. So whatever this focal length is, F we're going toe. Have a second focus that same distance f on the front side of the lens as well. It's just a tool that we need to use in order to draw diagrams properly. Okay, the most common type of converging lens and the one shown in the figure above is called a by convex lens. It's by convex because both sides are convex surfaces. Okay, and it looks convex. Either way, you look at it. You could rotate this mirror. I'm sorry, this lens and it's gonna look convex, no matter how you look at it. Okay, Just like with mirrors, we can draw rate diagrams to find information. Qualitative information about the image is formed by lenses, but we need an associate ID set of rules for lenses, just like we had a set of rules for mirrors. Okay, so those rules are gonna be presented here to draw diagrams for converging lenses. You need to draw two of the following lines, just like the same thing for mirrors, a line parallel to the central axis, then through the lens towards the far focus. By that, I mean the focus on the other side of the lens. Second, aligned through the near focus the focus on the side of the lens of the object, then through the lens parallel to central access. Okay and, lastly, aligned to the very center of the lens that passes through undefended, that line will not get refracted. It's gonna pass through with the exact same angle. Let's do an example to illustrate this process. Draw the image location for the following converging limbs. Is the image upright or inverted? And in order to draw diagrams, you need some sort of ruler or some sort of straight edged object. What I have is my trusty protractor, because that's what I'm using. Instead of a ruler. Now we're going to draw two of the lines and find where they intersect. We could draw the third line, and it would intersect where the other to do as well all we need to know where the image is located is to find a point where two lines intersect. So the first line I'm going to draw is parallel to the central axis and ferree diagrams. You always draw them to the center of the lens. Thes types of lenses that we're gonna be dealing with are called thin lenses. Which means that compared to the radius of curvature of the lens, they are very, very thin. Okay, so they're essentially occupying a central line. Okay, so you're always going to that center line that I have indicated then from the center line, through the focus. Okay, The next line is going to be from the object through the focus to the center line of the lens and then parallel to the central axis of our lens. And look, you there, I just barely caught it. So here is the point of convergence. Because this blue ray have blue Ray is just going to continue and right there is clearly the point of convergence. Now, is this image upright or inverted? We're going to use the same convention that we used for mirrors. If the conversion of light is below the horror of the central axis, the horizontal axis. Then it's inverted. If it's above the central axis, then it's upright. This is clearly below the central axis, so this image is inverted, all right. And that wraps up our talk on ray diagrams for converging lenses. Thanks for watching guys.
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Problem

If an object is placed within the focus of a converging lens (it’s at a distance of less than the focal length), will a real image form? If so, does it form at a distance less than or greater than the focal length?

3
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Ray Diagrams for Diverging Lenses

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Hey, guys, In this video, we're gonna talk about Ray diagrams for diverging lenses. We just took a look at Ray diagrams for converging lenses, so we know that these should be similar. But since the light diverges, we know ahead of time some things about the images that we're gonna be formed. All right, let's get to it. A diverging Linz will never focus light ever because when light rays pass through it, they spread further apart. They don't come closer together, so they will Onley produce virtual images. I have a picture here off initially column mated light passing through a diverging lens. And what it turns out toe happen is that if you were to look at the diverging light after it had passed through the lens, it all appears toe have come from a point. So we have an A parents convergence. This is almost identical to convex mirrors, except mirrors reflect light and lenses transmit light. Remember, just like with those convex mirrors, the light appears to focus on a point, which we call the apparent focus for good reason, though often times we'll just refer to it as a focus because physicist tend to be lazy now because light can pass through either side. We need to have a focus that exists on either side of the lens, just like we did for conversion lenses. Okay, This is also important in how we're going to draw our raid diagrams. Alright. The most common type of diverging lens is the one shown above, which is called a by con cave lens. It's by con cave because it's a con cave surface. Either way, you look at it. If you were to flip this lens, it would still look con cave Okay, just like with mirrors, weaken draw diagrams for these lenses to find out information about the images. We did it for converging lenses. Now we want to do it for diverging lenses and the rules. We're going to be very similar with slight differences. To draw diagrams for diverging lenses, you need to draw two of the following lines a line parallel to the central axis, then through the lens, away from the near focus. Okay, second, align towards the far focus, the focus on the other side of the lens, then through the lens and parallel to the central. Okay, axis. All right, And lastly, just like for converging lenses, a line through the center of the lens that passes through un deflected those. They're going to be our three. Raise that we're going to draw. We only need to draw two of them to find an intersection of light. But those were gonna be the three possible raise we can draw for ray diagrams of diverging lenses. Okay, let's do an example. Draw the image location for this. This should say diverging lens. Is the image upright or inverted? Okay, so before we even begin, is the image gonna be upright or inverted? What do you guys think? This is the diverging lens. So the Onley images that can produce our virtual images and virtual images air always upright. So before we do a single thing we know just through rationalization and our physics knowledge that this image is gonna have to be upright. I don't have to draw a single lot. If the question was is the image upright, you'd be done. But where is the image located for that? We do need to draw a diagram. So the first Ray is going to be from the object parallel to the central axis right to the center of the lens. That's where we always draw and then away from the near lens. Okay, so I'm drawing it on a line parallel to the near Linz, but away from it. And then I'm gonna trace the line back to the origin the apparent origin of that line. Because that's where your brain is gonna see that line coming from next. What I need to do is draw a line towards the far focus. Okay, but once it hits the center of the lens, then it becomes parallel to the central axis. Okay, And where does this line appear to come from? I need to trace it backwards. It appears to come from this direction, so you can see right there. There is an apparent convergence that is our virtual image. And because it's above the horizontal axis because it's above the central axis, we know that it's upright exactly as we had predicted. Alright, guys, that wraps up our discussion on ray diagrams for diverging lenses. Thanks for watching
4
Problem

If an object is placed within the focus of a diverging lens (it’s at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

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