Hey guys. Now what we're going to talk about are ray diagrams for converging lenses. Okay. We talked about ray diagrams for converging mirrors but a mirror's job is to reflect light and produce an image in front of it. A lens's job is to transmit light and produce an image behind it. So we're going to see how that works now conceptually with ray diagrams. Alright, 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 are going to 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, are lenses that allow the convergence of light. When you have initially collimated 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 point. 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 for mirrors. The thing about lenses though is that in order to draw ray diagrams properly, we have to represent focuses on both sides of the lens. Okay? So whatever this focal length is f, we're going to 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 ray diagrams properly. Okay? The most common type of converging lens and the one shown in the figure above is called a biconvex lens. Right? It's biconvex 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 going to look convex no matter how you look at it. Okay? Just like with mirrors, we can draw ray diagrams to find information, qualitative information, about the images formed by lenses, but we need an associated set of rules for lenses just like we had a set of rules for mirrors. Okay? So those rules are going to be presented here. To draw ray diagrams for converging lenses, you need to draw 2 of the following lines just like the same thing for mirrors. Okay? 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 the central axis. Okay? And lastly, a line to the very center of the lens that passes through undeflected. That line will not get refracted. It's going to pass through with the exact same angle. Okay? And let's do an example to illustrate this process. Draw the image location for the following converging lens. Is the image upright or inverted? And in order to draw ray 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 2 of the lines and find where they intersect. We could draw the 3rd line and it would intersect where the other 2 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 for ray diagrams you always draw them to the center of the lens. These types of lenses that we're going to 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 looky there I just barely caught it. So here's a point of convergence because this blue ray, I 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 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. Alright? And that wraps up our talk on ray diagrams for converging lenses. Thanks for watching guys.

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# Ray Diagrams For Lenses - Online Tutor, Practice Problems & Exam Prep

Ray diagrams for converging lenses illustrate how light rays converge at a focal point, producing real or inverted images. The biconvex lens allows light to pass through, bending towards the central axis. In contrast, diverging lenses, like biconcave lenses, spread light rays apart, creating virtual images that are always upright. Key rules for drawing these diagrams involve tracing light rays parallel to the central axis and through the focal points. Understanding these principles is essential for grasping concepts like refraction and image formation in optics.

### Ray Diagrams for Converging Lenses

#### Video transcript

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?

The image is virtual. Distance is greater than f.

The image is real. Distance is greater than f.

The image is virtual. Distance is less than f.

The image is real. Distance is less than f.

No image is formed

### Ray Diagrams for Diverging Lenses

#### Video transcript

Hey, guys. In this video, we're going to 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 are going to be formed. Alright? Let's get to it. A diverging lens 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 only produce virtual images. I have a picture here of initially collimated light passing through a diverging lens, and what it turns out to happen is that if you were to look at the diverging light after it had passed through the lens, it all appears to have come from a point. So, we have an apparent 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, oftentimes, we'll just refer to it as a focus because physicists 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 converging lenses. Okay? This is also important in how we're going to draw our ray diagrams. Alright? The most common type of diverging lens is the one shown above, which is called a biconcave lens. It's biconcave because it's a concave surface either way you look at it. If you were to flip this lens, it would still look concave. Okay? Just like with mirrors, we can draw ray 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 are going to be very similar with slight differences. To draw ray diagrams for diverging lenses, you need to draw 2 of the following lines: Align parallel to the central axis, then through the lens away from the near focus. Okay? 2nd, align towards the far focus, the focus on the other side of the lens, then through the lens and parallel to the central axis. Alright? And lastly, just like for converging lenses, aligned through the center of the lens that passes through undeflected. Those are going to be our 3 rays that we're going to draw. We only need to draw 2 of them to find an intersection of light, but those are going to be the 3 possible rays 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 going to be upright or inverted? What do you guys think? This is a diverging lens. So the only images it can produce are virtual images, and virtual images are always upright. So before we do a single thing, we know just through rationalization and our physics knowledge that this image is going to have to be upright. I don't have to draw a single line. 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 ray 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 lens but away from it. And then I'm going to trace the line back to the origin, the apparent origin of that line because that's where your brain is going to 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's 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.

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?

A real image is formed at a distance larger than f

A real image is formed at a distance less than f

A virtual image is formed at a distance larger than f

A virtual image is formed at a distance less than f

No image is formed

## Do you want more practice?

More sets### Here’s what students ask on this topic:

What are the key differences between ray diagrams for converging and diverging lenses?

Ray diagrams for converging lenses show how light rays converge at a focal point, producing real or inverted images. Converging lenses, like biconvex lenses, bend light rays towards the central axis. In contrast, ray diagrams for diverging lenses illustrate how light rays spread apart, creating virtual images that are always upright. Diverging lenses, such as biconcave lenses, cause light rays to diverge away from the central axis. Key rules for drawing these diagrams involve tracing light rays parallel to the central axis and through the focal points, but the direction of bending differs: towards the axis for converging lenses and away from the axis for diverging lenses.

How do you draw a ray diagram for a converging lens?

To draw a ray diagram for a converging lens, follow these steps: 1) Draw a ray parallel to the central axis from the object to the lens, then through the far focus on the other side. 2) Draw a ray from the object through the near focus, then parallel to the central axis after passing through the lens. 3) Optionally, draw a ray through the center of the lens, which passes undeflected. The intersection of these rays on the other side of the lens indicates the image location. If the intersection is below the central axis, the image is inverted; if above, it is upright.

What is the difference between real and virtual images in lens ray diagrams?

In lens ray diagrams, real images are formed when light rays converge at a point on the opposite side of the lens from the object. These images can be projected onto a screen and are typically inverted. Virtual images, on the other hand, are formed when light rays appear to diverge from a point on the same side of the lens as the object. These images cannot be projected onto a screen and are always upright. Converging lenses can produce both real and virtual images, while diverging lenses only produce virtual images.

Why do diverging lenses only produce virtual images?

Diverging lenses only produce virtual images because they cause light rays to spread apart rather than converge. When parallel light rays pass through a diverging lens, they diverge away from the central axis. If you trace these diverging rays backward, they appear to originate from a point on the same side of the lens as the object, creating an apparent convergence. This point is where the virtual image is formed. Since the light rays do not actually meet, the image cannot be projected onto a screen and is always upright.

How do you determine if an image is upright or inverted in a ray diagram for lenses?

To determine if an image is upright or inverted in a ray diagram for lenses, observe the position of the image relative to the central axis. For converging lenses, if the point of convergence (where the rays intersect) is below the central axis, the image is inverted. If it is above the central axis, the image is upright. For diverging lenses, the images are always virtual and upright because the light rays appear to diverge from a point above the central axis. This method applies to both real and virtual images formed by lenses.

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