Lesson Video: Concave Lenses | Nagwa Lesson Video: Concave Lenses | Nagwa

Lesson Video: Concave Lenses Science • Third Year of Preparatory School

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In this video, we will learn how to identify the optical properties of concave lenses.

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Video Transcript

In this video, we will learn how to identify the optical properties of concave lenses. Before talking about this type of lens, let’s understand what a lens is in the first place.

A lens can have any shape. The two important things about lenses are, first, light can pass through them. So here we have a ray of light. And instead of being blocked or reflected from the lens, we see it’s able to travel through it. That’s one property of lenses. The second thing all lenses have in common is that they bend or refract light. We can see that, here, the ray of light bends just a little bit when it crosses into the lens. And then, it also bends or refracts when it leaves. So then, all lenses, first, are transparent. That means we can see through them. Lenses might be made of a material like glass or clear plastic. And then second, all lenses bend or refract rays of light.

Let’s now clear some space and think about a particular kind of lens, a concave lens. Starting with a lens with this shape, we can make a concave lens from it. What we do is make two big circles of the same size. Then, we imagine cutting out material from this block to follow the shapes of these circles. So, now our lens looks like this. We now have a concave lens. Notice that this lens is thinner at the middle, and it’s thicker at the top and bottom. Whenever we see that shape and the sides of the lens follow a circular arc, then we know we have a concave lens.

Each of these two circles that we’ve used to define our lens has a center point. These are the points on the circles that are the same distance from any location on the circumference of the circle. That means then that each of these center points is the same distance from any point on the surface of the lens closest to that center. For this reason, each of these points is called a center of curvature. There’s the lens’s center of curvature on the left and the lens’s center of curvature on the right. The distance between each center of curvature and the nearest surface of the lens is called the radius of curvature.

Since these two circles are the same size, that is, they have the same radius, the radius of curvature of one is the same as the radius of curvature of the other. Say we clear away everything but the lens and its two centers of curvature. If we draw a line through these two points, we have created what’s called the optical or principal axis. This is the line that travels through the lens’s two centers of curvature, as well as passing through the exact center of the lens. The optical axis is helpful for showing us how rays of light will be refracted by this concave lens.

For example, say that we have an incoming ray of light that’s moving parallel to the optical axis. When this ray reaches our lens, rather than continuing on in a straight line, the lens will refract or bend the ray of light. As we see, this happens twice, when the ray enters and leaves the lens. So a concave lens does change the path of a ray of light. And if we had another incoming ray also parallel to the optical axis, we would see that once again the ray passes through the lens, but it’s refracted. Adding in a few more of these parallel rays, we see something interesting. The effect our concave lens has on the light is to spread it out. These rays get farther and farther away from one another after they pass through the lens.

When rays of light do this, we say that they are diverging. This means the distance between rays that are next to one another is increasing as the rays move forward in space. But that then raises a question. If our concave lens makes rays diverge, how can they ever cross one another to form an image? If the rays of light never meet, if they never intersect, then no image will be formed. To understand how this works, say that we were to put our eye right over here on this side of our lens. That means all these diverging rays of light would land on our eye. And what our eye would do is trace these refracted rays backward, straight backward.

So, for example, for this top ray of light, once it lands on our eye, our eye would perceive this ray of light to be traveling on a path like this that we’ve shown with the dashed line. And then, likewise, for this ray of light, our eye would trace it backward to perceive that it travels along this dashed line. The same thing goes for the other refracted rays. Our eye perceives them all to be moving in a straight line. And so it sees a point of intersection of those lines here. Since this is where all the rays seem to come to a focus, it’s called the focal point. This is where our eye would think all of these rays of light were originating, where they were coming from. This is where it sees an image.

The distance between the focal point and the very center of the lens here, say we measure that straight-line distance this way, is called the focal length. Now, here’s something very important. Just as both sides of our concave lens have a center of curvature, so both sides have a focal point and both sides have a focal length. We would see this focal point and this focal length get involved if we let rays of light approach the lens from this side. And they can do that. Rays of light can reach a lens from any side. Knowing all this about concave lenses, let’s look now at a few examples.

Which of the following is a concave lens?

We know that, in general, a lens is an object that lets light through. That is, it’s transparent. And when light passes through a lens, it is refracted or bent. All of our answer options (A), (B), (C), and (D) show objects that do those two things. They let light through and they refract it. All of these objects then are lenses, and we need to figure out which one is a concave lens.

A concave lens is one that is thinner in the middle portion and thicker at the top and bottom. The only one of our lenses shaped that way is lens (D). We see it’s thinner at the middle portion, wider or thicker at the top and bottom. And then, and this is another sign of a concave lens, the edges of the lens look like they’re made up of part of a circle. The lens in answer choice (D) does show that shape. Our answer then is that option (D) is a concave lens.

Let’s look now at another example.

The diagram shows a concave lens. Which line shows the optical axis of the lens?

Okay, so we see these five lines — line one, line two, line three, line four, and line five — passing through this concave lens. We want to know which line shows the lens’s optical axis. This axis passes directly through the center of the lens. However, we can see that all five lines do that. All of them pass right through that center point. So let’s remember something else about the optical axis of a concave lens. A concave lens, we could say, is made up of two surfaces. Here, the dashed pink line shows one surface, and the dashed orange line shows the other. Each of these surfaces is in the shape of a part of a circle.

So, for example, the top surface is part of a larger circle whose shape looks partly like this. The bottom surface of the lens is part of a larger circle that looks a bit like this. Each of these two circles, and we’re only seeing a part of each one, has a center point, some point which is the same distance from all points on the circumference of the circle. We don’t know exactly where those center points are. But if we had to make a rough guess, for the pink circle, we might put its center point here. And then, for the orange circle, its center might be located here. Wherever those center points are, they’re the same distance from either side of the circle.

The optical axis of a lens is a line that joins together the two centers of curvature of that lens. For our concave lens, this blue line is about where its optical axis would be. And notice that this blue line overlaps with one of our five lines. That then tells us the answer to this question. It’s line one that shows us the optical axis of the lens.

Let’s look now at another exercise.

The diagram shows a concave lens. Which points on the diagram mark the centers of curvature of the lens? Select all that apply. (A) Point one, (B) point two, (C) point three, (D) point four, (E) point five.

On our diagram, we see all of these five points labeled. We want to figure out which point or points mark the centers of curvature of this concave lens. Notice something about the lens. Its side surfaces are part of a larger circular shape. In other words, each side of our concave lens has a circular arc to it. We see the two larger circles sketched in in these orange dashed lines. Like any circle, these circles have a center point. It’s a point that’s the same distance from every point on the circumference of the circle.

When two circles define the shape of a concave lens, like these two circles do here, those center points are called the centers of curvature of the lens. We can see that the center point of the circle on the left is right here. That’s labeled point two. Then, the center of the circle on the right is located here. That’s at point five. These two points then, points two and five, are the centers of curvature of the concave lens. For our answer, we choose option (B), which is point two, and option (E), point five.

Let’s now look at one last example.

The diagram shows a concave lens. Which line shows the radius of curvature of the lens?

We see here three lines indicated: line one, line two, and line three. Before thinking about these lines, though, notice that there are two dots indicated on this diagram. One dot is here. That’s the point at the center of this dashed orange circle. The other dot is here, which is at the center of this concave lens. Notice that if we drew a vertical line through the center of the circle, then the beginnings of lines one, two, and three are all along this line. In other words, all three line up with the center of this orange circle.

But then, let’s look at where the lines end. Line one ends here, which is on the outer surface of this conclave lens. Line two though ends right here, which is in line with this second dot. Line two goes from the center of the circle to the center of the lens. Then, lastly, there’s line three, which goes from the center of the circle to the inner surface of the lens. We want to pick which of these three shows the lens’s radius of curvature.

There’s actually a name for this point at the center of the orange circle. It’s called the center of curvature of the lens. The distance from the center of curvature to any point on the inner surface of the lens is the same. And then, notice what that distance is. It’s from the center of the circle to the circumference. It’s equal to the circle’s radius. Because our circle helps to define the shape of a lens, this distance is called the radius of curvature. It tells us how much or how little the surface of the lens is curved.

Notice that what we’ve called the radius of curvature does not lie on top of any of our three lines. That’s actually okay because the radius of curvature is just a distance. Whichever of lines one, two, or three indicates the same distance is the radius of curvature of the lens. Remember, we saw that line one goes from a line through the center of curvature to the outer surface of the lens. Line one then is longer than the radius of curvature. Line two goes from the center of curvature to the center of the lens. This also is longer, just slightly than the radius of curvature. Line three, though, begins at the center of curvature and ends right here on the inner curved portion of the lens.

So then, the length of line three is the same as the length of this line we’ve drawn here that we’ve called the radius of curvature. And this gives us our answer. Line three is the line that shows the radius of curvature of this concave lens.

Let’s now finish this lesson by reviewing a few key points. In this video, we saw that a lens is an object that is transparent — that is, light passes through it — and that refracts or bends rays of light. A concave lens, a certain type of lens, is shaped as follows. The sides of a concave lens are shaped as part of a larger circle. Each of those circles has a center point, and together they’re called the centers of curvature of the lens. A line passing through both centers of curvature is called the optical axis or principal axis of the lens. When parallel rays of light reach and then pass through the lens, they’re spread apart from one another. The rays are said to be diverging.

However, if we trace the refracted rays backward, we see that those traces do cross. They cross at a location known as the focal point of the lens. Just as each side of the lens has a center of curvature, so each side has a focal point. A single focal point is sometimes called a focus. When we have more than one focus, we call them foci. And finally, if we measure the distance between one of the lens’s focal points and the center of the lens, that straight line distance is equal to what is called the lens’s focal length. This is a summary of concave lenses.

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