What is lenses in physics

Lenses are used in cameras, telescopes, binoculars, microscopes and corrective glasses. A lens can be convex or concave. A convex lens is thicker in the middle than it is at the edges. Parallel light rays that enter the lens converge. They come together at a point called the principal focus. A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens.

See Figure 6. Another important characteristic of a thin lens is that light rays through its center are deflected by a negligible amount, as seen in Figure 5. Thin lenses have the same focal length on either side. A thin lens is defined to be one whose thickness allows rays to refract but does not allow properties such as dispersion and aberrations.

Look through your eyeglasses or those of a friend backward and forward and comment on whether they act like thin lenses. Using paper, pencil, and a straight edge, ray tracing can accurately describe the operation of a lens.

The rules for ray tracing for thin lenses are based on the illustrations already discussed:. In some circumstances, a lens forms an obvious image, such as when a movie projector casts an image onto a screen. In other cases, the image is less obvious. Where, for example, is the image formed by eyeglasses? We will use ray tracing for thin lenses to illustrate how they form images, and we will develop equations to describe the image formation quantitatively.

Figure 7. Ray tracing is used to locate the image formed by a lens. Rays originating from the same point on the object are traced—the three chosen rays each follow one of the rules for ray tracing, so that their paths are easy to determine. The image is located at the point where the rays cross.

In this case, a real image—one that can be projected on a screen—is formed. Consider an object some distance away from a converging lens, as shown in Figure 7. The Figure shows three rays from the top of the object that can be traced using the ray tracing rules given above. Rays leave this point going in many directions, but we concentrate on only a few with paths that are easy to trace. The first ray is one that enters the lens parallel to its axis and passes through the focal point on the other side rule 1.

The second ray passes through the center of the lens without changing direction rule 3. The third ray passes through the nearer focal point on its way into the lens and leaves the lens parallel to its axis rule 4. The three rays cross at the same point on the other side of the lens.

Rays from another point on the object, such as her belt buckle, will also cross at another common point, forming a complete image, as shown. Although three rays are traced in Figure 7, only two are necessary to locate the image. It is best to trace rays for which there are simple ray tracing rules.

Before applying ray tracing to other situations, let us consider the example shown in Figure 7 in more detail. The image formed in Figure 7 is a real image , meaning that it can be projected. That is, light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye, for example. Figure 8 shows how such an image would be projected onto film by a camera lens. This Figure also shows how a real image is projected onto the retina by the lens of an eye.

Note that the image is there whether it is projected onto a screen or not. The image in which light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye is called a real image. Figure 8. Real images can be projected. Several important distances appear in Figure 7.

We define d o to be the object distance, the distance of an object from the center of a lens. Image distance d i is defined to be the distance of the image from the center of a lens. The height of the object and height of the image are given the symbols h o and h i , respectively.

Images that appear upright relative to the object have heights that are positive and those that are inverted have negative heights. Using the rules of ray tracing and making a scale drawing with paper and pencil, like that in Figure 7, we can accurately describe the location and size of an image. But the real benefit of ray tracing is in visualizing how images are formed in a variety of situations. To obtain numerical information, we use a pair of equations that can be derived from a geometric analysis of ray tracing for thin lenses.

The thin lens equations are. The minus sign in the equation above will be discussed shortly. We will explore many features of image formation in the following worked examples. A clear glass light bulb is placed 0.

Use ray tracing to get an approximate location for the image. Then use the thin lens equations to calculate both the location of the image and its magnification.

Verify that ray tracing and the thin lens equations produce consistent results. Figure 9. A light bulb placed 0. Ray tracing predicts the image location and size. Since the object is placed farther away from a converging lens than the focal length of the lens, this situation is analogous to those illustrated in Figure 7 and Figure 8.

Ray tracing to scale should produce similar results for d i. Thus the image distance d i is about 1. Similarly, the image height based on ray tracing is greater than the object height by about a factor of 2, and the image is inverted.

Thus m is about —2. The minus sign indicates that the image is inverted. The thin lens equations can be used to find the magnification m , since both d i and d o are known. Entering their values gives. Note that the minus sign causes the magnification to be negative when the image is inverted. Ray tracing and the use of the thin lens equations produce consistent results.

The thin lens equations give the most precise results, being limited only by the accuracy of the given information. Ray tracing is limited by the accuracy with which you can draw, but it is highly useful both conceptually and visually. Real images, such as the one considered in the previous example, are formed by converging lenses whenever an object is farther from the lens than its focal length.

This is true for movie projectors, cameras, and the eye. We shall refer to these as case 1 images. A summary of the three cases or types of image formation appears at the end of this section. The image is upright and larger than the object, as seen in Figure 10b, and so the lens is called a magnifier.

If you slowly pull the magnifier away from the face, you will see that the magnification steadily increases until the image begins to blur. Pulling the magnifier even farther away produces an inverted image as seen in Figure 10a. The distance at which the image blurs, and beyond which it inverts, is the focal length of the lens. To use a convex lens as a magnifier, the object must be closer to the converging lens than its focal length. This is called a case 2 image. Figure This is a case 1 image.

Note that the image is in focus but the face is not, because the image is much closer to the camera taking this photograph than the face. This is a case 2 image. Ray tracing predicts the image location and size for an object held closer to a converging lens than its focal length. Ray 1 enters parallel to the axis and exits through the focal point on the opposite side, while ray 2 passes through the center of the lens without changing path.

The two rays continue to diverge on the other side of the lens, but both appear to come from a common point, locating the upright, magnified, virtual image. Figure 11 uses ray tracing to show how an image is formed when an object is held closer to a converging lens than its focal length. Rays coming from a common point on the object continue to diverge after passing through the lens, but all appear to originate from a point at the location of the image.

The image is on the same side of the lens as the object and is farther away from the lens than the object. This image, like all case 2 images, cannot be projected and, hence, is called a virtual image. Light rays only appear to originate at a virtual image; they do not actually pass through that location in space.

A screen placed at the location of a virtual image will receive only diffuse light from the object, not focused rays from the lens. Additionally, a screen placed on the opposite side of the lens will receive rays that are still diverging, and so no image will be projected on it.

We can see the magnified image with our eyes, because the lens of the eye converges the rays into a real image projected on our retina. Finally, we note that a virtual image is upright and larger than the object, meaning that the magnification is positive and greater than 1. An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image.

Suppose the book page in Figure 11a is held 7. What magnification is produced? We therefore expect to get a case 2 virtual image with a positive magnification that is greater than 1. Ray tracing produces an image like that shown in Figure 11, but we will use the thin lens equations to get numerical solutions in this example.

We do not have a value for d i , so that we must first find the location of the image using lens equation. The procedure is the same as followed in the preceding example, where d o and f were known. Rearranging the magnification equation to isolate d i gives. Now the thin lens equation can be used to find the magnification m , since both d i and d o are known.

A number of results in this example are true of all case 2 images, as well as being consistent with Figure Magnification is indeed positive as predicted , meaning the image is upright. Each of the lens' two faces can be thought of as originally being part of a sphere. The fact that a double convex lens is thicker across its middle is an indicator that it will converge rays of light that travel parallel to its principal axis.

A double convex lens is a converging lens. A double concave lens is also symmetrical across both its horizontal and vertical axis. The two faces of a double concave lens can be thought of as originally being part of a sphere. The fact that a double concave lens is thinner across its middle is an indicator that it will diverge rays of light that travel parallel to its principal axis.

A double concave lens is a diverging lens. These two types of lenses - a double convex and a double concave lens will be the only types of lenses that will be discussed in this unit of The Physics Classroom Tutorial. As we begin to discuss the refraction of light rays and the formation of images by these two types of lenses, we will need to use a variety of terms.

Many of these terms should be familiar to you because they have already been discussed during Unit If you are uncertain of the meaning of the terms, spend some time reviewing them so that their meaning is firmly internalized in your mind.

They will be essential as we proceed through Lesson 5. These terms describe the various parts of a lens and include such words as. If a symmetrical lens were thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the lens.

This imaginary line is known as the principal axis. A lens also has an imaginary vertical axis that bisects the symmetrical lens into halves. As mentioned above, light rays incident towards either face of the lens and traveling parallel to the principal axis will either converge or diverge. If the light rays converge as in a converging lens , then they will converge to a point.