11.9: Image Formation by Lenses

Image Formation by Thin Lenses

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.

Consider an object some distance away from a converging lens, as shown in Figure (PageIndex{7}). To find the location and size of the image formed, we trace the paths of principal rays originating from one point on the object, in this case the top of the person’s head. The figure shows the three principal rays from the top of the object as described above. (Note that there are many light rays leaving this point going in many directions, but we concentrate on the three principal rays which can be traced by simple rules.) The first ray is one that enters the lens parallel to its axis and passes through the focal point on the other side (Principal Ray 1). The second ray passes through the center of the lens without changing direction (Principal Ray 2). The third ray passes through the nearer focal point on its way into the lens and leaves the lens parallel to its axis (Principal Ray 3). If correctly drawn, all three rays cross at the same point on the other side of the lens. The image of the top of the person’s head is located at this point. All rays, including those that are not principal rays, that come from the same point on the top of the person’s head are refracted in such a way as to cross at the point shown; the principal rays are what we use to find this point. 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 (PageIndex{7}), only two are necessary to locate the image. Before applying ray tracing to other situations, let us consider the example shown in Figure (PageIndex{7}) in more detail.

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Figure (PageIndex{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.

The image formed in Figure (PageIndex{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 (PageIndex{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.