18.6 Images Formed by Lenses

As with mirrors, we will find it extremely useful to look at three principal rays because it is easy to predict their behavior. They are sketched in Figure 18.16 and are very similar to the principal rays we have already seen in our study of mirrors. Ray 1 is an incoming ray parallel to the optic axis. For a converging lens, ray 1 is bent or refracted and passes through the focal point on the other side of the lens as shown. For a diverging lens, ray 1 is bent or refracted away from the optic axis and leaves the lens as though it originated from the focal point on the incoming side of the lens. Ray 2 is just the reversal of this ray. For a converging lens, ray 2 has passed through the focal point in front of the lens. It is bent or refracted, leaving the lens parallel to the optic axis. For a diverging lens, ray 2 is headed toward the focal point on the opposite side of the lens. It, too, is bent or refracted, leaving the lens parallel to the optic axis. Ray 3 passes through the center of the lens undeviated. The reason is the two surfaces of the lens at the optic axis are parallel!

Figure 18.16 Three principal rays will be very useful in understanding the formation of images.

We will now do with lenses what we earlier did with mirrors-their role in image formation is similar. Figure 18.17 shows an object placed some distance from a converging lens. We have again used a simple arrow. The tail of the arrow is again on the optic axis. An infinite number of rays leave the tip of the arrow but we will concentrate on only the three principal rays we have just defined. Having a real image means that all of the rays that leave the object and go through the lens will pass through a single point that locates the image. Figure 18.18 shows more ray diagrams for real images produced by various object distances.

Figure 18.17 Ray diagrams locate a real image. All the rays that leave a point on the object and go through the lens will pass through a common point if a real image is formed. For efficiency and convenience we concentrate on the three principal rays.

Figure 18.18 As the object is moved in from far away, the real image produced becomes larger, and is upside down. When the object distance is twice the focal length, the size of the image is the same as the size of the object; the image is still real and upside down. As the object moves closer to the focal point, the image size becomes larger than the object size.

Just as with mirrors, the magnification is the ratio of the image height to the object height. If Figures 18.17 and 18.18, when the object is far away, the image is smaller in size and is upside down so the magnification is small and negative, like M = - 0.50 or M = - 0.75. When the object distance is twice the focal length, the image is the same size as the object and is upside down so the magnification is M = - 1.00. As the object moves closer than this, the image increases in size but remains upside down so the absolute value of the magnification continues to increase although the magnification is still negative.

Figures 18.17 and 18 show a real image produced as long as the object distance is greater than the focal length. For a real image, the light actually passes through the image. If a card or screen is placed at the location of the image, an image will be projected on the card or screen. But a lens can also produce a virtual image. Figure 18.20 shows two examples of a lens producing a virtual image. One is with a converging lens; the other, a diverging lens. Converging lenses can produce either real or virtual images from a real object depending upon where the object is. If the object is beyond the focal point the converging lens will produce a real image; if the object is inside the focal point, a virtual image will be produced. Diverging lenses produce only virtual images from real objects. The virtual image, as before, can be seen quite clearly and looks like the object. But it can not be projected; that is what a virtual image means.

Figure 18.19 When the object is between the converging lens and the focal point, a virtual image is produced.

Figure 18.20 Ray diagrams locate a virtual image. All the rays that leave a point on the object and go through the lens leave as if they came from a common point when a virtual image is formed. We concentrate on the three principal rays because they are easy to handle. The dotted lines indicate where the light rays appear to have come from.

For virtual images formed by a single lens, the virtual image will always be right side up so the magnification will be positive. In the first examples of Figure 18.20, with a virtual image formed by a converging lens, the virtual image is larger than the object so the magnification is greater than one (M > 1.00). In the second example, with a virtual image formed by a diverging lens, the virtual image is smaller than the object so the magnification is smaller than one (M < 1.00).

Figure 18.H Converging lenses can produce enlarged or reduced images, depending upon the distance of the object from the lens.

Q: What kind of images can be produced by a converging lens?

A: Figure 18.18 illustrates several real images produced by a converging lens. By varying the object distance, the image may be reduced or enlarged in size. Figure 18.19 illustrates a virtual image produced by a converging lens.

Q: What kind of images can be produced by a diverging lens?

A: For a real object, a diverging lens produces only a virtual image that is reduced in size; this is illustrated in Figure 18.20.