19.3 Lenses in Combinations

When light passes through two lenses, the image produced by the first lens acts as the object for the second lens. This can be seen in Figure 19.11 where a real image I1 is formed by lens L1. Light coming from this image behaves just as if it were coming from an object at that same place. Therefore lens L2 forms an image I2 just as if there were an object located there. This is shown in the diagram at the bottom where a new and larger object has been used to make the ray diagram easier to see. For the lenses and spacing in this diagram, this image formed by L2 is an inverted, real image that may be projected on a screen. Since the first image I1 was also inverted, the final image I2 is back in the upright position. Since it is a real image, it may be projected onto a screen.

Figure 19.11 When two lenses are used in combination, the image produced by the first lens acts as the object for the second lens.

Corrective lenses-whether contact lenses or common eyeglasses-produce a virtual image in a region that the eye can focus upon to produce a clear image on the retina. Let us begin with a nearsighted or myopic eye, such as the one in Figure 19.9 or Figure 19.12. Such an eye can see objects clearly out to some distance, known as the far point. Beyond the far point, this myopic eye is unable to focus a clear image on the retina. A corrective lens produces an image located closer than the far point and the eye, using this image as if it were an actual object, then focuses a clear image on the retina. This is illustrated in Figure 19.12. The type of corrective lens needed is called a negative lens or a diverging lens; it is thicker at the edges and thinner in the middle.

Figure 19.12 The corrective lens for a nearsighted eye produces a virtual image inside the far point so the eye can focus an image clearly on the retina.

Now we consider a farsighted or hyperopic eye, such as the one in Figure 19.10 or Figure 19.13. Such an eye can see objects clearly if they are farther away than a certain distance known as the near point. Closer than the near point, this hyperopic eye is unable to focus a clear image on the retina. A corrective lens produces an image located farther away than the near point and the eye, using this image as if it were an actual object, then focuses a clear image on the retina. This is illustrated in Figure 19.13. The type of corrective lens needed is called a positive lens or a converging lens; it is thinner at the edges and thicker in the middle.

Figure 19.13 The corrective lens for a farsighted eye produces a virtual image beyond the near point so the eye can focus an image clearly on the retina.