26.6

Lenses

The lenses used in optical instruments, such as eyeglasses, cameras, and telescopes, are made from transparent materials that refract light. They refract the light in such a way that an image of the source of the light is formed. Figure 26-22a shows a crude lens formed from two glass prisms. Suppose an object centered on the principal axis is infinitely far from the lens so the rays from the object are parallel to the principal axis. In passing through the prisms, these rays are bent toward the axis because of refraction. Unfortunately, the rays do not all cross the axis at the same place, and, therefore, such a crude lens gives rise to a blurred image of the object.

Figure 26-22 (a) These two prisms cause rays of light that are parallel to the principal axis to change direction and cross the axis at different points. (b) With a converging lens, paraxial rays that are parallel to the principal axis converge to the focal point F after passing through the lens.

A better lens can be constructed from a single piece of transparent material with properly curved surfaces, often spherical, as in part b of the drawing. With this improved lens, rays that are near the principal axis (paraxial rays) and parallel to it converge to a single point on the axis after emerging from the lens. This point is called the focal point F of the lens. Thus, an object located infinitely far away on the principal axis leads to an image at the focal point of the lens. The distance between the focal point and the lens is focal length f. In what follows, we assume the lens is so thin compared to f that it no difference whether f is measured between the focal point and either surface of the lens or the center of the lens. The type of lens in Figure 26-22b is known as a converging lens because it causes incident parallel rays to converge at the focal point.
Another type of lens found in optical instruments is a diverging lens, which causes incident parallel rays to diverge after exiting the lens. Two prisms can also be used to form a crude diverging lens, as in Figure 26-23a. In a properly designed diverging lens, such as that in part b of the picture, paraxial rays that are parallel to the principal axis appear to originate from a single point on the axis after passing through the lens. This point is the focal point F, and its distance f from the lens is the focal length. Again, we assume that the lens is thin compared to the focal length.

Figure 26-23 (a) These two prisms cause parallel rays to diverge. (b) With a diverging lens, paraxial rays that are parallel to the principal axis appear to originate from the focal point F after passing through the lens.

Converging and diverging lenses come in a variety of shapes, as Figure 26-24 illustrates. Observe that converging lenses are thicker at the center than at the edges, whereas diverging lenses are thinner at the center.

Figure 26-24 Converging and diverging lenses come in a variety of shapes.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.