Going Further 12.1: Optical Lenses

There are two basic types of lenses used in many optical systems, as shown in Figure B.10.1: converging lenses and diverging lenses. If parallel light rays enter a converging lens, the light rays are bent inward and focus to a point, called the focal point, or focus. If parallel light rays enter a diverging lens, they are bent outward, such that they appear to emerge from a focal point behind the lens. Converging lenses are the type of lenses used in reading glasses and diverging lenses are the type used in glasses that aid in distance vision.

Figure B.12.1. (top) Converging lens. (bottom) Diverging lens. Credit: NASA/SSU/Aurore Simonnet

In Figure B.12.1, the horizontal line through the center of each lens is known as the optical axis. For converging lenses, light rays are bent toward the optical axis; for diverging lenses, light rays are bent away. In both cases, light bends only at the lens and not in mid-air.

When looking through these lenses, an observer sees an image of the object they are looking at, which might be larger or smaller than the original object, right side up or upside down, on the same side of the lens as the object, or on the opposite side. To determine where an image of an object will be formed by an optical lens, we can trace the path of a few rays of light emanating from an object, say, the tip of a candle. The rules for tracing the paths of the light rays are as follows:

1. A light ray emitted by the source object that travels parallel to the optical axis bends at the lens and passes through the focal point on the other side.
2. A light ray emitted by the source object that passes through the exact center of the lens is not bent and travels straight through.
3. A light ray emitted by the source object that passes through the focal point bends at the lens and emerges parallel to the optical axis.

An image is formed where these rays meet. These rules are illustrated in Figure B.12.2 for converging and diverging lenses. Of course these are not the only light rays emitted by the source object, but the diagrams are simpler if we only draw a few rays.

Figure B.12.2. Light rays are drawn for three possible object and lens configurations (A, B, C). For each case, the light rays are labeled 1, 2, and 3 following rules 1, 2, and 3. The optical axis is labeled, as is the focal point (F) in each case. The actual paths of the light rays are shown as solid lines; dotted lines are used to show where light appears to be coming from if the image and source are on the same side of the lens. (A) For a converging lens with the source outside the focal point, an image is formed on the opposite side of the lens; it is larger than the source, and inverted (upside down). (B) For a converging lens with the source inside the focal point, the image is on the same side as the source, is larger, and right side up. (C) For a diverging lens, an image is formed on the same side of the lens as the source, is smaller, and right side up. Credit: NASA/SSU/Aurore Simonnet