When light rays enter a piece of glass, they refract, or bend, because the speed at which they are travelling changes. If the glass is shaped certain ways, the image that results from the light's passage can appear larger, smaller, closer, or farther away than the original object. Magnifying glasses, eyeglasses, cameras, and microscopes are a few of the instruments that use lenses. The human eye is another example.

A convex lens (figure 1) is one that is thicker at the middle than the ends and converges light so it meets at a single point. Other important characteristics of a lens are shown in figure 2. The principal axis is the line that joins the centers of curvature of its surfaces. The focal point is the point where a beam of light parallel to the principal axis converges. The focal length is the distance from the center of the lens to the focal point.


Figure 1: A convex, or converging, lens is thicker in the middle than on the ends. Parallel light rays will meet at a point beyond the lens.

Figure 2: The focal points and principal axis of a convex (converging) lens.

The resultant image with a converging (convex) lens is dependent upon the relative positions of the object, the lens, and the screen (when the image is real). The possible cases are outlined below:

  1. If the object is within the focal length of the lens, its image will appear in the lens as a virtual image. It will be larger than the object and will be right side up. In this situation, the lens is a magnifying glass (figure 3).

    Figure 3: The light rays from an object within one focal length of a convex lens diverge through the lens. Therefore, the image formed is not real but virtual as the light rays appear to converge on the same side of the lens as the object.

  2. If the object is beyond the focal point of a convex lens, the light from the object will converge and can be focused on a screen. This type of image is known as a real image. Real images are inverted and can be larger, smaller, or the same size as the original object and is dependent of the distance between the object and the lens (figure 4). Converging lenses in these orientations are used to project slides and motion pictures. The lens on the eye is another important example. (Notice that the image that appears on the back of the eye is actually inverted! Our brains, fortunately, usually compensate for this.)



    Figure 4: When the object is beyond the focal point, the rays of light converge on the opposite side of the lens and form a real image. The image will be larger than the object if the object is within two focal lengths from the lens. Once the object is a distance greater than two focal lengths away, the image becomes smaller. Notice also that the image begins to approach the focal point as the object is farther from the lens.

  3. An object that is great distance from the lens, the sun for example, will emit light rays that are parallel upon reaching the lens. These rays will converge at the focal point on the opposite side of the lens (figure 5).


    Figure 5: Parallel rays of light arrive at a lens from an object a great distance away. These rays will converge at the focal point.


    Drawing ray diagrams to predict the image formed by a convex lens: Always choose a point such as the top of the object from which to start the light rays. Draw the first ray parallel to the principal axis until it reaches the center of the lens. Any ray that reaches the lens parallel to the axis will bend to pass through the focal point on the opposite side of the lens. Draw the second ray so it goes through the center of the lens. It will continue along the same path upon exiting the lens. The position where these rays intersect is the point where the image will form.