34.5.5 Diverging Lenses

A lens thicker at the edges than in the middle is called a diverging lens. FIGURE 34.36 shows three important sets of rays passing through a diverging lens. These are based on Figures 34.27 and 34.28, where you saw that rays initially parallel to the axis diverge after passing through a diverging lens.

FIGURE 34.36 Three important sets of rays passing through a thin diverging lens.

The figure illustrates a set of rays passing through a thin diverging lens.
The figure illustrates a set of rays passing through a thin diverging lens.
The figure illustrates a set of rays passing through the center of a thin diverging lens.
Full Alternative Text

Ray tracing follows the steps of Tactics Box 34.2 for a converging lens except that two of the three special rays in step 4 are different.

TACTICS BOX 34.3 Ray tracing for a diverging lens

1–3 Follow steps 1 through 3 of Tactics Box 34.2.

4 Draw the three “special rays” from the tip of the arrow. Use a straightedge.

  1. A ray parallel to the axis diverges along a line through the near focal point.

  2. A ray along a line toward the far focal point emerges parallel to the axis.

  3. A ray through the center of the lens does not bend.

5 Trace the diverging rays backward. The point from which they are diverging is the image point, which is always a virtual image.

6 Measure the image distance s′. This will be a negative number.

Workbook Exercise 24

EXAMPLE 34.9 Demagnifying a flower

A diverging lens with a focal length of 50 cm is placed 100 cm from a flower. Where is the image? What is its magnification?

MODEL The flower is in the object plane. Use ray tracing to locate the image.

VISUALIZE FIGURE 34.37 shows the ray-tracing diagram. The three special rays (labeled a, b, and c to match the Tactics Box) do not converge. However, they can be traced backward to an intersection ≈33 cm to the left of the lens. A virtual image is formed at s′=−33 cm with magnification

m=−s′s=−−33 cm100 cm=0.33

FIGURE 34.37 Ray-tracing diagram for Example 34.9.

The figure illustrates a ray tracing diagram of a concave lens.

The image, which can be seen by looking through the lens, is one-third the size of the object and upright.

REVIEW Ray tracing with a diverging lens is somewhat trickier than with a converging lens, so this example is worth careful study.

Diverging lenses always make virtual images and, for this reason, are rarely used alone. However, they have important applications when used in combination with other lenses. Cameras, eyepieces, and eyeglasses often incorporate diverging lenses.