College Physics

Figure 25.37Ray tracing predicts the image location and size for an object held closer to a converging lens than its focal length. Ray 1 enters parallel to the axis and exits

through the focal point on the opposite side, while ray 2 passes through the center of the lens without changing path. The two rays continue to diverge on the other side of the

lens, but both appear to come from a common point, locating the upright, magnified, virtual image. This is a case 2 image.

Virtual Image

An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image.

Example 25.7 Image Produced by a Magnifying Glass

Suppose the book page inFigure 25.37(a) is held 7.50 cm from a convex lens of focal length 10.0 cm, such as a typical magnifying glass might

have. What magnification is produced?

Strategy and Concept

We are given thatdo= 7.50 cmand f= 10.0 cm, so we have a situation where the object is placed closer to the lens than its focal length.

We therefore expect to get a case 2 virtual image with a positive magnification that is greater than 1. Ray tracing produces an image like that

shown inFigure 25.37, but we will use the thin lens equations to get numerical solutions in this example.

Solution

To find the magnificationm, we try to use magnification equation,m=–di/do. We do not have a value fordi, so that we must first find the

location of the image using lens equation. (The procedure is the same as followed in the preceding example, wheredoandf were known.)

Rearranging the magnification equation to isolatedigives

1 (25.35)

di

=^1

f

−^1

do

.

Entering known values, we obtain a value for1/di:

1 (25.36)

di

=^1

10.0 cm

−^1

7.50 cm

=−0.0333cm.

This must be inverted to finddi:

d (25.37)

i= −

cm

0.0333

= −30.0 cm.

Now the thin lens equation can be used to find the magnificationm, since bothdianddoare known. Entering their values gives

(25.38)

m= −

di

do

= −−30.0 cm

10.0 cm

= 3.00.

912 CHAPTER 25 | GEOMETRIC OPTICS

This content is available for free at http://cnx.org/content/col11406/1.7