Page 46 - Modern Optical Engineering The Design of Optical Systems

Gaussian Optics: The Cardinal Points 29

Figure 2.5b The formation of a
virtual image. See Example 2.2.

Notice that the image is formed to the left of the second focal point; in
fact, if the optical system is of moderate thickness, the image is to the
left of the optical system and also to the left of the object. From Eq. 2.6
we get the magnification

h′ f 10
m 5
h x 2
h′ mh (5) (5) 25 in

The magnification and image height are both positive. In this case the
image is a virtual image. A screen placed at the image position will not
have an image formed on it, but the image may be observed by viewing
through the lens from the right. A positive sign for the lateral magnifi-
cation of a simple lens indicates that the image formed is virtual; a nega-
tive sign for the magnification of a simple lens indicates a real image.
Figure 2.5 shows the relationships in these examples.

Example 2.3
If the object of Example 2.2 is 0.1-in thick, what is the apparent thick-
ness of the image? Since the lateral magnification was found to be 5
times in Example 2.2, the longitudinal magnification, by Eq. 2.9, is
2
approximately 5 , or 25. Thus the apparent image thickness is approxi-
mately 25 times (0.1 in), or 2.5 in. If an exact value for the apparent
thickness is required, the image position for each surface of the object
must be calculated. Assuming that the front of the object was given in
Example 2.2 as 2 in to the right of the first focal point, then its rear
surface must lie 1.9 in to the right of f 1 . Its image is located at

f 2 100
x′ 52.63 in
x 1.9
to the left of the second focal point. Thus the distance between the image
positions for the front and rear surfaces is 2.63 in, in reasonable agree-
ment with the approximate result of 2.5 in. Had we computed the
thickness for the case where the front and back surfaces of the object
were 1.95 and 2.05 in from the focal point, the results from the exact