PASCO OS-8500 INTRODUCTORY OPTICS SYSTEM - Manual (Page 52)

Introductory Optics System 012-02744K
®
46
Using each of the lenses as a magnifier, it should be clear that the magnification provided by a
converging lens is not unlimited. This does not mean that the equation m = -d
i
/d
o
is in error. This
equation does give the correct ratio between the image size and the object size. However, image
size is not the only important variable in determining the magnification of an optical system, such
as a magnifier. Equally important is the distance between the observer and the image he is looking
at. Just as a distant object appears smaller than the same object up close, an image viewed through
an optical system appears larger if the image is close than if it is farther away.
Figure 20.2 shows an object of height h
o
, a distance d
o
from the observer. The size of the image on
the retina of the observer is proportional to the angle
θ
eye
. For small angles, (the only angles for
which the Fundamental Lens Equation holds),
θ
eye
= h
o
/d
o
.
There is an important limitation to the magnitude of
θ
eye
. To see this, hold an object at arms length
and move it slowly toward your eye (with one eye closed). There is a distance—called the near
point—at which the image begins to blur, because the rays entering your eye from the object are
too divergent for your eye to focus. The near point differs for different people, but the average is
approximately 25 cm. Therefore
θ
eye-max
= h
o
/25 cm, where
θ
eye-max
is the maximum value of
θ
eye
for
which the eye can focus an image.
When using a magnifier, or any optical system for that matter, the apparent size of the image
depends on the size and location of the image rather than on the size and location of the object, so
that
θ
mag
, the angular magnification for the magnifier, is equal to h
i
/d
i
. From the Fundamental Lens
Equation h
i
= mh
o
= (-d
i
/d
o
) h
o
. Therefore, ignoring the minus sign,
θ
mag
= h
o
/d
o
, the same as without the magnifier.
This result seems to imply that a magnifier doesn't produce any magnification. However, using a
magnifier, the object can be brought closer to the eye than the near point, and yet still be focused
by the eye. If the object is placed at the focal point of the magnifier for example, the equation
θ
mag
= h
o
/d
o
becomes
θ
mag
= h
o
/f. Therefore, the magnifying power of a magnifier is a function of how
much closer it allows the observer to be to the object. This, in turn, is a function of the focal length
of the magnifying lens.
The magnifying power of a lens (called the angular magnification) is calculated as
θ
mag
/
θ
eye-max
= 25 cm/f.
➂ Calculate the angular magnification for the 75 mm and 150 mm focal length lenses. Are your
calculated magnifications consistent with your answer to question 1? ____________
________________________________________________________________________
________________________________________________________________________.
➃ Would a converging lens with a 50 cm focal length be useful as a magnifier? Why or why not?
____________________________________________________________________
________________________________________________________________________.