Biomedical Engineering Reference
In-Depth Information
A
x
θ
N
Reference distance
B
x
θ
′
N
f
Figure 12-6.
A.
When specifying effective magnification, manufacturers of magnifying
glasses usually assume a reference distance of 25 cm.
B.
The formula for effective
magnification assumes the object is held at the focal point of the plus lens.
is sometimes referred to as
M
25
or
effective magnification
. While labeling magnifiers
in this way may be of some benefit to people shopping for hand magnifiers, it is of
limited utility to practitioners.
Let's derive the formula for effective magnification. Figure 12-6A shows that an
object located at the reference distance subtends the angle
at the eye. Compare
this with Figure 12-6B, which shows that an object located at the focal point of a
plus lens forms the angle
θ
at the eye. The angular magnification,
M
25
, produced
by the plus lens is defined as
M
25
=
θ
′
θ
θ
′
where
θ
′
=
object size/focal length of plus lens and
θ
=
object size/reference distance.
Substituting, we have
reference distance
focal length
But since the reference distance is 0.25 m and
F
M
25
=
=
1/
f
, we can rewrite the equa-
tion as
F
M
25
=
4
