Biomedical Engineering Reference
In-Depth Information
NEWTON'S RELATION
As we have learned, when a thin lens is located in air (or any other single medium),
the primary and secondary focal lengths are equidistant from the lens. This is the
basis for Newton's relation, which can be used to locate the object and image with
respect to the focal points of a plus lens. Other than its application in the lensom-
eter, the device used to determine the back vertex power (defined in Chapter 6) of a
patient's corrective lenses, this relation isn't used much, but it is generally included
in courses on geometrical optics, so you should know about it. In Figure 4-13, an
object is located at the distance
x
from the primary focal point of a plus thin lens
and the image is located at a distance
x
′
from the secondary focal point. Newton's
relation tells us that
xx
′
=
f
2
In this topic, we'll designate the distances
x
and
x
′
—sometimes referred to as
extra-
focal distances—
as positive.
Let's take an example.
An object located 10.00 cm to the left of the primary focal
point of a lens results in an image that is 40.00 cm to the right of the secondary
focal point. What is the power of the lens?
Assume the lens is in air.
Using Newton's relationship, we find that
xx
′
=
f
2
(
+
10.00 cm)(
+
40.00 cm)
=
f
2
f
= +
20.00 cm
I
O
F
F
′
x
x
′
Figure 4-13.
The extrafocal distances,
x
and
x
′
, are designated as positive when
substituting into Newton's relation.
