First a little nomenclature. Optometrists (and opthamologists) use the
dioptric power measured in diopters. A diopter is
1
/
f
1
/
f
where f is measured in meters. The focal length of lenses in contact is
1
f
=
1
f
1
+
1
f
2
1
f
=
1
f
1
+
1
f
2
or using dioptric power
D
=
D
1
+
D
2
D
=
D
1
+
D
2
A "normal" eye will focus an object at infinity onto the retina with
the lens relaxed. As objects come closer the lens of the eye is made to bulge
to keep the object in focus. A nearsighted person (such as certain
Phys 201 prof's) has an eye that focuses the object at infinity in front of
the retina. This person has a far point beyond which things are focused
incorrectly. By using a lens that casts the object at infinity onto the far
point this problem can be corrected. Say someone's far point is at 2m. In this
case we want
1
f
=
1
s
o
+
1
s
i
1
f
=
1
s
o
+
1
s
i
1
f
=
1
∞
+
1
−
2
1
f
=
1
∞
+
1
−
2
a corrective lens with
f
=
−
2
m
f
=
−
2
m
or
D
=
−
1
2
D
=
−
1
2
Diopters.
Notice that the desired focal length is the far point (with the correct choice
of sign)Of course in practice we need to take into account the
distance between the glasses and the eye, but the above is valid for a contact
lens. In the case of eyeglasses you need to subtract off the distance
between the lense and the eye. For example if the distance between the eye and
the glasses is 2cm then the above
becomes
1
f
=
1
∞
+
1
−
1.98
1
f
=
1
∞
+
1
−
1.98
A far sighted person focuses objects at infinity behind the retina. Their eye
can accommodate the object at infinity but they have trouble with nearby
points. A normal eye should be able to focus objects as close as 25cm. A far
sighted person can focus to a near point that is greater than 25cm and so we
need to take the 25cm point and make it look like it is at the near point. Say
some one has a near point of 125cm then
1
f
=
1
−
1.25
+
1
.25
1
f
=
1
−
1.25
+
1
.25
which is
+
3.2
+
3.2
Diopters. Of
course again we should correct for the distance between the glasses and the
eye, which if that is 2cm makes the
equation:
1
f
=
1
−
1.23
+
1
.23
1
f
=
1
−
1.23
+
1
.23
Finally their are old guys like me who need bifocals. As one ages, the eye
lens becomes more rigid and it is harder and harder for it to deform and focus
on close in objects. Then if you are also nearsighted, then you have to
resort to bifocals.
