Biomedical Engineering Reference
In-Depth Information
(i.e., 40.00 cm/5
=
8.00 cm), which means that the equivalent viewing power is
+
12.50 D (i.e., 100/8.00 cm
12.50 D). Substituting, we have
Equivalent viewing power
+
+
=
(
M
) (add power)
+
12.50 D
=
(2.5) (add power)
5.00 D
The required lens cap is
add power
= +
+
5.00 D.
Adjusting tube length.
Lens caps are used because vergence amplification makes it difficult (or impossible)
to use a distance-focused telescope to view a near object. Is it possible to focus on
near objects with a telescope that does not have a lens cap? Yes, if the tube length
is increased sufficiently when viewing near objects, parallel light rays can be made
to emerge from the eyepiece. This is the case for both Galilean and Keplerian
telescopes.
How does this work? We can conceptualize the objective as consisting of two lenses:
one that acts as a lens cap and the other that contributes to the telescope magnifica-
tion. Think of a Galilean telescope that has a
+
20.00 D objective and
−
50.00 D eye-
piece. The angular magnification is 2.5
, and the tube length when focused for infinity
is 3.00 cm. If the patient wishes to focus at a distance 20.00 cm from the telescope, we
consider the
×
+
20.00 D lens to consist of a
+
5.00 D lens cap (i.e., 100/20.00 cm
=
5.00 D)
and
15.00 D objective that contributes to angular magnification. The angular magni-
fication of the newly created afocal telescope is
+
+
3.33
×
[i.e.,
−
(
−
50.00 D/(
+
15.00 D)
=
3.33
4.67 cm).
The same principles apply to a Keplerian telescope. Suppose a patient wishes to
use a terrestrial telescope (
×
]. The tube length is 4.67 cm (i.e., 6.67 - 2.00 cm
=
+
20.00 D objective and
+
50.00 D eyepiece; angular mag-
nification of
) to view an object located 20.00 cm from the telescope. The tube
length when focused for infinity is 7.00 cm. Again, we can think of the
+
2.5
×
+
20.00 D
lens as consisting of a
15.00 D objective lens that contributes
to angular magnification. The magnification of the newly created afocal telescope
is
+
5.00 lens cap and a
+
8.67 cm).
Based on these calculations, which would provide more angular magnification
when viewing an object at 20 cm: (1) a lens cap of
+
3.33
×
, and the tube length is 8.67 cm (i.e., 6.67
+
2.00 cm
=
+
5.00 D or (2) increasing the tube
length? Using a
telescope is equivalent to holding the
reading material at 8.00 cm (i.e., 20.00 cm/2.5
+
5.00 D lens cap with a 2.5
×
8.00 cm). In comparison, increas-
ing the tube length is equivalent to holding the reading material at 6.01 cm (i.e.,
20.00 cm/3.33
=
6.01 cm). Increasing the tube length provides greater angular mag-
nification. (Note that we obtain the same result for Galilean and terrestrial systems.)
=
SUMMARY
As the population ages, more patients will require the use of magnification devices
to carry out daily life functions. This chapter has concentrated on the optics of
near magnification. Equivalent viewing distance—the distance at which the reading
