Problem 35
A simple magnifier gives the maximum angular magnification when it forms a
virtual image at the near point of the eye instead of at infinity. For
simplicity, assume that the magnifier is right up against the eye, so that
distances from the magnifier are approximately the same as distances from the
eye. (a) For a magnifier with focal length \(f,\) find the object distance \(p\)
such that the image is formed at the near point, a distance \(N\) from the lens.
(b) Show that the angular size of this image as seen by the eye is
$$
\theta=\frac{h(N+f)}{N f}
$$
where \(h\) is the height of the object. [Hint: Refer to Fig. 24.15 .1 (c) Now
find the angular magnification and compare it to the angular magnification
when the virtual image is at infinity.
Problem 37
The eyepiece of a microscope has a focal length of \(1.25 \mathrm{cm}\) and the
objective lens focal length is \(1.44 \mathrm{cm} .\) (a) If the tube length is
\(18.0 \mathrm{cm},\) what is the angular magnification of the microscope? (b)
What objective focal length would be required to double this magnification?
Problem 38
Jordan is building a compound microscope using an eyepiece with a focal length
of \(7.50 \mathrm{cm}\) and an objective with a focal length of $1.500
\mathrm{cm} .\( He will place the specimen a distance of \)1.600 \mathrm{cm}$
from the objective. (a) How far apart should Jordan place the lenses? (b) What
will be the angular magnification of this microscope?
Problem 39
The wing of an insect is \(1.0 \mathrm{mm}\) long. When viewed through a
microscope, the image is \(1.0 \mathrm{m}\) long and is located \(5.0 \mathrm{m}\)
away. Determine the angular magnification.
Problem 40
A microscope has an eyepicce that gives an angular magnification of 5.00 for a
final image at infinity and an objective lens of focal length $15.0
\mathrm{mm}\(. The tube length of the microscope is \)16.0 \mathrm{cm} .$ (a)
What is the transverse magnification due to the objective lens alone? (b) What
is the angular magnification due to the microscope? (c) How far from the
objective should the object be placed?
Problem 41
Repeat Problem \(40(\mathrm{c})\) using a different eyepiece that gives an
angular magnification of 5.00 for a final image at the viewer's near point
\((25.0 \mathrm{cm})\) instead of at infinity.
Problem 42
A microscope has an objective lens of focal length \(5.00 \mathrm{mm} .\) The
objective forms an image \(16.5 \mathrm{cm}\) from the lens. The focal length of
the eyepiece is \(2.80 \mathrm{cm} .\)
(a) What is the distance between the lenses? (b) What is the angular
magnification? The near point is \(25.0 \mathrm{cm} .\) (c) How far from the
objective should the object be placed?
Problem 44
Use the thin-lens equation to show that the transverse magnification due to
the objective of a microscope is \(m_{o}=-U f_{o} .\) [Hints: The object is near
the focal point of the objective: do not assume it is at the focal point.
Eliminate \(p_{0}\) to find the magnification in terms of \(q_{0}\) and
$\left.f_{0} . \text { How is } L \text { related to } q_{0} \text { and }
f_{0} ?\right].$
Problem 45
Telescopes
(a) If you were stranded on an island with only a pair of 3.5 -D reading
glasses, could you make a telescope? If so, what would be the length of the
telescope and what would be the best possible angular magnification? (b)
Answer the same questions if you also had a pair of 1.3 -D reading glasses.
Problem 47
(a) What is the angular size of the Moon as viewed from Earth's surface? See
the inside back cover for necessary information. (b) The objective and
eyepiece of a refracting telescope have focal lengths \(80 \mathrm{cm}\) and
\(2.0 \mathrm{cm}\) respectively. What is the angular size of the Moon as viewed
through this telescope?
