46) The focal length of a magnifying glass is 15 cm. If the near point of a person is 25 cm, what
is the angular magnification of the glass for this person when his eyes are focused at infinity?
A) 1.7
B) 2.7
C) 3.7
D) 4.7
E) 5.7
47) The focal length of a converging lens is 10 cm. What is the angular magnification of this lens
if the image is viewed by a relaxed eye with a near point of 25 cm?
A) 0.50
B) 1.5
C) 2.5
D) 3.5
E) 4.5
48) What is the angular magnification of a magnifying glass of focal length 4.0 cm if the image
is to be viewed by a relaxed eye having a near point of 25 cm?
A) 2.0
B) 3.0
C) 3.6
D) 4.0
E) 6.3
49) A lens of focal length 90 mm is used as a magnifier by a person with a near point of 25 cm.
The object being viewed is 9.9 mm long, and is positioned at the focal point of the lens. What is
the angle subtended by the image at infinity, in milliradians?
A) 110 mrad
B) 73 mrad
C) 37 mrad
D) 147 mrad
E) 183 mrad
50) A lens of focal length 40 mm is used as a magnifier. The object being viewed is 5.3 mm
long, and is positioned at the focal point of the lens. The user of the magnifier has a near point at
25 cm. What is the angular magnification of the magnifier?
A) 6.3
B) 5.6
C) 6.9
D) 7.5
E) 8.1
51) A person having a near point of 25 cm uses a magnifying glass with a focal length of 10 cm.
What is the angular magnification of the glass for that person when her eyes are focused at
infinity?
A) 1.5
B) 2.5
C) 3.5
D) 4.5
52) A magnifying glass has a focal length of 7.0 cm. What is the angular magnification if the
image is viewed by a person having a relaxed eye with the near point of 25 cm?
A) 1.6
B) 2.6
C) 3.6
D) 4.6
53) A person uses a converging lens of focal length 5.0 cm as a magnifying glass. What is the
angular magnification if the person’s eye is relaxed and has a near point of 25 cm?
A) 4.0
B) 5.0
C) 6.0
D) 7.0
54) A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is
the angular magnification if the image is to be viewed by a relaxed eye with a near point of 25
cm?
A) 5.0
B) 3.0
C) 4.0
D) 1.0
E) 2.0
55) A compound microscope consists of an objective lens of focal length f0 and an eyepiece that
by itself produces an angular magnification 25.0. The microscope is designed so that the object
to be viewed is on the left side of the objective lens and is focused in a plane that is 28.00 cm
away from the right-hand (or inside) focal point of the objective lens. When properly adjusted,
the eyepiece and the objective lens are 29.90 cm apart. The eyepiece magnification is based on
an image at infinity and a near point at 25.0 cm. What is f0?
56) The objective lens of a microscope has a focal length of 2.4 mm and the eyepiece has an
angular magnification of 15. The object is positioned 0.060 mm beyond the focal point of the
objective. The focal point of the eyepiece is positioned at the real image formed by the objective.
The near point of the microscope user is at 25 cm. The magnitude of the overall magnification of
the microscope is closest to
A) 400.
B) 450.
C) 500.
D) 550.
E) 600.
57) A very delicate sample is placed 0.150 cm from the objective lens of a microscope. The focal
length of the objective is 0.140 cm, and that of the eyepiece is 1.0 cm. The near-point distance
of the person using the microscope is 25.0 cm. The magnitude of the final magnification of the
microscope is closes to
A) 375.
B) 300.
C) 250.
D) 125.
E) 100.
58) The objective lens of a microscope has a focal length of 2.4 mm and the eyepiece has an
angular magnification of 15. The object is positioned 0.060 mm beyond the focal point of the
objective. The focal point of the eyepiece is positioned at the real image formed by the objective.
The near point of the microscope user is at 25 cm. What is the distance between the objective
lens and the eyepiece?
A) 98 mm
B) 102 mm
C) 107 mm
D) 111 mm
E) 115 mm
59) A microscope has an objective lens of focal length 1.40 mm and an eyepiece of focal length
20.00 mm. It is adjusted for minimum eyestrain for persons with a near point of 25.0 cm. A
blood sample is placed 1.50 mm from the objective. How far apart are the lenses?
A) 20 mm
B) 21 mm
C) 23 mm
D) 41 mm
60) A microscope has an objective lens of focal length 1.40 mm and an eyepiece of focal length
20.00 mm. It is adjusted for minimum eyestrain for persons with a near point of 25.0 cm. A
blood sample is placed 1.50 mm from the objective. The magnitude of the overall magnification
is closest to
A) 18.
B) 37.
C) 180.
D) 370.
61) A compound microscope has an objective with a focal length of 3.00 mm and an eyepiece of
focal length 6.00 cm. It is adjusted for minimum eyestrain for persons with a near point of 25
cm. If the two lenses are separated by 40.0 cm, what is the total overall magnification?
A) 28
B) 56
C) 470
D) 550
E) 2200
62) A compound microscope has a 18-cm-long barrel and an objective lens with a focal length of
8.0 mm. What is the focal length of the eyepiece to give a total magnification of 240? It is
adjusted for minimum eyestrain for persons with a near point of 25 cm.
A) 1.3 m
B) 1.5 cm
C) 1.9 cm
D) 2.1 cm
E) 2.3 cm
63) The focal lengths of the objective lens and the eyepiece in a microscope are 2.90 mm and
2.50 cm, respectively. An object is placed 3.00 mm from the objective. The image of this object
is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point of 25
cm. What is the distance between the objective and the eyepiece?
A) 9.9 cm
B) 9.0 cm
C) 15 cm
D) 11 cm
E) 13 cm
64) The focal lengths of the objective lens and the eyepiece in a microscope are 0.29 cm and 2.50
cm, respectively. An object is placed at 0.30 cm from the objective lens and the image of this
object is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point
of 25 cm. The magnitude of the final overall magnification of the microscope is closest to
A) 100
B) 200
C) 300
D) 410
E) 500
65) The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0
cm, respectively, and their separation adjusted for minimum eyestrain is 6.0 cm. If the
microscope is focused on a small object, what is the distance between the object and the
objective lens?
A) 0.31 cm
B) 0.42 cm
C) 0.49 cm
D) 0.57 cm
E) 0.73 cm
66) The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0
cm, respectively, and their separation is 6.0 cm when adjusted for minimum eyestrain for a
person with a near point of 25.0 cm. If the microscope is focused on a small object, the
magnitude of its final overall magnification is closest to
A) 50.
B) 100.
C) 150.
D) 200.
E) 250.
67) The distance between the object to be viewed and the eyepiece of a compound microscope is
18.0 cm. The focal length of its objective lens is 0.80 cm and the eyepiece has a focal length of
2.3 cm. The near-point distance of the person using the microscope is 25.0 cm. What is the
magnitude of the total magnification of the microscope if it is designed for minimum eyestrain?
A) 120
B) 184
C) 200
D) 360
E) 480
68) The distance between the object to be viewed and the eyepiece of a compound microscope is
25.0 cm. The focal length of its objective lens is 0.200 cm and the eyepiece has a focal length of
2.60 cm. What is the magnitude of the total magnification of the microscope when used by the
person of normal eyesight if it is designed for minimum eyestrain?
A) 1070
B) 204
C) 520
D) 477
E) 772
69) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25
mm, respectively. The objective produces a real image 30 times the size of the object, with the
final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the
distance between the object and the focal point of the objective lens?
A) 0.13 mm
B) 0.18 mm
C) 0.23 mm
D) 0.28 mm
E) 0.33 mm
70) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25
mm, respectively. The objective produces a real image 30 times the size of the object, with the
final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the
distance between the objective lens and the real image that it produces?
A) 116 mm
B) 120 mm
C) 124 mm
D) 128 mm
E) 132 mm
71) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25
mm, respectively. The objective produces a real image 30 times the size of the object, with the
final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the
magnitude of the overall magnification of the microscope?
A) 250
B) 300
C) 350
D) 400
E) 450
72) The eyepiece of a compound microscope has a focal length of 2.50 cm, and the objective has
a focal length of 1.60 cm. The two lenses are separated by 14.0 cm. The microscope is used by a
person with normal eyes, having a near point at 25 cm. What is the magnitude of the
magnification of the microscope?
A) 72
B) 88
C) 180
D) 219
E) 115
73) A refracting telescope has an eyepiece of focal length -80 mm and an objective of focal
length 36 cm. What is the magnification of this instrument?
74) A student wishing to build a telescope has available an eyepiece of focal length -5.0 cm.
What focal length objective is needed to obtain a magnification of 10?
75) The objective lens of a telescope has a focal length of 1.90 m. When viewed through this
telescope, the Moon appears 5.25 times larger than normal. How far apart are the objective lens
and the eyepiece when this instrument is focused on the Moon?
76) Mary builds a simple refracting telescope using two lenses of focal length 80 cm and 5.0 cm.
The respective diameters are 60 mm and 10 mm. How many degrees wide does the moon appear
through the telescope if it appears only 1/2 degree wide with the “naked eye”?
77) You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16.0 cm. If you could
use any two of these lenses to build a telescope, what is the maximum magnification you could
achieve for comfortable viewing of a planet?
A) 2.0
B) 4.0
C) 6.0
D) 8.0
78) You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16 cm. If you could
use any two of these lenses to build a telescope, what is the lens separation for the telescope to
provide the maximum magnification for comfortable viewing of a planet?
A) 10.0 cm
B) 12.0 cm
C) 18.0 cm
D) 24.0 cm
79) The objective lens of a telescope has a focal length of 2.0 m and its eyepiece has a focal
length of 1.0 cm. What is the magnification of this telescope when viewing Jupiter?
A) 0.0050
B) 0.50
C) 2.0
D) 20
E) 200
80) A student constructs an astronomical telescope and wishes it to have a magnification of 10.
If the telescope has an objective lens of focal length 0.50 m, what must be the focal length of the
eyepiece?
A) 2.5 cm
B) 5.0 cm
C) 10 cm
D) 25 cm
81) A student constructs an astronomical telescope with a magnification of 10. If the telescope
has an objective lens of focal length 0.50 m, what is the resulting length of the telescope?
A) 53 cm
B) 55 cm
C) 60 cm
D) 75 cm
82) A person is designing a telescope with a magnification of 10. If the telescope is limited to a
length of 0.20 m, what is the approximate focal length of the objective?
A) 16 cm
B) 17 cm
C) 18 cm
D) 19 cm
83) A telescope has an angular magnification of 250 when used with a 20 mm eyepiece. What is
the focal length of the objective lens?
A) 5.0 cm
B) 25 m
C) 5000 cm
D) 5.0 m
E) 2.5 m
84) Cal is viewing the Moon with his new telescope, using a 10-mm focal length eyepiece. For
greater detail, he wishes to double the magnification of his telescope. An eyepiece having which
one of the following characteristics will accomplish this for him?
A) 40 diopters
B) 8 mm
C) 12 mm
D) 200 diopters
E) 5 diopters
85) The focal length of the objective lens of a telescope is 75.0 cm, and the eyepiece has a focal
length of 6.00 cm. What is the magnification of this telescope?
A) 0.0800
B) 0.645
C) 450
D) 12.5
E) 200
86) The length of a telescope is 2.00 m and the focal length of the objective lens is 2.0 cm. What
is the focal length of the eyepiece?
A) 200 cm
B) 202 cm
C) 101 cm
D) 2.0 cm
E) 198 cm
87) The length of a telescope is 2.20 m and the focal length of the eyepiece is 1.9 cm. What is the
focal length of the objective lens?
A) 41 cm
B) 45 cm
C) 111 cm
D) 218 cm
E) 16 cm
88) The focal length of the objective lens of a telescope is 0.20 m and the eyepiece has a focal
length of 1.6 m. What is the length of this telescope?
A) 8.0 m
B) 1.4 m
C) 0.90 m
D) 1.6 m
E) 1.8 m
89) The length of the telescope is 1.60 m, and it has a magnification of 60.0. What is the focal
length of the objective lens?
A) 60.0 cm
B) 157 cm
C) 100 cm
D) 128 cm
E) 96.0 cm
90) The length of a telescope is 1.60 m and it has a magnification of 60.0. What is the focal
length of the eyepiece?
A) 2.62 cm
B) 60.0 cm
C) 100 cm
D) 1.16 cm
E) 96.0 cm
91) The objective lens of a refracting astronomical telescope has a focal length of 60 cm, and the
eyepiece has a focal length of 2.0 cm. How far apart should the lenses be placed in order to form
a final image at infinity?
A) 44 cm
B) 58 cm
C) 76 cm
D) 60 cm
E) 62 cm
92) An astronomical refracting telescope is made from two lenses. The objective lens has a focal
length of and the eyepiece lens has a focal length of
(a) What is the total length of the telescope?
(b) What is the angular magnification of the telescope?
(c) What is the magnification by turning the telescope around and looking through the objective
lens first?
A) (a) 131 cm
(b) 6.71
(c) 0.15
B) (a) 97 cm
(b) 0.15
(c) 6.71
C) (a) 262 cm
(b) 0.87
(c) 1.15
D) (a) 194 cm
(b) 1.18
(c) 0.85
93) The angular magnification of a refracting telescope is 40. When the object and final image
are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The
telescope is used to view a distant radio tower. The real image of the tower, formed by the
objective, is 6.0 mm in height. The focal point of the eyepiece is positioned at the real image.
What is the focal length of the objective lens?
A) 138 cm
B) 139 cm
C) 140 cm
D) 141 cm
94) The angular magnification of a refracting telescope is 40. When the object and final image
are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The
telescope is used to view a distant radio tower. The real image of the tower, formed by the
objective, is 6.0 mm in height. The focal point of the eyepiece is positioned at the real image.
What is the angle subtended by the final image of the tower?
A) 0.15 rad
B) 0.17 rad
C) 0.19 rad
D) 0.21 rad
E) 0.23 rad
95) The objective and the eyepiece of a refracting astronomical telescope have focal lengths of
320 cm and 4.0 cm, respectively. The telescope is used to view Neptune and the final image is
set at infinity. The diameter of Neptune is 4.96 × 107 m, and its distance from Earth at the time
of observation is 4.4 × 1012 m. What is the angle (in milliradians) subtended by the final
telescopic image of Neptune?
A) 0.90 mrad
B) 1.1 mrad
C) 1.3 mrad
D) 1.5 mrad
E) 1.7 mrad
96) Treat the pupil of your eye as a circular aperture of diameter 3.5 mm. Light of wavelength
500 nm is used to view two point sources that are 283 m distant from you. How far apart must
these two point sources be if they are to be just barely resolved by your eye, assuming that the
resolution is limited by diffraction?
97) Even with perfect optics, what is the resolution limit (in radians) of the Hubble Space
Telescope when it is focusing light of wavelength 400 nm? The mirror diameter is 2.4 m.
98) The world’s largest refracting telescope is operated at the Yerkes Observatory in Wisconsin.
It has an objective lens of diameter of 1.02 m. Suppose such an instrument were mounted on a
satellite at an elevation of 300 km above the ground and used to map surface details. If the
telescope is forming images with light of wavelength 550 nm, what is the minimum separation of
two objects on the ground whose separation could be clearly resolved by this lens?
99) What is the minimum distance between two points on the Moon that could be just resolved
by the Keck telescope in Hawaii using a wavelength of 600 nm and having perfect optics? The
diameter of this telescope mirror system is 10 m, and the distance to the Moon is 380,000 km.
100) A camera with a 20-cm diameter lens is recording images using a filter that allows only
light of wavelength 600 nm to pass through.
(a) What is the limit on the angular resolution (in microradians) in this case?
(b) What is the diameter of the minimum-sized features that could be resolved on Mars with this
camera? The distance to Mars at the time is 9.0 × 107 km.
101) In one particular case, the limiting angle of resolution for an eye is 1.4 × 10-4 rad. What is
the minimum separation between two point sources of light that the eye can distinguish if they
are at a distance of 40 m from the observer?
A) 2.8 mm
B) 5.6 mm
C) 1.4 mm
D) 8.4 mm
E) 4.7 mm
102) A camera used for aerial mapping has a lens with a 30-cm diameter maximum aperture and
a 42-cm focal length. Light of 550 nm wavelength is used to form the image. Assuming that the
resolution of the camera is limited only by diffraction, what is the smallest angle (in milliradians)
subtended by an object on the ground that can be resolved by this camera at maximum aperture?
A) 1.6 mrad
B) 2.2 mrad
C) 3.2 mrad
D) 4.5 mrad
E) 6.3 mrad
103) Assuming a pupil diameter of 3 mm, what is the angular resolution of the human eye for
light at the middle of the visible spectrum (550 nm)?
A) 0.8°
B) 0.2°
C) 2 mrad
D) 0.01°
E) 2°
104) Suppose your telescope has perfect mirrors and is limited only by diffraction. If you are
viewing with light of 400 nm wavelength, what diameter mirror in a space telescope would have
1.0-km resolution of objects on Mars when viewed from above the earth at a time when the
Earth-Mars distance of 80 million kilometers?
A) 39 km
B) 3.9 m
C) 3.9 km
D) 39 m
E) 390 m
105) Astronomers are proud of their telescopes and often say they can “resolve a dime at so
many miles.” How many miles from a telescope mirror can you place a coin of
diameter 3.0 cm and just resolve the coin using light of wavelength (1 mi = 1.609 km)
A) 19 mi
B) 9.7 mi
C) 40 mi
D) 190,000,000 mi
106) A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of
resolution for this telescope when it is forming images using light of wavelength 620 nm?
A) 1.11 × 10-7 rad
B) 3.11 × 10-7 rad
C) 2.70 × 10-7 rad
D) 1.35 × 10-7 rad
E) 4.05 × 10-7 rad
107) The two stars in a binary star system have an angular separation of 1.0 × 10-5 rad. If the
wavelength of the light from the system is 500 nm, what is the smallest diameter aperture
telescope that could just resolve this system to show that it contains two stars?
A) 0.50 cm
B) 0.61 cm
C) 5.0 cm
D) 6.1 cm
108) The pupil of a person’s eye changes from a diameter of 3.5 mm to 1.5 mm as the
illumination is increased. By what factor does the minimum angle of resolution change?
A) 0.43
B) 0.65
C) 2.0
D) 2.3
109) What is the limiting angle of resolution for a lens of radius 2.0 mm when viewing with light
having a wavelength of 600 nm?
A) 1.3 × 10-4 rad
B) 1.5 × 10-4 rad
C) 1.8 × 10-4 rad
D) 1.5 × 10-7 rad
E) 1.8 × 10-7 rad
110) A camera lens having a 50-mm focal length is set to f/4.0. What is the minimum spacing of
two objects located 12 m from the lens if the objects are just barely resolved in the image using
light of wavelength 500 nm?
A) 1.66 mm
B) 4.72 mm
C) 0.024 mm
D) 4.9 × 10-5 m
E) 0.59 mm