Deck 24: Optical Instruments

Question 1

A camera lens has a focal length of 50.0 mm and an aperture setting of f/4.00. What is the aperture diameter of this lens?

A) 12.5 mm
B) 10.1 mm
C) 13.6 mm
D) 14.2 mm
E) 15.0 mm

Answer 1

12.5 mm

Question 2

A person's eye lens is 2.7 cm away from the retina. This lens has a near point of 25 cm and a far point at infinity.
(a) What must the focal length of this lens be in order for an object placed at the near point of the eye to focus on the retina?
(b) What must the focal length of this lens be in order for an object placed at the far point of the eye to focus on the retina?

Answer 2

(a) 2.4 cm
(b) 2.7 cm

Question 3

The near point of a person's uncorrected eyes is 125.0 cm and the far point is at infinity. What is the focal length of a contact lens that will move the near point to 25.0 cm from this person's eyes?

A) -100 cm
B) -31.3 cm
C) 10.2 cm
D) 20.8 cm
E) 31.3 cm

Answer 3

31.3 cm

Question 4

If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged?

A) The resolving power quadruples.
B) The resolving power doubles.
C) The resolving power is reduced to 1/2 of its original value.
D) The resolving power is reduced to 1/4 of its original value.
E) The resolving power does not change unless the focal length changes.

Question 5

A man is nearsighted and cannot see things clearly beyond 110from his eyes. What is the focal length of the contact lenses that will enable him to see very distant objects clearly?

A) 50 cm
B) -50 cm
C) -110 cm
D) 110 cm
E) -30 cm

Question 6

A myopic (nearsighted) dancer wears eyeglasses that allow him to have clear distant vision. The power of the lenses of his eyeglasses is -3.00 diopters. Without eyeglasses, what is the far point of the dancer?

A) 0.33 m
B) 0.25 m
C) 0.17 m
D) 0.42 m
E) 0.50 m

Question 7

The near point of a farsighted person's uncorrected eyes is 80 cm. What power contact lens should be used to move the near point to 25 cm from this person's eyes?

A) 2.8 diopters
B) -2.8 diopters
C) -4.0 diopters
D) -4.2 diopters
E) 4.2 diopters

Question 8

A 35-mm camera equipped with a 95 mm focal length lens is used to photograph a tree that is 8.0 m tall. A 32 mm high image of the tree on the film is needed. The required distance, between the tree and the camera lens, to take the photograph is closest to

A) 24 m.
B) 25 m.
C) 26 m.
D) 27 m.
E) 29 m.

Question 9

In a 35.0-mm single lens reflex camera (SLR), the distance from the lens to the film is varied in order to focus on objects at varying distances. Over what distance range must a lens of 55-mm focal length vary if the camera is to be able to focus on objects ranging in distance from infinity down to 0.60 m from the camera?

A) 5.55 mm
B) 4.44 mm
C) 16.7 mm
D) 22.2 mm
E) 7.77 mm

Question 10

What is the uncorrected near point of a person who has a near point that is 25 cm from his eyes when he is wearing 3.33-diopter contact lenses?

A) 1.5 m
B) 0.50 m
C) 1.9 m
D) 0.75 m
E) 0.60 m

Question 11

A singer is farsighted and cannot see objects clearly that are closer than 80.0 cm from his unaided eye. What is the refractive power of the contact lenses that will move his near point to a distance of 25.0 cm from his eye?

A) 2.75 diopters
B) -2.75 diopters
C) -4.72 diopters
D) 4.72 diopters
E) 7.00 diopters

Question 12

The focal length of a thin lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

A) f/4.0
B) f/2.0
C) f/5.6
D) f/0.30
E) f/0.40

Question 13

A nearsighted physicist cannot see things clearly beyond 90 cm from her eyes. What is the power of the contact lenses that will enable her to see very distant objects clearly?

A) 1.1 diopters
B) -1.1 diopters
C) -1.7 diopters
D) -2.2 diopters
E) 2.2 diopters

Question 14

A nearsighted person has her distant vision corrected using a -2.0-diopter contact lens. Her uncorrected near point is 15 cm. What is her near point using this lens if the lens is 2.0 cm from the eye?

A) 17 cm
B) 20 cm
C) 13 cm
D) 18 cm
E) 15 cm

Question 15

A person can read the newspaper when it is held at 60 cm from his eyes. What should the focal length of his contact lenses be to allow him to read the newspaper comfortably at a distance of 30 cm?

A) -30 cm
B) 30 cm
C) -60 cm
D) 60 cm
E) 90 cm

Question 16

Which one of the following is a characteristic of a compound microscope?

A) The objective is a diverging lens.
B) The eyepiece is a diverging lens.
C) The final image is real.
D) The image formed by the objective is virtual.
E) The image formed by the objective is real.

Question 17

A simple refracting telescope provides large magnification by employing

A) a short focal length objective and a short focal length eyepiece.
B) a short focal length objective and a long focal length eyepiece.
C) a long focal length objective and a short focal length eyepiece.
D) a long focal length objective and a long focal length eyepiece.

Question 18

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is 60 cm?

A) -60 cm
B) -30 cm
C) +30 cm
D) +60 cm
E) +130 cm

Question 19

A lens is designed to work in the visible, near-infrared, and near-ultraviolet. The best resolution of this lens from a diffraction standpoint is

A) the same for all wavelengths.
B) in the near-ultraviolet.
C) in the visible.
D) in the near-infrared.
E) indeterminate.

Question 20

What power contact lens must be used to correct the vision of a nearsighted person whose far point is 40 cm?

A) 2.5 diopters
B) -2.5 diopters
C) -3.6 diopters
D) -4.0 diopters
E) 4.0 diopters

Question 21

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 (image at the far point) having a near point of 25 cm and a far point at infinity?

A) 2.0 x
B) 3.0 x
C) 3.6 x
D) 4.0 x
E) 6.3 x

Question 22

The focal lengths of the objective 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 (with the eye focused at the far point). The near point of the person using the microscope is 25 cm and the far point is at infinity. What is the final overall magnification of the microscope?

A) -190 x
B) -240 x
C) -300 x
D) -320 x
E) -470 x

Question 23

An astronomical telescope has an objective of diameter 20 cm with a focal length of 180 cm. The telescope is used with an eyepiece of focal length 30 mm. What is the angular magnification of this telescope?

A) 360 x
B) 60 x
C) 540 x
D) 6 x
E) 180 x

Question 24

The focal lengths of the objective and the eyepiece of a microscope are 0.50 cm and 2.0 cm, respectively, and their separation adjusted for minimum eyestrain (with the final image at the viewer's far point) is 6.0 cm. The near point of the person using the microscope is 25 cm and the far point is infinity.
(a) If the microscope is focused on a small object, what is the distance between the object and the objective lens?
(b) If the microscope is focused on a small object, what is its final magnification?

Question 25

The angular magnification of a refracting telescope is 40 x. 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) 137 cm
B) 138 cm
C) 139 cm
D) 140 cm
E) 141 cm

Question 26

You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16.0 cm.
(a) If you were to use any two of these lenses to build a telescope, what is the maximum magnification you could achieve?
(b) If you were to use any two of these lenses to build a telescope, what is the lens separation for the maximum magnification telescope?

Question 27

The objective lens of a refracting telescope has a focal length of 60 cm and the eyepiece a focal length of 8.0 cm. What is the angular magnification of the telescope?

A) 34 x
B) 480 x
C) 68 x
D) 0.13 x
E) 7.5 x

Question 28

A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye (image at the far point) having a near point of 25 cm and a far point at infinity?

A) 5.0 x
B) 3.0 x
C) 4.0 x
D) 1.0 x
E) 2.0 x

Question 29

The objective and the eyepiece of a microscope have focal lengths of 4.00 mm and 25.0 mm, respectively. The objective produces a real image 30 times the size of the object. The final image is viewed at infinity, and the near point of the microscope user is at 25.0 cm. What is the distance between the object and the focal point of the objective?

A) 0.13 mm
B) 0.18 mm
C) 0.23 mm
D) 0.28 mm
E) 0.33 mm

Question 30

A person having a near point of 25 cm and a far point at infinity uses a converging lens of focal length 5.0 cm as a magnifying glass. What is the magnification if the person's eye is relaxed (with the image at his far point)?

Question 31

What is the focal length of a magnifying glass that produces an angular magnification of 7.0 x when used by a person with a near point at 28 cm?

A) 2.0 cm
B) 3.0 cm
C) 4.0 cm
D) 5.0 cm
E) 6.0 cm

Question 32

A magnifying lens has a focal length of 10 cm. A person has a near point of 25 cm and a far point at infinity. What is the angular magnification of the lens for that person when their eyes are focused at infinity?

Question 33

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 the distance from the earth at the time of observation is 4.4 × 10¹² m. What is the angle (in mrad) 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

Question 34

The distance between the object 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. A person with a near point of 25.0 cm and a far point at infinity is using the microscope.
(a) What is the angular magnification obtainable using the eyepiece alone as a magnifying lens if the final image is at the person's far point?
(b) What is the total magnification of the microscope when used by the person of normal eyesight?

Question 35

A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +1.75 diopters. With these eyeglasses, what is the near point of the machinist?

A) 17 cm
B) 14 cm
C) 10 cm
D) 21 cm
E) 24 cm

Question 36

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 15.0 cm. The microscope is used by a person with normal eyes (near point at 25 cm). What is the angular magnification of the microscope?

A) 78 x
B) 94 x
C) 195 x
D) 234 x
E) 125 x

Question 37

The focal lengths of the objective and the eyepiece in a microscope are 0.290 cm and 2.50 cm, respectively. An object is placed 0.300 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain (image at the far point of the eye) for a person with normal vision. What is the distance between the objective and the eyepiece?

A) 9.85 cm
B) 10.1 cm
C) 10.4 cm
D) 11.2 cm
E) 11.5 cm

Question 38

The angular magnification of a refracting telescope is 40 x. 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

Question 39

The focal lengths of the objective and eyepiece in a compound microscope are 0.80 cm and 2.5 cm, respectively. The image formed by the objective is 16 cm from it and the final image is 25 cm from the eye. What is the total overall magnification of the microscope?

A) -19 x
B) -11 x
C) -2.0 x
D) -100 x
E) -200 x

Question 40

The distance between the object 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 total overall magnification of the microscope?

A) -120 x
B) -184 x
C) -200 x
D) -360 x
E) -480 x

Question 41

A camera used for aerial surveillance has a lens with a 30-cm maximum aperture and a 42-cm focal length. Assume light of 550-nm wavelength is used and that the resolution of the camera is limited solely by diffraction. What is the angular resolution of the camera at maximum aperture?

A) 1.6 µrad
B) 2.2 µrad
C) 3.2 µrad
D) 4.5 µrad
E) 6.3 µrad

Question 42

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, the wavelength of the light is 600 nm, and index of refraction of the liquid in the eye is 1.34?

A) 0.42 mrad
B) 0.21 mrad
C) 0.14 mrad
D) 0.11 mrad
E) 0.26 mrad

Question 43

A radio telescope 200 m in diameter is used to investigate sources emitting a 21-cm wavelength wave. What is the minimum angular separation of the sources that can be resolved by this system?

A) 0.073°
B) 0.030°
C) 0.0013°
D) 0.154°
E) 0.0026°

Question 44

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is 5.0 × 10^-4 rad and the person has excellent vision?

A) 1.3 km
B) 5.0 km
C) 4.8 km
D) 0.65 km
E) 2.6 km

Question 45

Treat each of your eyes as a circular aperture of diameter 3.5 mm. Light of wavelength 500 nm is used to view two point sources that are 894 m distant from you. How far apart must these two point sources be if they are to be just resolved by your eye? Assume that the resolution is diffraction limited and use Rayleigh's criterion.

Question 46

Light of wavelength 633 nm from a He-Ne laser passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The diameter of the central bright area is 5.4 cm. What is the diameter of the aperture?

A) 110 μm
B) 2.0 μm
C) 6600 μm
D) 960 μm

Question 47

A certain astronomical telescope has a diameter of 5.60 m. Considering only the limitation due to diffraction, what is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A) 0.111 µrad
B) 0.311 µrad
C) 0.270 µrad
D) 0.135 µrad
E) 0.405 µrad

Question 48

A 10-inch telescope (25.4 cm in diameter) is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close (in angle) can the two stars be and still be resolved by this telescope if it is focusing light of wavelength of 550 nm? (Consider only the limitation due to diffraction.)

A) 4.2 × 10^-8 degree
B) 2.6 × 10^-6 degree
C) 3.0 × 10^-4 degree
D) 1.5 × 10^-4 degree
E) 6.6 × 10^-8 degree

Question 49

Light of wavelength 500 nm illuminates a round 0.50-mm diameter hole. A screen is placed 6.3 m behind the slit. What is the diameter of the central bright area on the screen?

A) 15 mm
B) 270 μm
C) 7.7 mm
D) 3800 μm