Deck 34: Geometric Optics

Question 1

A object is 12 cm in front of a concave spherical mirror,and the image is 3.0 cm in front of the mirror.What is the focal length of the mirror?

A) 0.25 cm
B) 15 cm
C) 4.0 cm
D) 2.4 cm
E) 1.3 cm

Answer 1

2.4 cm

Question 2

A convex spherical mirror with a focal length of magnitude 25 cm has a 4.0-cm tall flower placed 100 cm in front of it.What is the height of the image of the flower?

A) 0.80 cm
B) 20 cm
C) 4.0 cm
D) 1.6 cm
E) 8.0 cm

Answer 2

0.80 cm

Question 3

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.

Answer 3

The image formed by the objective is real.

Question 4

A man's face is 30 cm in front of a concave spherical shaving mirror.If the image is erect and 1.5 times as large as his face,what is the radius of curvature of the mirror?

A) 40 cm
B) 60 cm
C) 100 cm
D) 140 cm
E) 180 cm

Question 5

A convex lens has a focal length f.An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens.The image is located at what distance from the lens?

A) farther than 2f
B) 2f
C) between f and 2f
D) f
E) between the lens and f

Question 6

The spherical side mirror on a car is convex and has a radius of curvature of 25 cm.Another car is following,20 m behind the mirror.If the height of the car is 1.6 m,how tall is its image?

A) 5.0 cm
B) 2.0 cm
C) 4.0 cm
D) 3.0 cm
E) 0.99 cm

Question 7

A convex spherical mirror with a radius of 50 cm has a 4.0 cm tall object placed 100 cm in front of it.What is the position of the image relative to the mirror?

A) 20 cm behind the mirror
B) 25 cm behind the mirror
C) 100 cm in front of the mirror
D) 25 cm in front of the mirror
E) 20 cm in front of the mirror

Question 8

Suppose you place your face in front of a concave mirror.Which one of the following statements is correct?

A) If you position yourself between the center of curvature and the focal point of the mirror, you will not be able to see a sharp image of your face.
B) No matter where you place yourself, a real image will be formed.
C) Your image will always be inverted.
D) Your image will be diminished in size.
E) None of these statements are true.

Question 9

An object is placed in front of a lens which forms an image of the object.

A) If the lens is convex, the image cannot be virtual.
B) If the image is real, then it is also inverted.
C) If the image is real, then it is also upright.
D) If the image is virtual, then it is also inverted.
E) If the image is virtual, the lens must be a diverging lens.

Question 10

A concave spherical mirror with a radius of 20 cm creates a real image 30 cm from the mirror.How far is the object from the mirror?

A) 50 cm
B) 20 cm
C) 15 cm
D) 7.5 cm
E) 5.0 cm

Question 11

The image of a plant is 4.0 cm from a concave spherical mirror having a radius of curvature of 10 cm.Where is the plant relative to the mirror?

A) 2.2 cm in front of the mirror
B) 4.4 cm in front of the mirror
C) 9.0 cm in front of the mirror
D) 1.0 cm in front of the mirror
E) 20 cm in front of the mirror

Question 12

A convex lens has a focal length f.An object is placed at a distance between f and 2f on a line perpendicular to the center of the lens.The image formed is located at what distance from the lens?

A) 2f
B) between f and 2f
C) f
D) between the lens and f
E) farther than 2f

Question 13

Which statements are true about a VIRTUAL image? (There may be more than one correct choice.)

A) Its location can be calculated, but it cannot be viewed directly by your eye without using auxiliary lenses.
B) It cannot be photographed.
C) It cannot be viewed on a screen.
D) A plane mirror always forms a virtual image.
E) A concave lens always forms a virtual image.

Question 14

As you walk away from a vertical plane mirror,your image in the mirror

A) is always the same height.
B) may or may not decrease in height, depending on where the observer is positioned.
C) is always a real image, no matter how far you are from the mirror.
D) changes from being a virtual image to a real image as you pass the focal point.
E) decreases in height.

Question 15

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 16

How far are you from your image when you stand 0.750 m in front of a vertical plane mirror?

A) 0.375 m
B) 0.750 m
C) 1.50 m
D) 3.00 m

Question 17

A convex lens has focal length f.If an object is located extremely far from the lens (at infinity),the image formed is located what distance from the lens?

A) infinity
B) 2f
C) between f and 2f
D) f
E) between the lens and f

Question 18

An object 4.0 cm in height is placed 8.0 cm in front of a concave spherical mirror with a focal length of 10.0 cm.What is the position of its image in relation to the mirror,and what are the characteristics of the image?

A) 40.0 cm on the other side of mirror, real, 6.0 times bigger
B) 10.0 cm on the other side of mirror, virtual, 10.0 times bigger
C) 18.0 cm on the same side of mirror, virtual, 2.25 times bigger
D) 10.0 cm on the same side of mirror, real, 6.0 times bigger
E) 40.0 cm on the other side of mirror, virtual, 5.0 times bigger

Question 19

A swimming pool is filled to a depth of 2.0 m.How deep does the pool appear to be from above the water,which has an index of refraction of 1.33?

A) 1.5 m
B) 1.33 m
C) 2.5 m
D) 3.0 m
E) 4.0 cm

Question 20

An object 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror.The radius of curvature of the mirror has a magnitude of 52 cm.
(a)How far is the image from the vertex of the mirror?
(b)What is the height of the image?

Question 21

An object is placed 100 cm in front of a lens of focal length 20 cm.A second lens is placed 35 cm beyond the first,this second lens having a focal length of 8.0 cm.If the height of the object is 6.0 cm,what is the height of the final image?

A) 1.5 cm
B) 12 cm
C) 9.0 cm
D) 3.0 cm
E) 6.0 cm

Question 22

In the figure,the thin lens forms a real image of the object 94.0 cm from the object.What is the focal length of the lens?

A) 22.0 cm
B) 25.5 cm
C) 27.5 cm
D) 55.8 cm
E) 86.0 cm

Question 23

In the figure,the radius of curvature of the curved part of the lens is 24.0 cm,and the refractive index of the lens material is 1.750.What is the focal length of the lens?

A) +32.0 cm
B) -32.0 cm
C) -16.0 cm
D) +13.8 cm
E) -13.8 cm

Question 24

An object is placed 10 cm from a convex lens of focal length 20 cm.What is the lateral magnification of the object?

A) 0.50
B) 1.0
C) 1.5
D) 2.0
E) 2.5

Question 25

An object is placed 100 cm in front of a diverging lens with a focal length of magnitude 25 cm.A converging lens having a focal length of magnitude 33.33 cm is placed 30 cm past the first lens.Where is the final image formed?

A) 30 cm after the second lens
B) 20 cm in front of the first lens
C) 3.0 meters before the second lens
D) 100 cm after the second lens
E) 3.0 cm before the second lens

Question 26

In the figure,the radius of curvature of the curved part of the lens is 35.0 cm,and the refractive index of the lens material is 1.620.What is the focal length of the lens?

A) +56.5 cm
B) -56.5 cm
C) +28.2 cm
D) +21.6 cm
E) -21.6 cm

Question 27

It is desired to project the image of an object four times its actual size using a lens of focal length 20 cm.How far from the lens should the object be placed?

A) 100 cm
B) 80 cm
C) 4.0 cm
D) 25 cm
E) 5.0 cm

Question 28

A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (n_water = 1.33)

A) 2.66 m
B) 0.67 m
C) 1.5 m
D) 0.38 m

Question 29

When an object 1.15 cm tall is placed 12 cm from a lens,the lens produces an upright image of the object that is 5.75 cm tall.What is the focal length of the lens?

A) 24 cm
B) 18 cm
C) 60 cm
D) 15 cm
E) 9.0 cm

Question 30

A thin converging lens is found to form an image of a distant building 24 cm from the lens.If an insect is now placed 16 cm from this lens,how far FROM THE INSECT will its image be formed?

A) 64 cm
B) 72 cm
C) 32 cm
D) 96 cm
E) 48 cm

Question 31

In the figure,the image is viewed on a screen and is 13.5 mm tall.What is the focal length of the lens?

A) +14.6 cm
B) -14.6 cm
C) +20.4 cm
D) -89.3 cm
E) +124 cm

Question 32

An object 1.25 cm tall is placed 100 cm in front of a convex lens with a focal length of magnitude 50 cm.A concave lens with a focal length of magnitude 20 cm is placed 90 cm beyond the first lens.Where is the final image located?

A) 10 cm in front of the second lens
B) 20 cm past the second lens
C) 17 cm past the second lens
D) 10 cm past the second lens
E) 20 cm in front of the second lens

Question 33

A 4.0-cm tall object is placed 60 cm away from a converging lens of focal length 30 cm.What are the nature and location of the image? The image is

A) real, 2.5 cm tall, and 30 cm from the lens on the same side as the object.
B) virtual, 2.5 cm tall, and 30 cm from the lens on the side opposite the object.
C) virtual, 2.0 cm tall, and 15 cm from the lens on the side opposite the object.
D) virtual, 4.0 cm tall, and 60 cm from the lens on the same side as the object.
E) real, 4.0 cm tall, and 60 cm from the lens on the side opposite the object.

Question 34

A goldfish bowl is spherical,8.0 cm in radius.A goldfish is swimming 3.0 cm from the wall of the bowl.Where does the fish appear to be to an observer outside? The index of refraction of water is 1.33.Neglect the effect of the glass wall of the bowl.

A) 3.3 cm inside the bowl
B) 3.9 cm inside the bowl
C) 2.5 cm inside the bowl
D) 3.0 cm inside the bowl
E) 1.7 cm inside the bowl

Question 35

A convex-concave thin lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm.If the glass used has index of refraction 1.500,what is the focal length of this lens?

A) -32.0 cm
B) 32.0 cm
C) 113 cm
D) 67.5 cm
E) -113 cm

Question 36

An object 1.80 cm tall is placed 100 cm in front of a diverging lens having a focal length of magnitude 25 cm.A converging lens with a focal length of magnitude 33.33 cm is placed 30 cm past the first lens.What is the lateral magnification of this system of lenses?

A) 2.5
B) -2.5
C) -0.40
D) 1.0
E) 0.40

Question 37

A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed.How deep does the stream appear to the fisherman? The index of refraction of the water is 1.33.

A) 29 cm
B) 52 cm
C) 33 cm
D) 45 cm

Question 38

The left-hand end of a glass rod is ground to a spherical surface.The glass has index of refraction 1.50.A small object 4.00 mm tall is placed on the axis of the rod,37.0 cm to the left of the vertex of the spherical surface.The image is formed in the rod,50.0 cm to the right of the vertex.
(a)What is the magnitude of the radius of curvature of the spherical surface at the end of the rod?
(b)What is the height of the image?

Question 39

A 4.0-cm tall object is placed 50.0 cm from a diverging lens having a focal length of magnitude 25.0 cm.What are the nature and location of the image? The image is

A) real, 4.0 cm tall, and 20 cm from the lens on the side opposite the object.
B) virtual, 4.0 cm tall, and 20 cm from the lens on the side opposite the object.
C) virtual, 2.0 cm tall, and 10 cm from the lens on the side opposite the object.
D) virtual, 1.3 cm tall, and 16.7 cm from the lens on the same side of the object.
E) real, 1.3 cm tall, and 16.7 cm from the lens on the same side of the object.

Question 40

An optical system comprises in turn,from left to right: an observer,a lens of focal length +30 cm,an erect object 20 mm high,and a convex mirror of radius 80 cm.The object is between the lens and the mirror,20 cm from the lens and 50 cm from the mirror.The observer views the image that is formed first by reflection and then by refraction.What is the position of the final image,measured from the mirror?

A) 90 cm
B) 102 cm
C) 114 cm
D) 126 cm
E) 138 cm

Question 41

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

Question 42

A lens is made with a focal length of -40 cm using a material with index of refraction 1.50.A second lens is made with the SAME GEOMETRY as the first lens,but using a material having refractive index of 2.00.What is the focal length of the second lens?

A) -40 cm
B) -80 cm
C) -53 cm
D) -20 cm
E) -30 cm

Question 43

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 44

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

Question 45

A double-convex thin lens is made of glass with an index of refraction of 1.52.The radii of curvature of the faces of the lens are 60 cm and 72 cm.What is the focal length of the lens?

A) 70 cm
B) 63 cm
C) 75 cm
D) 66 cm
E) 58 cm

Question 46

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 47

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 48

A double-concave lens has equal radii of curvature of An object placed from the lens forms a virtual image from the lens.What is the index of refraction of the lens material?

A) 1.90
B) 1.98
C) 1.82
D) 1.77

Question 49

A compound lens is made by joining the plane surfaces of two thin plano-convex lenses of different glasses.The radius of curvature of each convex surface is 80 cm.The indices of refraction of the two glasses are 1.50 and 1.60.What is the focal length of the compound lens?

A) 67
B) 69
C) 71
D) 73
E) 75

Question 50

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 51

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 52

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 53

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?

Question 54

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 55

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 56

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 57

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 58

A thin double convex lens is to focus the image of an object onto a screen so that the image is life-sized.The lens surfaces have equal radii of curvature of 112 cm,and the refractive index of the lens material is 1.500.
(a)How far from the lens should the screen be placed?
(b)How far is the screen from the object?

Question 59

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 60

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 61

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 62

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 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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 71

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 72

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 73

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 74

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 75

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 76

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 77

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 78

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 79

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 80

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