1. An object that is 5.0 cm high is placed 35.0 cm from a converging lens that has a focal
length of 25.0 cm.
a) Is the image real or virtual? Explain
b) Is the image inverted or upright (non-inverted)?
2. An object 2 cm in height is placed 7 cm from a converging lens with a focal length of
2 cm. Determine the height and position of the image
3. An object 15 cm in height is placed 30 cm in front of a converging lens. The focal
length is 10 cm.
What will the magnification be?
4. A child’s toy consists of a small light bulb that lights a picture of Scooby Doo. The
light from this picture then passes through a convex lens and is projected on the wall.
The picture of Scooby Doo is 2.1 cm from the lens, and the focal length of the lens is
2.0 cm. The child holds the toy so that the image of Scooby Doo is perfectly focused
on the wall. At what distance is the lens from the wall?
5. An object 7.0 m high is 15 m from a converging lens having a focal length of 10 m.
Use two methods described below to find the magnification of the image
a) Draw the ray diagram to construct the image of the object. Make sure the object is
drawn to scale (for example 1m or 2 m is equal to 1 cm on your diagram). After the
construction, use the definition (physical meaning) of magnification to find its value
b) Use formulas only (do not draw the ray diagram)
6. You want to project the image of a slide on a screen. The slide is 35 mm high. The
projector lens has a focal length of 15 cm. The screen is placed at a distance of 6.15 m
from the lens. The diagram below illustrates the situation. What is the height of the
image projected on the screen?
Screen
Converging
Lens
Projector
Slide
7. A manufacturer of slide projectors wants to produce images 1.5 m in height on a
screen that is placed 5.0 m from the lens of the projector. If the height of the slides is
30 mm, calculate the focal length of the lens
8. A 4.0 cm tall smurf is 7.0 cm away from a converging lens (f = 2.0 cm). What is the
height of the image formed?
9. How far from a converging lens with a focal length of 10 cm must an object be placed
in order to form an upright (that is non-inverted) image 5 times larger than the object?
10. An object that is 40.0 m away from a lens forms a real inverted image 10.0 cm from
the lens.
The lens is then used to view an object 8.0 cm from the lens.
Determine the magnification caused by the lens on the closer object.
11. A magnifying glass with a power of +18.0 d is used to observe an insect in the biology
lab. Its image appears to be magnified 4 times. What is the distance between the insect
and its virtual image?
12. Nadia is conducting a physics experiment using a converging lens on an optical bench.
The professor has said that the object must be 64.0 cm from the screen. Nadia is told
that the focal length of the lens is 12.0 cm. How far from the object must Nadia place
the lens to obtain a clear and larger image on the screen?
64.0 cm
Object
screen
Lens
13. In order to show your friends slides of your holidays, you decide to use a special slide
projector. It has the following characteristics:
- It has two converging lenses, A and B, which have focal lengths of 4 cm and 10 cm,
respectively.
- These two lenses are placed 23 cm apart in the slide projector.
- A slide 3 cm high is placed 6 cm from lens A, as shown in the diagram below.
lens A
slide
lens B
4 cm
F
6 cm
F
10 cm
?
23 cm
screen
a) How far away from lens B must the screen be placed in order to produce a clear
image of these slides?
b) What will the size of the image be on the screen?
14. Sandra views the letter F while looking through a double convex lens with a focal
length of 10 cm. She notices the following:
Object
F
Image
1.0 cm
0.50 cm
How close is Sandra holding the lens from the letter?
15. Bobby is having fun with lenses in the physics lab. He discovers that you can project
real images onto vertical screens using a converging lens. Using a lens with a focal
length of 20.0 cm, he is able to form an image that is 3 times larger than the original
object. How far is the object from the lens?
16. When an object is placed 10.0 cm in front of a converging lens, an image, 6.0 cm
behind the lens, appears on a screen (see the picture). The object is subsequently
moved 7.0 cm closer to the lens. What will be the magnification of the image after the
move?
Screen
Lens
Object
10.0 cm
6.0 cm
17. An object placed 20 cm from a lens produces a virtual image that is 3 times larger than
the object.
What is the focal length of this lens?
18.
An insect is magnified four times using a magnifying glass
(convex lens) with a focal length of 19 cm.
At what distance from the magnifying glass is the upright
image of the insect formed?
19. A rabbit 0.10 m in height is located 1.5 m from a converging lens with a focal length
of 0.50 m. What is the height of the rabbit’s image?
20. A 15.0 cm high vase is placed 50.0 cm in front of a diverging lens. The focal point is
30.0 cm away from the lens. Find the height of the image of the vase.
21. A 2.0 cm tall object is located 4.0 cm from a converging lens that has a focal length of
12 cm. What is the magnification of the image?
22. A student wishes to draw a picture of an insect for a project. The insect is 2 cm long
and its image must have a magnification of 5. He uses a converging lens (f = 15 cm) as
a magnifying glass.
How far away from the insect is its image?
23. An object 3.00 cm high is placed 11.0 cm from a converging lens that has a focal
length of 20.0 cm.
a)
Make a scale drawing of this situation.
b)
Calculate the position and size of the image. (These values must be calculated, not
measured from your diagram.)
24. During an experiment on converging lenses, four teams determined the distances
given in the table below.
DISTANCE
Team
Object Distance (do)
(m)
Image Distance (di)
(m)
1
2
3
4
0.90
0.60
1.20
2.00
0.45
0.30
0.60
0.50
Which two teams had a converging lens with the same focal length?
A)
1 and 2
C)
2 and 4
B)
1 and 3
D)
3 and 4
25. A spy satellite outfitted with a camera is located 150 km above the Earth’s surface.
The objective lens of the camera has a focal length of 120 cm. If the camera is aimed
at an airport runway that is 2.00 km long, what will be the size of the image formed by
this camera?
26. A numismatist studies a rare coin and tries to determine the inscribed date using a
magnifying glass. He holds the coin 5.0 cm from the magnifying glass and reads the
date clearly, five times larger than the real coin. What is the focal length of the
magnifying glass?
27. An image must be projected onto a screen from a picture slide that is 3.50 cm high.
The focal length of the projector’s converging lens is 15.00 cm. The screen is placed
615 cm away from the lens. What is the height of the projected image?
28. Ann wants to project the image of an object on a vertical screen using a converging
lens with a focal length of 50 cm. The image must be 4 times larger than the object.
How far from the object must she place the lens?
29. In an experiment, you found the focal length of a lens system to be 25 cm.
What is the optical power of this system?
A)
4.0 cm
B)
4.0 d
C)
0.04 cm
D)
0.04 d
30. Calculate the optical power of a system of two lenses placed close together which
have the following characteristics :
Lens A : ƒ = 20 cm
Lens B : ƒ = -60 cm
31. To repair a microscope a technician needs a lens combination with a power of 5.0
dioptres. Which two of the following lenses could be used?
Lens A = fA = 10.0 cm
Lens B = fB = 15.0 cm
Lens C = fC = -5.0 cm
Lens D = fD = -20.0 cm
32. Stuart uses three lenses to construct an optical device. The first lens has an optical
power of -2.00 diopters. The second lens has a focal length of 20.0 cm.
What is the focal length of the third lens if the total optical power of the combination must
be 1.50 diopters?
33. You want to make a camera lens using a lens combination. This camera lens must
have a focal length of 50 mm. You have five lenses whose optical powers are given in
the table below.
Lens
1
2
3
4
5
Optical Power
(diopters)
-10
-6.0
4.0
12
14
Find one possible lens combination that will enable you to make your camera lens.
34. As part of an experiment, Justin determined that the focal length of a three-lens system
was +4.0 cm. Justin’s partner, James, was supposed to record the individual focal
lengths of the three lenses. Unfortunately, in his hurry to get to lunch, James only
recorded the values for two of the lenses: +40.0 cm and +12.5 cm.
What was the focal length of the third lens?
35. While assembling a telephoto lens for a Science Fair, you realize that you need only
use the 2 lenses described below:
-
The first lens is double concave and has a focal length of 12 cm.
-
The second lens is double convex and has identical radii of curvature of 10 cm. It is made of a
transparent material. The index of refraction of this material is 1.7.
Calculate the optical power of a telephoto lens if it were made up of these two lenses
36. A student carries out an experiment to determine the focal length of five lenses.
The results are shown in the following table.
Lens
A
B
C
D
E
Focal length in (cm)
+15
+25
-15
-25
-2.67
What lens or combination of lenses should the student use to get an overall power
of -2.67 d?
A)
Lens E Only
B)
Lens A and Lens D
C)
Lens B and Lens C
D)
Lens C and Lens D
37. Maryam and Harris were working on their final physics lab exam in which they were
given a pair of lenses. After a quick inspection, they determined that one lens was a
converging lens and that the other was a diverging lens.
They recorded that a real inverted image was formed 20 cm from the converging lens
when an object was placed 20 cm from the lens.
When they placed both lenses together using the same object distance, they noticed that a
real image was formed 60 cm from the lenses.
What was the focal length of the diverging lens?
38. Two lenses with focal lengths of 20.0 cm and -35.0 cm are placed side by side. A 4.0
cm high candle is placed 120 cm in front of the lens system. Determine the image
distance and its height
120 cm
39. In a recent experiment using a system of four lenses, you obtained the following data:
Lens
Focal length (m)
Optical power (d)
3
4
All 4 lenses
together
1
2
-0.500
+0.227
-2.50
+0.100
+4.40
-0.400
10.0
In another experiment, you used only lens number 3 to project an image of an object onto
a screen. The object is located 50.0 cm from the lens.
How far is the lens from the screen?
40. An optical system is made of two lenses placed next to each
other, one a convergent lens and the other divergent. The power
of the system is 2.0 dioptres. The focal length of the diverging
lens is 60 cm.
What is the focal length of the converging lens?
41. In the laboratory storage room, you discover a box of lenses with the following focal
lengths: 0.105 m, -0.075 m and 0.05 m. To conduct an experiment, you place the
lenses in contact.
What is the power of this lens system?
42. An achromatic lens is a combination of two thin lenses close together. The power of
the achromatic lens is 4 dioptres (d). The focal length of one of the thin lenses is -17
cm. What is the power of the other thin lens?
43. To correct John's vision, two thin lenses have to be incorporated into a lens system in
preparation for his prescription glasses. One of the lenses has a focal length of 16.0
cm. What should be the focal length, in cm, of the other lens to obtain an optical
power of 2.0 diopters?
44. A system of three lenses is found to have a power of 15 diopters.
Data for two of the lenses is given below. Determine the focal length of lens C in metres.
Lens
A
B
C
Focal Length (m)
0.05
0.20
?
45. A lens combination consists of the following lenses :
a lens with a focal length of 25 cm;
a lens with a focal length of −50 cm.
What is the optical power of this lens combination?
46. During an experiment on optical power and lens combinations, Sophie came up with a
calculated optical power of 0 dioptres for a set of two lenses. Hassan, her lab partner,
concluded that the result could not be possible. Who is right?
How would you justify your answer from an optics point of view? Support your answer,
in a short written justification, using all three of the following concepts:
optical power
focal length
magnification
47. Look at the diagram below. A 12 cm tall object is placed in front of a concave mirror.
The focal length is 30 cm. The object is located 70 cm from the top of the mirror.
What will be the height of the image reflected by the mirror? How far is the image
from the object?
Object
C
F
48. Haran is manipulating a concave mirror that has a focal length of 10.0 cm. His physics
teacher tells him that the difference between do and di is 15.0 cm and that the image is
larger than the object and has a negative magnification.
Where should Haran place the object to obtain the desired image?
A)
do = 15.0 cm and di = 30.0 cm
B)
do = 30.0 cm and di = 15.0 cm
C)
do = 5.0 cm and di = -10.0 cm
D)
do = 10.0 cm and di = -5.0 cm
49. Alex places a 5.00 cm tall candle 30.0 cm in front of a mirror that has a focal length of
-50.0 cm. What is the magnification of the candle?
50. An object is placed 7.5 cm in front of a concave mirror.
What is the radius of curvature of the mirror if the image size is the same as the object?
51. An object with a height of 6.00 cm is placed in front of a spherical, concave lens at
do = 30.00 cm. Its image forms at di = 20.00 cm (see the picture). What is the height
of the image?
18 cm
Object
Focus
Image
8 cm
Note: The diagram is not to scale.
52. You place an object 30 cm from a concave mirror. There is a real image 15 cm from
the mirror. Next, you move the object closer so it is 6.0 cm from the mirror.
What is the new position of the image? Also, indicate if it is in front or behind the mirror
53. An object, 45.0 cm high, is placed in front of a convex mirror. A virtual image,
15.0 cm high, is formed. The focal length of the mirror is 30.0 cm.
At what distance is the object from the mirror?