13.

3 Images in Lenses
In Activity 13.2, you noticed that two things affect the characteristics of the
image formed: the kind of lens (converging or diverging) and the location
of the object. You can determine the image characteristics by drawing ray
diagrams, just as you did with converging and diverging mirrors. As before,
you need to draw only two light rays to locate the image. The only difference is
that with mirrors you considered reflected rays, but with lenses you consider
refracted rays.
In order to understand how to draw ray diagrams for lenses, it is important
to understand how the incident and emergent rays are related to each other.
emergent ray the light ray that leaves The emergent ray is the ray that leaves the lens, being refracted as it goes from
a lens after refraction the lens back into air. Find out about their relationship by doing the activity
“Exploring the Rectangular Prism.”

T RY THIS EXPLORING THE RECTANGULAR PRISM

SKILLS HANDBOOK
SKILLS: Predicting, Performing, Observing, Analyzing 1.B., 3.B.
Equipment and Materials: ray box; single-slit mask; 3. Aim the light ray at the prism so that you can see an
rectangular prism; blank sheet of paper emergent ray on the other side of the prism. Carefully
examine how the incident ray and the refracted ray are
1. Lay the rectangular prism on its large flat face in the middle
positioned relative to each other. (If you notice another ray
of the sheet of paper.
going between the prism and the paper, press down on the
When handling the glass prism, take care not to cut your prism slightly.)
fingers if it is chipped.
4. Now place the prism on its thin side and repeat step 3.
2. Use the ray box and the single-slit mask to produce
A. How did the rectangular prism on its large flat surface affect
a light ray.
the emergent ray? T/I
When unplugging the ray box, do not pull the electric cord. B. What changed when you laid the prism on its thin side? T/I

Pull the plug itself.

C. How would the incident ray and the emergent ray compare
if you had used an extremely thin rectangular prism? T/I
D. If a very thin rectangular prism is available, test your
prediction by repeating this experiment. T/I

You can use a rectangular prism to understand how a lens works. An

incident ray directed at a rectangular glass prism undergoes two refractions.
The first is at the air–glass boundary as the ray enters the prism. The second
is at the glass–air boundary when the ray emerges from the prism. In a
rectangular prism, these two boundaries are parallel because the two surfaces
of the prism are parallel to each other. So the emergent ray is parallel to the
incident ray but displaced sideways. The amount of sideways displacement
depends on the thickness of the prism (Figure 1).

556 Chapter 13 • Lenses and Optical Devices NEL

 very little Figure 1 The emergent ray through
(a) (b) sideways a rectangular prism is parallel to the
displacement incident ray but displaced sideways.
noticeable Reducing the width of the prism greatly
sideways reduces the amount of sideways
displacement displacement.

A very thin rectangular prism results in very little displacement of the

emergent ray (Figure 1(b)). If the prism is thin enough, the emergent ray
appears to be almost unaffected by the presence of the prism. This fact is
important when considering images formed by converging lenses.

How to Locate the Image

in a Converging Lens
The three imaging rules for converging lenses are shown in Figure 2.

1 A ray parallel to the principal axis is

refracted through the principal focus (F ).
1
2 A ray through the secondary principal
optical centre focus (F ) is refracted parallel to the
2
principal axis principal axis. This rule comes from the
reversibility of light.
2F  F O F 2F
3 A ray through the optical centre (O)
continues straight through without being
3 refracted. This is true because the middle
F   secondary principal focus F  principal focus
part of the lens acts like a very thin
rectangular prism with no noticeable
sideways displacement.
Figure 2 Imaging rules for a converging lens

Note that these rules are true only for thin lenses. We will only discuss
thin lenses in this chapter.

Images in a Converging Lens

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You can investigate the images formed by a converging lens. If you place a
luminous source at a distance greater than 2F ʹ, you can locate an image of
this source by moving a paper screen back and forth on the other side of the
lens. The image is smaller, inverted, and located somewhere between F and
2F. This image is real. Light is actually arriving at the image location, and
you can see the image on a paper screen.
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Deborah Crowle 13.3 Images in Lenses 557
Pass 2nd pass
 WRITING TIP Using the imaging rules for a converging lens, you can show how the lens
Writing a Critical Analysis produced this image. You can also predict how the lens produces images for
Imagine that you are writing a critical other object locations (Figure 3).
analysis of a camera that has a lens
with a fixed focal length. You might refer - smaller
to the imaging rules for converging - inverted
- between F and 2F
lenses in the first paragraph to set the object - real
context for your analysis. beyond
2F 2F F F 2F
(a)

- same size
- inverted
- at 2F
object - real
at
2F 2F F F 2F

(b)

- larger
- inverted
- beyond 2F
object - real
between
F and 2F 2F F F 2F
Figure 3 A converging lens (c)
produces a real image for these
three object locations.

READING TIP When an object is located beyond 2F ʹ, the image is smaller than the
Making Connections object and is between 2F and F. As you slowly move the object toward the
Compare Figure 4 on this page with lens, the image gets larger and larger. Eventually, the image and the object
the three diagrams for the concave are the same size when the object is located at 2F ʹ; the image is now at 2F.
mirror in Figure 6 in Section 11.9 on If you continue moving the object between 2F ʹ and F ʹ, you get a larger
page 497. Examine how the image image than the object; the image is now outside 2F. Note that for all these
characteristics are related.
image positions, the image is always inverted and real.
When you move the object to the secondary principal focus (F ʹ), no image
is produced. The refracted rays are parallel and do not cross to form an
image (Figure 4). Even if you extend the rays backwards, there is no virtual
image. The reason is that the rays are parallel and do not form a virtual source.

no clear image formed

(emergent rays are parallel)

2F  F F 2F

Figure 4 No image is produced when

an object is at F ʹ.

558 Chapter 13 • Lenses and Optical Devices NEL

 No real image is produced when the object is between F ʹ and the lens. The
refracted rays spread apart or diverge. However, the human brain projects these
rays backwards and produces a virtual image behind the object (Figure 5).
(Note that virtual images are often described as being behind the lens because
light rays do not actually arrive at the image location; they only appear to.)

• larger
• upright
• behind the lens
• virtual
2F  F F 2F

Figure 5 A larger, virtual image is produced on the same side as the object when the object
is between F' and the lens.

Table 1 summarizes the image characteristics in a converging lens.

Table 1 The Imaging Properties of a Converging Lens

OBJECT IMAGE
Location Size Attitude Location Type
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beyond 2F ʹ smaller inverted between 2F and F real

at 2F ʹ same size inverted at 2F real

between 2F ʹ and F ʹ larger inverted beyond 2F real

at F ʹ no clear image

inside F ʹ larger upright same side as object (behind lens) virtual

How to Locate the Image in

a Diverging
Ontario Science 10 SB Lens
The imaging rules for a diverging lens are similar to those for a converging
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CrowleArt only appear to (Figure 6).
Deborah Crowle 1 A ray parallel to the principal axis is
Pass 2nd pass refracted as if it had come through
Approved the principal focus (F ).

Not Approved 2 A ray that appears to pass through

1 1 A ray the
parallel to the principal
secondary principal axis
focusis (F' )
2 optical centre refracted as if it had
is refracted cometothrough
parallel the principal axis.
the principal focus (F ).
3 A ray through the optical centre (O )
2 A ray continues
that appears to pass
straight through
through on its path.
2F F O F 2F 
1 the secondary principal focus (F' )
2 optical centre is refracted parallel to the principal axis.

3 3 A ray through the optical centre (O )

F  principal focus O F   secondary principal focus continues straight through on its path.
2F F F 2F 
Figure 6 Imaging rules for a diverging lens

3
F  principal focus F   secondary principal focus
NEL 13.3 Images in Lenses 559
 Images in a Diverging Lens
A diverging lens always produces the same image characteristics no matter
where the object is. The image is always smaller, upright, virtual and on the
To investigate lenses by using same side of the lens as the object (Figure 7). The human brain perceives
computer simulations, this virtual image by extending the diverging rays backwards to a virtual
GO TO NELSON SCIENCE source.

• smaller
• upright
• same side as object
• virtual

2F F F 2F 

Figure 7 A diverging lens always forms a smaller, upright, virtual image that is on the same side of
the lens as the object.

UNIT TASK Bookmark

How can you use the image characteristics of lenses as you plan your optical device for the
Unit Task described on page 588? C13-F17-UDOS10SB.ai

IN SUMMARY
• A converging lens produces both real and virtual • A diverging lens always produces a smaller,
images. The image size and attitude will vary upright, virtual image.
depending
Ontario onSB
Science 10 the location of the object.
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Deborah Crowle
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Approved
Not Approved

560 Chapter 13 • Lenses and Optical Devices NEL

 CHECK YOUR LEARNING
1. (a) In your own words, state the imaging rules for 4. Copy Figure 10 into your notebook. T/I C

converging lenses. (a) A screen is used to cover half of the lens (Figure 10(i)).
(b) How are these rules slightly different for diverging Use light rays to locate the image on the diagram.
lenses? K/U (b) A screen is used to cover half of the object (Figure 10(ii)).
2. Copy Figure 8 into your notebook. T/I C
Use light rays to locate the image on the diagram.
(a) Add light rays to the diagrams to locate the image
for each object. screen

(b) Describe the image characteristics for each object.

(i)
2F  F F 2F

(i)
2F  F F 2F
screen

(ii)
2F  F F 2F

(ii)
2F  F F 2F
Figure 10

5. Why does a diverging lens never produce a real

image? K/U
6. How is the virtual image produced by a converging lens
(iii) different from the virtual image produced by a diverging
2F  F F 2F
lens? K/U
7. Write a general statement that is valid for both kinds of
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lenses that summarizes the relationship between the type
and the attitude of the image. K/U T/I
(iv) 8. When you watch a movie projected onto a screen, you are
2F F F 2F  seeing an image. Traditional-style movie projectors include a
light and a lens to project the picture onto the screen. T/I C
Figure 8 Ontario Science 10 SB (a) What type of lens is used in the projector? Explain.
0-17-635528-6 (b) Draw a ray diagram that includes the film (the object),
FN C13-F20-UDOS10SBthe lens, and the image on the screen.
3. Copy Figure 9 into your notebook. Use light rays to
CO CrowleArt Group
(c) Describe the characteristics of this image.
locate F. T/I C C13-F18-UDOS10SB.ai
Deborah Crowle
object
Pass 1st pass
Approved
Not Approved

image
Figure 9
e 10 SB

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Deborah Crowle
1st pass

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NEL 13.3 Images in Lenses 561