13.1
Lenses and the Formation of Images
OVERALL EXPECTATIONS
Time
• demonstrate an understanding of various characteristics and properties of
light, particularly with respect to reflection in mirrors and reflection and
refraction in lenses
30–45 min
Vocabulary
SPECIFIC EXPECTATIONS
Understanding Basic Concepts
• explain the conditions required for partial reflection/refraction and for total
internal reflection in lenses, and describe the reflection/refraction using
labelled ray diagrams
• describe the characteristics and positions of images formed by converging
lenses, with the aid of ray diagrams
• identify the factors, in qualitative and quantitative terms, that affect the
refraction of light as it passes from one medium to another
• converging lens
• diverging lens
• optical centre
• principal focus
Assessment Resources
Assessment Rubric 1:
Knowledge and
Understanding
Assessment Summary 1:
Knowledge and
Understanding
Other Program Resources
KEY CONCEPTS
Science Perspectives 10
website www.nelson.com
/sciencepersectives/10
• A lens is a transparent object used to change the path of light.
• Parallel light rays are refracted through a focus when they pass through a
converging lens.
Related Resources
EVIDENCE OF LEARNING
Gizmos: Refraction
Look for evidence that students can
Gizmos: Ray Tracing
(Lenses)
• distinguish between the shapes of converging and diverging lenses
• understand the properties of converging and diverging lenses
Kirkland, Kyle, and Sean
M. Grady. Optics, Facts
on File Library. Infobase
Publishing, 2006.
• understand how light achieves a principal focus point after passing through a lens
SCIENCE BACKGROUND
Lenses
• The Nimrud lens is the oldest lens
on record, dating back 3000 years
to ancient Assyria. Experts disagree
as to whether it was a burning glass
used to start fires or a true magnifying
glass for close-up viewing. Simple
glass lenses are shown in Egyptian
hieroglyphs dating back to the
8th century BCE. The Greeks had
burning glasses as well, which
featured a pair of convex lenses to
focus and intensify the Sun’s rays
into a super hot point. The Romans
noted that the emperor Nero used an
“emerald” to watch the gladiators
fight, which is presumed to have been
a lens to improve sight.
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▼
• A lens is an optical device with axial
symmetry, which means its shape is
a perfect or approximately perfect
arc from a central point, including a
flattened outer edge. A lens is usually
formed from glass, transparent plastic,
or living tissue, but other transparent
materials, such as water or paraffin
wax, can act as a lens as well. A lens
transmits or allows light to pass through
it but can also refract or redirect the
path of light. A simple lens consists
of a single optical element, whereas a
compound lens has a combination of
simple lenses that together can provide
a single coherent image.
▼
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• The word lens comes from the lentil
plant. A double convex lens is shaped
like a lentil. Early Muslim physicist and
mathematician Ibn Sahl (940–1000 CE)
used formulas to calculate the shape
of lenses. Ibn al-Haytham (965–1038)
(Section 13.5) wrote the Book of
Optics, which was the first major
work on the topic and also contained
historical proof of the use of a
magnifying lens. This was a convex
lens that magnified an image. After
the Book of Optics was translated into
Latin in the 12th century, it influenced
many other scientists.
• Other early lens examples include the
Visby lenses, which were rock crystals
polished into a smooth, rounded
shape. The Visby lenses were found
in a Viking gravesite in Greenland
and were mounted in silver. They may
have been worn as a pendant and
could have been used to start fires, as
their optic qualities were comparable
to modern glass. Visby lenses may
have been a trading item from
another culture, but other evidence
from Viking sites indicates that rock
crystals were polished and worked
locally as jewellery or lenses. They
may have also been “reading stones”
used to magnify text. The invention
of spectacles in the 1200s rendered
reading stones unnecessary, although
modern versions are made of plastic
and still used today.
• There are two basic lens shapes:
converging and diverging. Converging
lenses cause incident parallel rays of
light to pass through a single point
after refraction. Diverging lenses cause
incident parallel rays of light to diverge
after refraction.
• For converging lenses, the optical
centre (O) is the exact centre of a lens.
The principal focus (F) is a point on
the principal axis through which all
refracted rays converge.
• For a diverging lens, the principal focus
is the point at which the diverging rays
would converge if projected backward.
POSSIBLE MISCONCEPTIONS
Identify
• Students may confuse converging and diverging lenses.
Clarify
• Explain that a converging lens is a convex lens, whereas a diverging lens is
concave. Light comes together or converges after it passes through a converging
lens, whereas it spreads out or diverges from a diverging lens. A converging lens
can form real images. Diverging lens images are always virtual.
Ask What They Think Now
• At the end of the section ask, When a real image forms from a lens, what kind
of lens must it be? Students should be able to recognize that only a converging
lens can produce a real image.
TEACHING NOTES
Engage
• Ask students how many different items with lenses they can name that
they use in everyday life. The list may include eyeglasses, cameras, movie
projectors, flashlights, overhead projectors, magnifying glasses, microscopes,
and electronic motion sensors. Discuss some of the devices. For example, for
a camera, ask, What function does the lens serve in a camera? Students should
be able to determine that the lens serves to focus an image of real-world
objects on the sensor (or film) inside the camera. Explain that in this section,
they will be learning how lenses form images—a concept that has important
real-world applications.
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Unit E: Light and Geometric Optics
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Explore and Explain
• Have students examine the illustrations and photos of lenses and light. Copy
some of these on the board and trace the rays of light. Ask students to trace
the rays on the images in their book with their fingers. Suggest that they trace
more than one of the beams of light to record the total effect of refraction
through a lens. Remind students to note the direction of arrows on each
beam of light, as this is important for understanding the function of any lens.
• Explain to students that the shape of the lens determines the action of the light
rays passing through it. Trace how a concave lens brings light into the principal
axis and a convex lens spreads light out away from the principal axis as it
emerges from the lens. Make sure students understand that you must project
diverging rays backward to see how a virtual image forms in a diverging lens.
• Go through the lens terminology. Draw a diagram like Figure 4 on page 552
of the Student Book on the board. Point to each term and define the term:
O, the optical centre; F, the principal focus; F´, the secondary principal focus;
the principal axis. Repeat this process for Figure 5 on page 553, a diverging
lens. Have students draw the diagrams in their notebooks and make notes to
help them remember these key terms.
• Emphasize the key difference between a converging and diverging lens. In the
converging lens, F, the principal focus, is on the opposite side of the lens as
the incoming light rays; in a diverging lens, F is on the same side of the lens
as the incoming light.
• Students may fail to understand the significance of the paragraph explaining
the actual path of light through a lens and the “shortcut” path of light.
Explain that without the shortcut, finding the path of the light would be a
complex process that would involve using the index of refraction for both the
air and the lens.
Extend and Assess
• Conclude the lesson by drawing one converging lens and one diverging lens
on the board. Invite volunteers to identify and label the following features
in each lens: O, the optical centre; F, the principal focus; F´, the secondary
principal focus; the principal axis; the central line. Discuss similarities and
differences between the two lens types. Ask, Which lens has F on the same side
as the light entering the lens? (diverging) Which lens has F on the opposite side
of the light entering the lens? (converging). Finally, have students speculate
the answer to this question: Which type of lens is likely to create a real image?
Inform students that they will learn the answer to this question and will learn
about images formed in these lenses in the next two sections.
• Have students complete the Check Your Learning questions on page 519
of the Student Book.
CHECK
YOUR LEARNING
Suggested Answers
1. Your eyes use lenses to see the world. An understanding of lenses can also be helpful in taking better photographs.
Scientific and everyday devices such as telescopes, microscopes, surveying equipment, and binoculars use lenses.
2. In a converging lens, light rays come together, or converge, after refraction; in a diverging lens, light rays spread
out, or diverge, after refraction.
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3. (a) Two refractions. The diagram should show the incident light ray bending toward the normal as it hits the lens,
then bending away from the normal as it exits the lens on the other side.
first refraction
second refraction
(b) We only care about the directions of the ray entering and leaving the lens, and a central dashed line shows this
with one refraction.
4. Yes, there is a focus on each side of the lens at the same distance from the optical centre. This is because the
converging lens has a symmetrical shape and will behave the same way if light is shone on it from the opposite side.
5. Yes, I can tell these lenses apart by feeling their shape. The converging lens will feel thicker in the middle than at
the ends; the diverging lens will feel thinner in the middle than at the ends.
6. (a) The principal focus of a converging lens is located on the side opposite where incident light enters. This is
where the refracted rays come together or converge to a common point.
(b) The principal focus of a diverging lens is located on the same side as the incident light entering the lens.
(c) They are different because one curves in and the other curves out, causing light to take a different path through them.
DIFFERENTIATED INSTRUCTION
At Home
Ask students to look
around their homes
for examples of both
converging and diverging
lenses. Ask them to make
a list of the objects they
find that contain lenses
and to bring it to class the
next day if possible. Begin
the next day’s class with
a discussion of the items
that students identified in
their homes as containing
lenses.
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• Assess visual/spatial learners’ understanding of the lesson by challenging
them to create a poster for the class that includes labelled diagrams of both
converging and diverging lenses, showing F (principal focus), F´ (secondary
principal focus), O (optical centre), the principal axis, and rays of light
entering and exiting the lens.
• Have verbal/linguistic learners work together to define and describe the terms
and features of the poster described above. Bodily/kinesthetic learners can use
a pointer to trace the path of light in each situation while verbal/linguistic
learners describe events.
• Bodily/kinesthetic learners can demonstrate their understanding by showing
how both converging and diverging lenses work using hand and body
motions. As suggested above, bodily/kinesthetic learners can work together
with verbal/linguistic learners to make a joint verbal/kinesthetic presentation.
ENGLISH LANGUAGE LEARNERS
• Have English learners look up converge and diverge in the dictionary. Point
out the prefixes con- and di- as well as the base word verge to help students
make distinctions between converging and diverging lenses. One meaning
of verge is to “incline in a certain direction.” Since con can indicate “coming
together,” the combination of con-verge would mean to “come together in a
certain direction.” Di in this case refers to split in two directions, so diverge
would mean “split in different directions.”
Unit E: Light and Geometric Optics
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