Unit
7.2
context
Focusing devices:
Lenses and curved mirrors
Light rays often need to be controlled
and focused to produce images in optical
instruments such as microscopes,
cameras and binoculars, and to change
the focus for people wearing contact lenses
or glasses. We can control and focus light by
using lenses and curved mirrors. Lenses use
refraction to focus light. Curved mirrors
use reflection.
Orientation
Images can be the same way up as the original object.
If so, they are referred to as being upright. Inverted
images are those that have been turned upside-down.
Fig 7.2.1 Curved mirrors focus light into a point. Here an array of
curved mirrors is being used to focus sunlight on a tower to boil water
and generate electricity.
The language of optics
Lenses and curved mirrors focus light to produce a
variety of different types of images. Special terms are
used to describe the images formed.
226
Real and virtual
Images are either real or virtual.
Virtual images do not have light rays actually
passing through them. Instead, they are found by
extending the light rays until they cross. Virtual images
cannot be ‘captured’ on a screen or directly on film. The
image seen in the bathroom mirror is virtual.
Real images are formed wherever light rays cross.
Real images are difficult to see as they ‘float’ in space
and need to be ‘captured’ on a wall, a sheet of paper or a
screen. Once captured, they are easily seen and can
actually be touched. The light energy contained in a
real image will cause reactions in chemicals on
photographic film which will permanently record the
image. This cannot be done with a virtual image. A
projector produces a real image that cannot be seen
until a screen is placed in its way.
Magnification
An image is described as enlarged if it is bigger than
the original object. It is described as diminished if it
is smaller.
Magnification specifies exactly how enlarged or
diminished the image is. To calculate magnification,
divide the size of the image by the size of the object.
For example, if a 2 cm object produces a 10 cm image,
then its magnification is 10 " 2 # 5 times. If the image
is diminished, then magnification will be a fraction.
For example, if an object is 8 cm high and the image
is 4 cm, then its magnification is 4 " 8 # ½ or 0.5.
Lenses
The two main types of lenses are:
• convex lenses—these curve outwards
Prac 1
and are fatter in the middle
p. 234
• concave lenses—these curve inwards
(a little like a cave) and are thinner in the middle.
Convex lens
parallel rays of light
F
principal axis
focal
length
Concave lens
F
principal axis
parallel rays
of light
focal
length
Fig 7.2.2 The focus can be found by shining light rays directly onto the
lens. The focus of a convex lens is very obvious. The focus of a concave
lens is not as obvious but can be found by tracing back the refracted rays.
Prac 2
p. 235
7.2
• Real images—if the object is at a distance greater
than the focal length of the lens, an inverted real
image is formed. A real image can be projected onto
a screen or even onto film, which will then
permanently record the image.
• Virtual images—if the object is at a
distance less than the focal length of the
lens, a magnified, upright virtual image is
formed. This image can’t be projected
onto a screen.
Unit
Convex lenses
Convex lenses produce two different types of images,
depending on where the object is located.
Fig 7.2.3 The shape of a
lens can affect its focal
length.
strong lens
weak lens
short focal
length
long focal length
Fig 7.2.4 A real image is
Convex lens
Ray tracing diagram
formed by a convex lens
when the object is beyond
the focus.
What you see
screen
focus
focus
object
real image
focus
real
image
object
a scale drawing that allows you to predict the size
and location of the image produced by the lens
Fig 7.2.5 A virtual image
Convex lens
Ray tracing diagram
What you see
virtual
image
is formed by a convex
lens when the object is
inside the focus. This is
how a simple magnifying
glass works.
virtual
image
focus
focus
object
eye traces rays back to form a virtual image
227
Focusing devices
Concave lenses
Concave lenses produce only upright, diminished virtual images.
Ray tracing diagram
What you see
eye traces
rays back
to form a
virtual image
object
focus virtual
image
virtual
image
object
Fig 7.2.6 Virtual image formation in a concave lens.
Finding the focal length
Rays coming into a lens from a distant object are almost parallel
and form an image very close to the focus. Focal length can be
found by measuring the distance from the lens to the image.
approximate focal length
distant object
almost parallel rays
convex lens
real, inverted image
Fig 7.2.7 An image of a distant object can be used to find the approximate focal length of a convex lens.
Science
Clip
Worksheet 7.3 Lenses
Prac 3
p. 236
Focusing devices
The eye
Focusing in the eye is performed in two stages by two
separate lenses. Most of the focusing is performed when
the light first enters the eye and passes into the cornea.
The cornea is a curved transparent membrane that acts
as half a convex lens. The cornea collects the light rays
228
What’s in a name?
The word ‘lens’ means ‘lentil’ in
Latin. Lentil seeds have the same
shape as small convex lenses.
from the world around us and helps them to converge
onto a second lens sitting just behind the cornea. The
curvature of the second lens is adjustable and focuses the
light rays on to the back of the eye where the retina
detects the images and sends them to the brain.
light rays
object
Eye for an eye
cornea
The ciliary muscles stretch and relax
the jelly-like lens in the human eye so
it gets thinner or thicker. Its curvature
therefore changes, allowing us to focus
on objects at different distances.
pupil
7.2
Clip
lens
Unit
Science
image
Prac 4
p. 237
Fig 7.2.8 Light from an object is focused first by the cornea and then by the lens, which projects a
real image onto your retina. The image projected onto the back of our eye is actually upside-down but
our brain automatically inverts the image.
missing
<<SF3_2_7_02_10>>
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<SF3_2_7_02_10>>
Fig 7.2.9 A magnifying glass is
a simple microscope that helps
you see small objects.
Magnifying glass
A magnifying glass is a simple microscope consisting of
a single convex lens—allowing you to view small
objects. For the magnifying glass to work, the object
being viewed must be less than one focal length from
the lens. However, this creates a virtual image that
cannot be projected onto a screen. Therefore you need
the lenses in your eye to refocus the diverging light rays
to form a real image on the back of your eye—allowing
you to view the magnified image.
229
Focusing devices
virtual image formed
by eyepiece lens
convex eyepiece
lens (thick)
telescope
F
real image formed
by objective lens
convex objective
lens (thin)
Fig 7.2.10 When you look through a telescope you see an image of
an image.
concave mirror
parallel rays of light
Telescopes
Telescopes make small, distant objects appear larger. By
itself, a single lens will only produce smaller images of
objects a long way away. The stars and the Moon would
appear even smaller! In order to produce a magnified
image of such objects, two lenses are used. The objective
lens in a telescope produces a real, inverted image just
inside the focus of a second lens, called the eyepiece
lens. The image produced by the first lens now acts as
the object for the second lens. Because the first image is
inside the focus of the second lens, the second image
(the one seen by the telescope user) is virtual and
enlarged compared to the first one.
The thinner the first lens (objective lens), the larger
the first image. But thin lenses have longer focal
lengths—this is why telescopes are long instruments.
A telescope is focused by adjusting the distance between
the two lenses. The image produced by a simple
telescope is upside down, but this is usually not
important when viewing objects such as planets and
stars.
Curved mirrors
Prac 5
Curved mirrors and lenses have many
p. 237
similarities. Like lenses, curved mirrors have
a principal focus and a focal length. Curved mirrors
can also form both real and virtual images. As a result,
mirrors can also be used to magnify and project images.
There are two main types of curved mirrors:
• convex mirrors—these bulge out in the middle
• concave mirrors—these are thinner in the middle.
230
principal axis
focus
focal length
convex mirror
parallel rays of light
principal axis
focus
focal length
Fig 7.2.11 The focus of a curved mirror can be found by shining light
rays directly onto it. The focus of a concave mirror is very obvious. The
focus of a convex lens is not as obvious, but it can be found by tracing
back the reflected rays.
Concave mirrors
Concave mirrors produce an enlarged (magnified)
virtual image of an object placed close to the mirror.
These enlarged close-up views make them useful when
shaving or applying makeup, or when a dentist needs to
look at some tooth decay.
focus
object
outside
the focus
7.2
object is held at a
large distance from a
concave mirror, a
real, inverted image is
produced.
Unit
Fig 7.2.12 If an
Ray tracing diagram
What you see
real
image
Fig 7.2.13 When an
object is a very large
distance from a
concave mirror but
directly in front of it,
a very small, real
image is produced at
a point known as the
‘focus’.
focus
light from distant object
image of distant object
Convex mirrors
Convex mirrors gather rays of light from a wide area to
produce a smaller, virtual image behind the mirror.
Convex mirrors are useful when a wide view is needed.
They are used in shops for security across the whole
store, at dangerous intersections where vision is difficult,
and in some car rear-vision mirrors to give a wider view
of what is behind the car.
Worksheet 7.4 Mirrors
Prac 6
p. 238
Prac 7
p. 238
Fig 7.2.14 A convex mirror produces a wider view than a flat mirror.
virtual
image
object
focus
Ray tracing diagram
What you see
Fig 7.2.15 A convex mirror produces only virtual, smaller images.
231
Focusing devices
7.2
QUESTIONS
Remembering
a
1 Recall the two main types of lenses and curved mirrors,
sketching and naming each type.
2 Draw a diagram to recall how to find the focal point
of a concave:
a mirror
short-sightedness
retina
distant
object
b
eye
long-sightedness
retina
b lens
close
object
3 Specify the two parts of the human eye that focus light.
Understanding
eye
4 Define the terms:
Fig 7.2.16
a focal length
Applying
b principal axis
c myopic
10 Copy the lenses in Figure 7.2.17 and identify each as concave
or convex.
d hyperopic L
5 At the movies you see real images, not virtual ones. Explain
how you can tell.
6 Copy the following and modify any incorrect statements so
that they become true.
a Real images formed by convex lenses are always bigger
than the original object.
b Virtual images formed by convex lenses are always bigger
than the original object.
c Concave lenses can form only virtual images.
d Images in a concave lens are always the right way up.
e Real images in a concave lens are always the right way up.
7 Use the ray tracing diagrams (pages 227 and 228) to describe
what happens to the image when a distant object is brought
closer to:
Fig 7.2.17
11 Copy and complete the ray tracing diagrams in Figure 7.2.18
to demonstrate the path taken by the light rays.
a
F
a a convex lens
b a concave lens
F
b
8 Describe how a lens or mirror could be used to start a fire.
9 An image must be formed on the retina for it to be seen clearly.
Explain how convex and concave lenses are used in spectacles
and contact lenses to correct each vision defect shown in Figure
7.2.16. Illustrate your answers with a diagram.
232
F
Fig 7.2.18
F
Unit
a a convex lens
b a concave lens
13 Convex lenses can form real images, virtual images and an
unfocused blur. Identify where the object would need to be to
produce each type of image.
14 A camper is using a magnifying glass to set a piece of paper
on fire. Identify what type of lens is being used and what the
‘hot spot’ on the paper is an image of.
15 Demonstrate what the following terms mean by re-drawing
the stick figure in Figure 7.2.19:
a inverted
19 A curved mirror produces a large upright image when held
close to an object. Identify the type of mirror it is likely to be.
Analysing
20 A convex lens can produce an enlarged image of an insect.
Analyse why it can’t produce an enlarged image of the Moon.
7.2
12 The terms diverging (moving apart) and converging (coming
together) may be used to describe lenses. Identify which term
applies to:
Evaluating
21 You have two lenses—one thick and one thin—to build a
telescope. Propose which one you should use for the eyepiece
and which one for the objective lens.
Creating
22 Construct a diagram that shows why no image is formed of an
object placed at the focus of a convex lens.
23 Figure 7.2.20 shows the image of a person as seen in a
dessert spoon.
b magnified
c diminished
a Identify whether the spoon is acting as a lens or a mirror
and whether it is convex or concave.
b Use the language of optics to describe the image as fully
as you can.
c Construct a ray diagram showing how the image was
formed in the spoon.
Fig 7.2.19
16 You look into a magnifying glass at an ant.
a State whether you can touch the ant or its image.
b Identify whether the image is real or virtual.
17 Calculate the magnification in each case for images produced
by various lenses. N
Object height
Image height
2 cm
6 cm
5 cm
20 cm
25 mm
5 mm
16 mm
4 mm
8 mm
160 mm
18 Identify which type of mirror would be best for use:
a at a dangerous intersection
b by a dentist
Fig 7.2.20
.2.20
233
Focusing devices
7.2
INVESTIGATING
Investigate your available resources (for example, textbooks,
encyclopaedias, internet) to complete the following tasks.
1 Research the history of an optical instrument such as the
telescope or camera. Include the following information:
a what causes the defect
a who invented it and when
b the symptoms displayed (include diagrams if applicable)
b what improvements have been made over the years
and by whom
c any treatment(s) available to control or cure the defect.
c a diagram of the first instrument developed and a diagram
of a modern version of this instrument—include a
discussion of some of the differences or improvements
between the original and modern versions of the
instrument.
Present your information in a written report that includes a
timeline. L
7.2
Present your research as an information leaflet that may be
found in a doctor’s surgery. L
e –xploring
To explore how telescopes, microscopes, binoculars
and cameras work, a list of web destinations can be
found on Science Focus 3 Second Edition Student Lounge.
PRACTICAL ACTIVITIES
1 Water lenses
Aim
To investigate how water droplets can be used as a lens
Equipment
•
•
•
•
2 Research one type of sight defect such as long-sightedness,
short-sightedness, cataracts, night blindness or colour
blindness. Find out the following information:
eye dropper or pipette
a printed A4 sheet of glossy paper with fonts of various sizes
small beaker of water
wire loop as shown in Figure 7.2.21
Method
Part A
1 Use the eye dropper or pipette to place droplets of water on
the printed A4 sheet.
2 Observe how the size of the droplet affects the appearance of
the text below it.
Part B
Does it matter if a lens is hollow on the inside? Will
curved surfaces with nothing (but air) in between have
the same effect as a solid lens? Design your own
experiment to examine these questions.
?
Questions
1 Identify if the water droplet is behaving as a convex or a
concave lens.
2 Explain why text below a smaller droplet appears bigger.
Fig 7.2.21
234
DYO
Unit
7.2
2 Lenses and a light box
Aim
To investigate the refraction of light through various lenses
Equipment
•
•
•
•
ray box
light box and multiple-slit slide
12 volt power supply
light box lenses set
sheet of paper
Method
lens
1 Adjust the light box (using the knob on top) to produce a wide
beam of light with parallel edges on a piece of paper.
2 Direct a wide beam of light through a lens shape with no slide
inserted in the light box.
3 Now use the slide with multiple slits to direct several parallel
beams of light through the lens. Use a pencil to mark parts of
the light paths.
Fig 7.2.22
4 Remove the lens and light box from the paper and rule the
complete light paths.
5 Repeat steps 1 to 4 for several different lenses, including
concave lenses. (Use a new piece of paper in each case.)
Questions
1 Describe in words the effect of:
a a convex lens
b a concave lens
2 Compare the light path through a wide convex lens with that
through a thin one.
3 Identify whether there are any individual light rays that are not
bent by the lens in each case.
4 What were the focal lengths of the lenses you used? Construct
a trace or sketch of each lens and write the focal length under
each one.
>>
235
Focusing devices
3 Images in a convex lens
Aim
To investigate the image formed by different convex lenses
Equipment
•
•
•
•
•
•
convex lens
concave lens
white card or screen
plasticine or lens holder
metre ruler
candle or small globe with power supply
Fig 7.2.23
6 Attempt to repeat this experiment with a concave lens and
record your results.
Method
1 Set up your apparatus as shown in Figure 7.2.23.
2 Determine the focal length of your lens by using it to form an
image of a window 5 metres or more away on your card/
screen. Measure the distance of the image/screen from the
lens—this is the focal length.
3 Use your apparatus to obtain the sharpest possible image on
the screen with the candle or lamp more than two focal
lengths from the lens. A darkened room will help.
Copy the table below, and record your measurements.
5 Repeat for the other positions described in the table below.
Questions
1 Describe what happened as the object was brought closer to
the lens.
2 Summarise the circumstances in which:
a a real image (on a screen) is obtained
b a virtual image (one that cannot be ‘caught’ on a screen)
is obtained
c no image is obtained
3 Assess whether it is possible to form a real image (one that
may be ‘caught’ on a screen) using a concave lens.
4 Explain how the image changes as the object-to-lens distance
is varied.
Convex lens focal length: _________ cm
Object
Diagram
Description of position
Object more than two focal lengths
from lens
Object two focal lengths from lens
Object between one and two focal
lengths from lens
Object less than one focal length from
lens (i.e. object inside the focal length)
Object exactly at the focus (one focal
length from lens)
236
Image
Distance from
lens (cm)
Distance from
lens (cm)
Description (e.g.
larger/smaller,
inverted/upright)
Unit
3 Record at what point the image becomes unrecognisable.
Aim
4 Simulate an eye that is long-sighted by moving the screen
towards the lens and describe what happens to the image.
To investigate the images formed by convex and concave mirrors
5 Record at what point the image becomes unrecognisable.
Equipment
6 Refocus the image then cover ¹/³ of the lens with the extra
piece of card and record what happens to the image.
•
•
•
•
•
•
convex lens
white card or screen
extra piece of card
plasticine or lens holder
metre ruler
candle or small globe with power supply
Method
1 Set up your apparatus as shown in Figure 7.2.23 (Prac 3) so
that you project a sharp, well-focused image onto the screen.
2 Simulate an eye that is short-sighted by moving the screen
away from the lens and describe what happens to the image.
7 Increase the fraction of the lens that is covered by the card
and record your observations.
Questions
1 Calculate the percentage difference between the focal point
and the position where the image becomes unrecognisable for
long- and short-sighted simulations.
2 Describe what happens to the image as more of the lens is
blocked by the card.
3 Explain what this tells us about how the lens forms the image
and draw a ray diagram to demonstrate your explanation.
objective lens
5 Telescopes and microscopes
Aim
To investigate how telescopes and microscopes form images
7.2
4 Simulating imperfect vision
translucent screen
Equipment
• two convex lenses—one thin (e.g. focal length 25 cm) and
one thick (e.g. focal length 5 cm)
• cardboard
• scissors
• tracing paper or other translucent material (e.g. thin plastic
from a shopping bag)
• lamp
• small object to view
eyepiece lens
Fig 7.2.24
Method
Part A: The telescope
1 Construct and assemble the apparatus as shown in
Figure 7.2.24.
2 Place the object a large distance (e.g. 1 metre) from the
objective lens, and move the eyepiece lens and screen to obtain
the sharpest possible image looking through the eyepiece lens.
Note the size of the image compared with the object.
3 While looking through the eyepiece lens and observing the
image, remove the screen. You should still see the image!
Think about why.
Part B: The microscope
1 Now move the object close to the lens (but not closer than the
focal length).
2 Adjust the position of the lenses to obtain an image that is
larger than the object.
Questions
1 Distinguish between a telescope and a microscope.
2 Describe how the removal of the screen changes the image in
Part A (step 3) above.
237
Focusing devices
6 Exploring curved surfaces:
spoons
Aim
To explore the properties of the images reflected in the curved
surfaces of spoons
Equipment
Method
1 Place the concave side of a metal soup spoon very close to
your eye and describe what you see.
2 Move the spoon away from your eye and describe
your observations.
3 Repeat this procedure for the convex side of the spoon.
Questions
• metal soup spoon
1 Identify when the images you are viewing are real images and
when you are viewing virtual images.
2 Explain why the image in the concave side of the spoon
inverts as you move the spoon further away.
7 Forming images with curved
mirrors
Method
Part A: Concave mirror
1 Arrange the apparatus as shown in Figure 7.2.25.
Aim
2 Move the screen until you obtain a clear image of the candle.
To investigate the images formed by convex and concave mirrors
3 Investigate the different images produced with the candle at
different distances from the mirror. Is there a position where it
is impossible to obtain an image on the screen? Can you see a
virtual image in the mirror?
Equipment
•
•
•
•
convex mirror
concave mirror
candle
screen
Part B: Convex mirror
1 Hold the mirror at arm’s length and look at your image.
2 Gradually move the mirror towards you, noting any changes in
the image as you do so.
screen
Questions
image
concave
mirror
1 Explain what happens to the image as an object is brought
closer to:
a a concave mirror
b a convex mirror
2 Identify which type(s) of image are possible in each
type of mirror.
plasticine
candle (object)
Fig 7.2.25
238