Objectives
• Describe how a lens forms an
image. (30.1)
• Explain what determines the
type of image formed by a lens.
(30.2)
30 LENSES
........
LENSES
THE BIG
• Construct ray diagrams. (30.3)
IDEA
• Distinguish between the types
of images formed by lenses.
(30.4)
• Describe some optical
instruments that use lenses.
(30.5)
• Describe the main parts of the
human eye. (30.6)
• Describe the three common
vision problems. (30.7)
• Describe the types of
aberrations that can occur in
images. (30.8)
discover!
drinking straw,
transparent tape, newspaper,
water, eyedropper
MATERIALS
EXPECTED OUTCOME Students
will observe that the image
of the object depends on
whether the water surface is
convex or concave.
ANALYZE AND CONCLUDE
1. When the water surface
is convex, the image is
magnified. When the
surface is concave, the
image is reduced.
2. The image would be the
same size as the object.
3. Convex lenses form either
real or virtual images.
Concave lenses always form
reduced virtual images.
602
Lenses change
the paths of light.
A
light ray bends as it enters glass and bends
again as it leaves. The bending (refraction) is due to the difference between
the average speed of light in glass and the average speed in air. Light passing through glass of
a certain shape can form an image that appears
larger, smaller, closer, or farther than the object
being viewed. For example, magnifying glasses have
been used for centuries and were well known to the early
Greeks and medieval Arabs. Today, eyeglasses
allow millions of people to read in comfort, and cameras, telescopes,
and microscopes widen our
view of the world.
discover!
What Types of Images Are Formed by
Convex and Concave Lenses?
1. Cut off a one-centimeter length from the end
of a drinking straw.
2. Cover one end of the short straw segment
with a piece of transparent tape.
3. Place the taped end of the straw over a
small object such as a letter or numeral
in a newspaper.
4. Use an eye dropper, or the longer segment of
the straw, to fill the short piece of the straw
with water. Add water until the surface bulges
outward above the top of the straw.
5. View the object through the straw from the
time the water forms a convex surface until,
as the water leaks out, the surface of the
water becomes concave.
602
Analyze and Conclude
1. Observing Describe the appearance of the
image of the object as seen through the
water when the surface of the water was
convex and when it was concave.
2. Predicting How would the image appear if
the surface were flat, that is, neither convex
nor concave?
3. Making Generalizations What types of images
do you think are formed by convex and
concave lenses?
30.1 Converging and Diverging
Lenses
A lens is a piece of transparent material, such as glass, that refracts
light. A lens forms an image by bending rays of light that pass
through it.
Learning about lenses
is a hands-on activity.
Not manipulating
lenses while learning
about them is like taking swimming lessons
out of water.
Shapes of Lenses The shape of a lens can be understood by considering a lens to be a large number of portions of prisms, as shown
in Figure 30.1. When arranged in certain positions, the prisms bend
incoming parallel rays so they converge to (or diverge from) a single
point. The arrangement shown in Figure 30.1a is thicker in the middle; it converges the light. The arrangement in Figure 30.1b is thinner
in the middle; it diverges the light.
30.1 Converging
and Diverging
Lenses
FIGURE 30.1
A lens may be thought of as
a set of prisms. a. Incoming
parallel rays converge to a
single point. b. Incoming
rays seem to diverge from a
single point.
In both arrangements, the most net bending of rays occurs at the
outermost prisms, for they have the greatest angle between the two
refracting surfaces. No net bending occurs in the middle “prism,” for
its glass faces are parallel and rays emerge in their original direction.
Real lenses are made not of prisms, of course, but of solid pieces
of glass or plastic with surfaces that are usually ground to a spherical shape. Figure 30.2 shows how smooth lenses refract rays of light
and form wave fronts. The lens in Figure 30.2a is a converging lens.
A converging lens, also known as a convex lens, is thicker in the
middle, causing rays of light that are initially parallel (straight wave
fronts) to meet at a single point called the focal point. The lens in
Figure 30.2b is a diverging lens. A diverging lens, also known as
a concave lens, is thinner in the middle, causing the rays of light
to appear to originate from a single point.
This chapter is an extension
of the previous chapter. It
applies refraction to lenses,
and introduces the ideas of
ray optics. It may be omitted
without consequence to the
chapters that follow.
Key Terms
lens, converging lens,
convex lens, diverging lens,
concave lens, principal axis,
focal point, focal plane,
focal length
Teaching Tip Distribute
diverging and converging lenses
to your students. Let them
play with the lenses for a few
minutes. Ask them to describe
what they see. Point out the need
to define terms and then do so.
Demonstration
Show, with an actual prism,
how a prism refracts a ray
of light. Then introduce ray
tracing on the board.
FIGURE 30.2
Wave fronts travel more
slowly in glass than in air.
a. In the converging lens,
the wave fronts are retarded
more through the center of
the lens, and the light converges. b. In the diverging
lens, the waves are retarded
more at the edges, and the
light diverges.
CHAPTER 30
LENSES
603
Teaching Tip Contrast the
deviation of light in a prism with
the absence of deviation in a
pane of glass. Show that a pane
only displaces light rays, and
show how thicker panes produce
greater displacements.
603
Teaching Tip Discuss the
key features of a converging
lens (Figure 30.3). Sketch a ray
diagram for parallel light along
the principal axis to define the
focal point.
......
Key Features of Lenses Figure 30.3 illustrates some important
features of a lens. The principal axis of a lens is the line joining the
centers of curvature of its surfaces. The focal point for a converging
lens is the point at which a beam of light parallel to the principal axis
converges. The focal plane is a plane perpendicular to the principal
axis that passes through either focal point of a lens. For a converging lens, any incident parallel beam converges to a point on the focal
plane. A lens affects light coming from the right in the same way as
light coming from the left (or has the same effect on light incident
from either side). Therefore, a lens has two focal points and two focal
planes. When the lens of a camera is set for distant objects, the film is
in the focal plane behind the lens in the camera.
A lens forms an
image by bending
rays of light that pass through it.
CONCEPT
CHECK
Teaching Resources
• Reading and Study
Workbook
• Laboratory Manual 81, 82
• PresentationEXPRESS
FIGURE 30.3 • Interactive Textbook
The key features of a
converging lens include
the principal axis, focal
point, and focal plane.
30.2 Image
Formation by a Lens
Key Term
real image
For a diverging lens, an incident beam of light parallel to the
principal axis is not converged to a point, but is diverged so that the
light appears to originate from a single point. The focal length of
a lens, whether converging or diverging, is the distance between the
center of the lens and its focal point. When the lens is thin, the focal
lengths on either side are equal, even when the curvatures on the two
sides are not.
......
Teaching Tip Allow students
to cast images of the windows
on the wall, or ceiling lights on
their desks, using converging
lenses. Have them cast images of
closer brightly illuminated objects
(bright enough to cast a clearly
seen image).
CONCEPT
CHECK
Ask is there a relationship
between the image distance
(distance from the lens to the
place where a sharp image
appears) and the object distance
(from object to lens)? Yes, the
farther the object, the nearer the
image.
30.2 Image Formation by a Lens
For: Links on lenses
Visit: www.SciLinks.org
Web Code: csn – 3002
604
How does a lens form an image?
604
With unaided vision, an object far away is seen through a relatively
small angle of view, as shown in Figure 30.4a. When you are closer,
the same object is seen through a larger angle of view, as illustrated
in Figure 30.4b. This wider angle allows the perception of more detail.
Magnification occurs when the use of a lens allows an image to be
observed through a wider angle than would be observed without the
lens, and so more detail can be seen. A magnifying glass is simply
a converging lens that increases the angle of view and allows more
detail to be seen. The type of image formed by a lens depends on
the shape of the lens and the position of the object.
Teaching Tip Pass around the
class a box with a pinhole and
a translucent viewing screen on
opposite ends. Using a simple
ray diagram, describe how real
images are formed, and why
they are inverted. Discuss Activity
43 on page 621. Note that the
size of the hole compared to
the distance from the viewing
screen affects the amount of
light that makes the image and
the sharpness of the image. A
larger hole will admit more light,
but overlapping images through
different parts of the hole reduce
sharpness. A large hole covered
by a lens solves both problems.
FIGURE 30.4 With unaided vision, the size of an object appears to change depending
on your distance to the object. a. A distant object is viewed through a
narrow angle. b. When the same object is viewed from a closer distance
and thus through a wider angle, more detail is seen.
Images Formed by Converging Lenses When you use a
magnifying glass, you hold it close to the object you wish to see
magnified. This is because a converging lens will magnify only when
the object is between the focal point and the lens, as shown in
Figure 30.5. The magnified image will be farther from the lens than
the object and right-side up (erect). If a screen were placed at the
image distance, no image would appear on the screen because no
light is actually directed to the image position. The rays that reach
your eye, however, behave as if they came from the image position,
so the image is a virtual image. Recall from Chapter 29 that a virtual
image originates from a location where light does not actually reach.
FIGURE 30.5 A converging lens can be
used as a magnifying glass
to produce a virtual image
of a nearby object.
FIGURE 30.6
A converging lens forms a
real, upside-down image
of a more distant object.
When the object is far enough away to be beyond the focal point
of a converging lens, light originating from the object and passing
through the lens converges and can be focused on a screen, as illustrated in Figure 30.6. An image formed by converging light is called a
real image. A real image formed by a single converging lens is
upside down (inverted). Converging lenses are used for projecting
motion pictures onto a screen.
CHAPTER 30
LENSES
605
Teaching Tip Choose a bright
scene with noticeable depth, so
perspective plays a role when
the scene is viewed from close
positions (for example, from
each eye). Due to perspective,
the images viewed through
far-apart holes are noticeably
different. When these different
images are combined by a lens,
parts of the composite image are
fuzzy. A composite image viewed
through closely spaced holes is
sharp. This is why photographers
take pictures through a small
aperture for “depth of field”
in their photographs. When a
fuzzy background is desirable,
the aperture of the camera is
opened wide. The focal plane is
set for sharpness of the object,
and things closer or farther away
appear fuzzy.
Ask When the aperture
setting of a camera is small,
should the exposure time be
correspondingly longer or
shorter? The smaller aperture
means less light enters, so the
film should be exposed to light
for a longer time.
605
......
The type of image
formed by a lens
depends on the shape of the lens
and the position of the object.
CONCEPT
CHECK
FIGURE 30.7 A diverging lens always
produces a virtual image.
Teaching Resources
• Reading and Study
Workbook
• PresentationEXPRESS
• Interactive Textbook
• Next-Time Question 30-1
Images Through
Ray Diagrams
Key Term
ray diagram
Learning takes place not in
seeing diagrams made, but in
making them. It is fruitless
to show the techniques of ray
diagram construction without
students constructing their
own. Your students should have
a lens in hand, and an object
and image to observe when they
make their constructions. Let
your discussion of this topic be
a class activity.
think!
Why is the greater part of
the photograph in Figure
30.7 out of focus?
Answer: 30.2
Images Formed by Diverging Lenses When a diverging lens
is used alone, the image is always virtual, right-side up, and smaller
than the object, as can be seen in Figure 30.7. It makes no difference how far or how near the object is. A diverging lens is often used
for the viewfinder on a camera. When you look at the object to be
photographed through the viewfinder, you see a right-side up virtual
image that approximates the same proportions as the photograph
to be taken.
CONCEPT What determines the type of image
......
30.3 Constructing
CHECK
formed by a lens?
30.3 Constructing Images Through
Ray Diagrams
Teaching Tip Reproduce
Figure 30.8 on the board using a
different color for each ray. Stress
that the three rays are samples
of an immense number of rays
leaving every part of the object.
If the top part of the lens were
covered, for example, the entire
image would still appear, but it
would be dimmer.
FIGURE 30.8 606
606
In a ray diagram, the three
useful rays from the object
converge on the image.
Ray diagrams show the principal rays that can be used to determine
the size and location of an image. An example of a ray diagram is
shown in Figure 30.8. The size and location of the object, its distance from the center of the lens, and the focal length of the lens are
used to construct a ray diagram.30.3 An arrow is used to represent the
object (which may be anything from a microbe viewed in a microscope to a galaxy viewed through a telescope). For simplicity, one end
of the object is placed right on the principal axis.
The Three Principal Rays To locate the position of the image,
you only have to know the paths of two rays from a point on the
object, represented by the vertical arrow. Any point except for the
point on the principal axis will work, but it is customary to choose a
point at the tip of the arrow.
The path of one refracted ray is known from the definition of the
focal point. A ray parallel to the principal axis will be refracted by the
lens to the focal point, as shown in Figure 30.8.
Another path is known: through the center of the lens where the
faces are parallel to each other. A ray of light will pass through the
center with no appreciable change in direction. Therefore, a ray from
the tip of the arrowhead proceeds in a straight line through the center of the lens.
A third path is known: A ray of light that passes through the focal
point in front of the lens emerges from the lens and proceeds parallel
to the principal axis.
All three paths are shown in Figure 30.8, which is a typical ray
diagram. The image is located where the three rays intersect. Any two
of these three rays is sufficient to locate the relative size and location
of the image.
We use these particular
rays only because their
paths through the lens
are easy to predict. You
should know that all
light passing through
a lens contributes to
image formation.
FIGURE 30.9
The ray diagram for a magnifying glass shows that when
the object is less than one
focal length from the lens
the image is virtual, rightside up, and magnified.
The ray diagram for a converging lens used as a magnifying glass
is shown in Figure 30.9. In this case, where the distance from the lens
to the object is less than the focal length, the rays diverge as they leave
the lens. The rays of light appear to come from a point in front of the
lens (same side of the lens as the object). The location of the image is
found by extending the rays backward to the point where they converge. The virtual image that is formed is magnified and right-side up.
CHAPTER 30
LENSES
607
Teaching Tip Show how
changing the position of the
object changes the position of
the image.
Demonstration
Show students how they
can calculate the diameter
of the sun by measuring the
image of the sun formed by a
pinhole. On a sunny day, go
outside with your class and
call attention to the round
spots of light that are found
beneath trees. Small spaces
between leaves in the trees act
as pinholes and cast images of
the sun on the ground. If the
sun is overhead, the images
will be circles. If it is low in the
sky, they will be ellipses. Hold
a piece of cardboard with a
small hole in it in the sunlight
and note the circle of light
on the ground. Place a coin
over the image and adjust the
position of the pinhole until
the image is the same size as
the coin. (If the image is an
ellipse, the short diameter
of the ellipse should equal
the diameter of the coin.)
Measure the distance from
the pinhole to the image.
The ratio of the diameter
of the image (i.e., diameter
of the coin) to the image’s
distance from the pinhole is
equal to the ratio of the sun’s
diameter to its distance from
the pinhole (150,000,000 km).
Letting x represent the
diameter of the sun, use
the proportion “diameter
of coin/image distance 5
x/150,000,000 km” to calculate
x. Students’ answers should be
approximately 1,400,000 km,
which agrees with the
accepted value.
607
It is quite profound that
average students can calculate
the diameter of the sun armed
only with a meterstick and a
coin! This is a striking example
of how the richness in life is
found by not only looking at the
world with wide-open eyes, but
knowing what to look for. You
are the guide to that richness,
for you are their physics
teacher. How nice that your
students can go home after
school and tell their families
that they measured the sun’s
diameter with a meterstick!
The most profound concepts
in physics are sometimes the
simplest.
FIGURE 30.10 The ray diagrams illustrate
the formation of an image
when the object is at various positions in relation to
a converging lens of focal
length f.
Object position: distance
f from lens (at the focal point)
Image position: at infinity
Object position: between
f and 2f from lens
Image position: beyond 2f from lens
Image size: magnified
Demonstration
Poke an extra hole in your
piece of cardboard and hold
it between a bright region
(window or overhead light)
and a dark viewing area. Two
holes produce two images;
three holes produce three
images; many holes produce
many images—one for each
hole. Place a convex lens
behind (or in front of) the
holes and show that all the
images are focused in one
place. At the proper distance
they neatly overlap to produce
a clear and brighter image.
An appropriately placed lens
simply directs a multitude of
images atop one another!
Object position: distance
2f from lens
Image position: distance 2f from lens
Image size: same as object
Object position: beyond
2f from lens
Image position: between f and 2f from lens
Image size: smaller
Teaching Tip Discuss the rules
for ray diagram construction.
The summary of ray diagram
construction is well worth class
time.
For: Mirrors and Lenses
Visit: PHSchool.com
Web Code: csp – 3003
608
608
Object position: at infinity
Image position: distance f from lens
(at the focal point)
Demonstration
The three rays useful for the construction of a ray diagram are
summarized:
1. A ray parallel to the principal axis that passes through the focal
point on the opposite side.
2. A ray passing through the center of the lens that is undeflected.
3. A ray through the focal point in front of the lens that emerges
parallel to the principal axis after refraction by the lens.
Interestingly, when half
a lens is covered, half
as much light forms the
image. This does not
mean half the image is
formed! Even a piece
of broken lens can form
a complete image on a
screen. Try it and see.
Demonstrate the ray diagrams
in Figure 30.10. Darken the
room and use a candle or an
unfrosted bulb on an optical
bench with length markings.
A converging lens with a focal
length of 20–25 cm works
nicely.
Teaching Tip Draw Figure
30.11 on the board using a
different color for each ray.
Differentiate among the lens, the
principal axis, and the rays.
Ray Diagrams for Converging and Diverging Lenses
The ray diagrams in Figure 30.10 show image formation by a converging lens as an object initially at the focal point is moved away
from the lens along the principal axis. Since the object is not located
between the focal point and the lens, all the images that are formed
are real and inverted.
As illustrated in Figure 30.11, the method of drawing ray diagrams applies also to diverging lenses. A ray parallel to the principal
axis from the tip of the arrow will be bent by the lens as if it had
come from the focal point. A ray through the center goes straight
through. A ray heading for the focal point on the far side of the lens
is bent so that it emerges parallel to the axis of the lens.
Teaching Tip The focal
point of a lens depends on the
curvature and material of the
lens, not on the location of any
object.
Teaching Tip Although ray
diagrams usually show three rays,
there are an infinite number of
rays that can be drawn between
the object and its image.
FIGURE 30.11
......
The ray diagram shows
how a virtual image is
formed by a diverging lens.
The size and location
of the object, its
distance from the center of the
lens, and the focal length of the
lens are used to construct a ray
diagram.
CONCEPT
CHECK
Teaching Resources
• Reading and Study
Workbook
......
On emerging from the lens, the three rays appear to come from
a point on the same side of the lens as the object, which defines the
position of the virtual image. The image is nearer to the lens than the
object, smaller than the object, and right-side up. The image formed
by a diverging lens is always virtual, reduced, and right-side up.
CONCEPT
CHECK
• Concept-Development
Practice Book 30-1
• Laboratory Manual 83, 84,
85, 86
• Transparencies 72, 73
What information is used to construct a ray diagram?
• PresentationEXPRESS
• Interactive Textbook
• Next-Time Question 30-2
CHAPTER 30
LENSES
609
609
30.4 Image
Formation
Summarized
......
Teaching Tip Summarize
converging and diverging lenses,
real images and virtual images,
and image position and object
position.
A converging lens
forms either a real or
a virtual image. A diverging lens
always forms a virtual image.
CONCEPT
CHECK
30.4 Image Formation Summarized
think!
Where must an object be
located so that the image
formed by a converging
lens will be (a) at infinity?
(b) as near the object as
possible? (c) right-side
up? (d) the same size?
(e) inverted and enlarged?
Answer: 30.4
Teaching Resources
• Reading and Study
Workbook
• PresentationEXPRESS
......
• Interactive Textbook
A converging lens forms either a real or a virtual image. A
diverging lens always forms a virtual image.
A converging lens is a simple magnifying glass when the object is
within one focal length of the lens. The image is then virtual, magnified, and right-side up. When the object is beyond one focal length, a
converging lens produces a real, inverted image. The location of the
image depends on how close the object is to the focal point. If it is
close to (but slightly beyond) the focal point, the image is far away
(as with a slide projector or movie projector). If the object is far from
the focal point, the image is nearer (as with a camera). In all cases
where a real image is formed, the object and the image are on opposite sides of the lens.
When the object is viewed with a diverging lens, the image is virtual, reduced, and right-side up. This is true for all locations of the
object. In all cases where a virtual image is formed, the object and the
image are on the same side of the lens.
CONCEPT
CHECK
What types of images are produced by lenses?
30.5 Some Common
30.5 Some Common Optical
Instruments
Optical Instruments
Key Terms
eyepiece, objective lens
Teaching Tip If possible,
show disassembled samples of
the variety of optical instruments
discussed in the text. Note
the simplicity of the diagrams
of these instruments in the
text, compared to their actual
construction.
FIGURE 30.12 In a simple camera, the
lens forms a real, inverted
image on the film.
A valuable lesson is learned
looking for the simplicity
that underlies the seemingly
complex.
Teaching Tip Show students
a camera and its lens. Point out
the diaphragm and the focusing
mechanism.
610
610
The advent of eyeglasses probably occurred in Italy in the late 1200s.
If anybody at the time or before viewed objects through a pair of
lenses held far apart, one in front of the other, there is no record
of it, for curiously enough, the telescope wasn’t invented until some
300 years later. Today, lenses are used in many optical instruments.
Optical instruments that use lenses include the camera, the
telescope (and binoculars), and the compound microscope.
Camera A camera consists of a lens and sensitive film (or lightdetecting chip) mounted in a light-tight box. In many cameras, the
lens is mounted so that it can be moved back and forth to adjust the
distance between the lens and film. The lens forms a real, inverted
image on the film or chip. Figure 30.12 shows a camera with a single
simple lens. In practice, most cameras make use of compound lenses
to minimize distortions called aberrations.
The amount of light that gets to the film is regulated by a shutter and a diaphragm. The shutter controls the length of time that the
film is exposed to light. The diaphragm controls the opening that light
passes through to reach the film. Varying the size of the opening (aperture) varies the amount of light that reaches the film at any instant.
Telescope A simple telescope uses a lens to form a real image of a
distant object. The real image is not caught on film but is projected in
space to be examined by another lens used as a magnifying glass. The
second lens, called the eyepiece, is positioned so that the image produced by the first lens is within one focal length of the eyepiece. The
eyepiece forms an enlarged virtual image of the real image. When you
look through a telescope, you are looking at an image of an image.
Figure 30.13 shows the lens arrangement for an astronomical telescope. The image is inverted, and thus the image of the man on the
moon would appear upside down.
Teaching Tip Tell students
that the telescope was invented
in 1608 by Dutch optician Hans
Lippershey.
FIGURE 30.13 An astronomical telescope
forms an inverted image.
(For simplification, the
image is shown close
here; it is actually located
at infinity.)
Teaching Tip If a refracting
astronomical telescope is
available, show it to the students.
In better telescopes, the primary
lens is combined with a concave
lens.
Teaching Tip Show students
a terrestrial telescope and a pair
of binoculars.
Teaching Tip Borrow a
compound microscope from your
school’s biology department.
Use it to show the class how the
objective lens forms a real image
of the object being viewed and
how the eyepiece forms a virtual
image of the real image.
A third lens or a pair of reflecting prisms is used in the terrestrial
telescope, which produces an image that is right-side up. A pair of
these telescopes side by side, each with a pair of prisms, makes up a
pair of binoculars like those shown in Figure 30.14.
Since no lens transmits 100% of the light incident upon it,
astronomers prefer the brighter, inverted images of a two-lens telescope to the less bright, right-side-up images that a third lens or
prisms would provide. For non-astronomical uses, such as viewing
distant landscapes or sporting events, right-side-up images are more
important to the viewer than brightness, so the additional lens or
prisms are used.
Teaching Tidbit A real
image is formed where light
rays intersect at a single point. A
virtual image is formed by light
rays that only appear to intersect.
FIGURE 30.14 Each side of a pair of
binoculars uses a pair
of prisms that flip the
image right-side up.
Link to TECHNOLOGY
The Digital Camera Rather than focusing an
image onto film, the lens in a digital camera
focuses light onto an array of millions of tiny
light-sensitive semi-conductor photocells. Each
cell produces an electrical signal in proportion
to the amount of light hitting it. Usually,
red, green, and blue filters on the different
photocells make them sensitive to a particular
color of light. All of the intensity and color information is relayed from
the photocell array to a computer chip. Software processes the raw
information to produce an image.
CHAPTER 30
LENSES
611
611
......
Optical instruments
that use lenses
include the camera, the
telescope (and binoculars), and
the compound microscope.
CONCEPT
CHECK
FIGURE 30.15 A compound microscope
uses two converging lenses.
Teaching Resources
• Reading and Study
Workbook
• Problem-Solving Exercises in
Physics 15-1
Compound Microscope A compound microscope uses two
converging lenses of short focal length, arranged as shown in Figure
30.15. The first lens, called the objective lens, produces a real image
of a close object. Since the image is farther from the lens than the
object, it is enlarged. A second lens, the eyepiece, forms a virtual
image of the first image, further enlarged. The instrument is called a
compound microscope because it enlarges an already enlarged image.
• PresentationEXPRESS
• Interactive Textbook
30.6 The Eye
Teaching Tip Borrow a model
of an eye from the biology
department. Use it to show
students the parts of the eye
mentioned in the text.
Teaching Tip Discuss the
function of the rods and cones
in the retina of the eye. Explain
that color cannot be perceived
in dim light, and that colored
stars appear white to us, whereas
they show up clearly colored in
camera time exposures.
......
Key Terms
cornea, iris, pupil, retina
CONCEPT
CHECK
The giant squid has
the largest eyes in the
world.
I show a colored photo that I
took of the stars and discuss
the curved lines encircling the
north star. Then I get into
a discussion of how long the
camera shutter was held open.
Name some optical instruments that use lenses.
30.6 The Eye
In many respects, the human eye is similar to the camera. A diagram
of the eye is shown in Figure 30.16. The main parts of the eye are
the cornea, the iris, the lens, and the retina. Light enters through the
transparent covering called the cornea. The amount of light that
enters is regulated by the iris, the colored part of the eye that surrounds the pupil. The pupil is the opening in the iris through which
light passes.30.6 Light passes through the pupil and lens and is focused
on a layer of tissue at the back of the eye—the retina —that is
extremely sensitive to light. Different parts of the retina receive light
from different directions.
FIGURE 30.16 Light enters the human
eye through the cornea,
passes through the pupil
and lens, and is focused
on the retina.
The retina is not of uniform sensitivity. There is a small region in
the center of our field of view where vision is most distinct. This spot
is called the fovea. Much greater detail can be seen at the fovea than off
to the side.
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612
Demonstration
The Blind Spot There is also a spot in the retina where the nerves
carrying all the information leave the eye in a narrow bundle. This
is the blind spot. You can demonstrate that you have a blind spot in
each eye if you hold this book at arm’s length, close your left eye, and
look at the round dot in Figure 30.17 with only your right eye. You
can see both the round dot and the X at this distance. If you now
move the book slowly toward your face, with your right eye still fixed
upon the dot, you’ll reach a position about 20 to 25 cm from your eye
where the X disappears. To establish the blind spot in your left eye,
close your right eye and similarly look at the X with your left eye so
that the dot disappears. With both eyes opened, you’ll find no position where either the X or the dot disappears because one eye “fills
in” the part of the object to which the other eye is blind. Repeat the
exercise of Figure 30.17 with small objects on various backgrounds.
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FIGURE 30.17
Try to find your blind spot in
each eye.
......
......
CHECK
Teaching Tip Although the
pupil of the eye looks black,
flashbulb photos often show
it to be red. This is largely
because the light from the flash
reflects directly back from the
assemblage of blood vessels on
the retina.
Teaching Tip Tell students
that the particularly bright
reflection from the eye pupils of
many animals when illuminated
at nighttime can cause them to
look luminous. The reflection
from a thin membrane called the
tapetum, located behind the rods
in the animal’s eyes, provides a
“second chance” for the animal
to perceive light that initially
misses a photoreceptor. This
arrangement, common in owls,
cats, and other night predators,
results in excellent night vision.
The Camera and the Eye In both the camera and the eye, the
image is upside down, and this is compensated for in both cases.
You simply turn the camera film around to look at it. Your brain has
learned to turn around images it receives from your retina!
A principal difference between a camera and the human eye has
to do with focusing. In a camera, focusing is accomplished by altering
the distance between the lens and the film or chip. In the human eye,
most of the focusing is done by the cornea, the transparent membrane
at the outside of the eye. Adjustments in focusing of the image on the
retina are made by changing the thickness and shape of the lens to
regulate its focal length, as shown in Figure 30.18. This is called accommodation and is brought about by the action of the ciliary muscle,
which surrounds the lens.
CONCEPT
Stand at a corner of the room
and shake brightly colored
cards, first turned backward
so the color is hidden and
students can adjust the
position of their heads
(looking toward the other
corner of the room). When
they can just barely see the
moving cards at the corners of
their eyes, turn them over and
display the color. Try this with
different colors. Your
students will see the cards
as they move, but not their
colors.
The main parts of the
eye are the cornea,
the iris, the lens, and the retina.
CONCEPT
CHECK
Name the main parts of the human eye.
Teaching Resources
• Reading and Study
Workbook
FIGURE 30.18
The shape of the lens
changes to focus light
on the retina.
CHAPTER 30
LENSES
• PresentationEXPRESS
• Interactive Textbook
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613
30.7 Some Defects
in Vision
Physics on the Job
Key Terms
farsighted, nearsighted,
astigmatism
Photographer
Photography blends art with
physics. A photographer’s ideas
are based on artistry, but the
execution relies on a savvy use of
physics and, for most
photographers now, computer
technology. A photographer
knows that a camera seldom
records just what the eye sees.
Our eyes can discern detail simultaneously both in dark shadows
and in light that is millions of times brighter; neither film nor digital
image sensors can do this. Hence, the photographer experiments
with brightness and contrast. The photographer who has knowledge
of the physics of light and optics is better able to use available
software to turn a digital image into a work of art.
Teaching Tip In Figure 30.19,
it appears that the outside of the
lens is convex and the inside is
concave. This is true, but the lens
is still thicker in the center than
at the edges so it is a converging
lens. Similarly, the lens in Figure
30.20 is a diverging lens. It is
thinner in the center than at the
edges.
Demonstration
Simulate the human eye with
a spherical flask filled with a
bit of fluorescent dye. Paint an
“iris” on the flask and position
appropriate lenses behind the
iris for normal, farsighted and
nearsighted vision. Then show
how corrective lenses placed in
front of the eye focus the light
on the retina.
30.7 Some Defects in Vision
If you have normal vision, your eye can accommodate to clearly
see objects from infinity (the far point) down to 25 cm (the near
point, which normally recedes for all people with advancing age).
Unfortunately, not everyone has normal vision. Three common
vision problems are farsightedness, nearsightedness, and
astigmatism.
Farsightedness A farsighted person has trouble focusing on
nearby objects because the eyeball is too short or the cornea is too
flat so that images form behind the retina. As Figure 30.19 illustrates,
farsighted people have to hold things more than 25 cm away to be
able to focus them. The remedy is to increase the converging effect of
the eye. This is done by wearing eyeglasses or contact lenses with converging lenses. Converging lenses will converge the rays that enter the
eye sufficiently to focus them on the retina instead of behind it.
FIGURE 30.19 The eyeball of the farsighted eye is too short.
A converging lens moves
the image closer and
onto the retina.
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......
Three common
vision problems are
farsightedness, nearsightedness,
and astigmatism.
CONCEPT
CHECK
FIGURE 30.20
The eyeball of the nearsighted eye is too long. A
diverging lens moves the
image farther away and
onto the retina.
Teaching Resources
• Reading and Study
Workbook
• Concept-Development
Practice Book 30-2
Nearsightedness A nearsighted person can see nearby objects
clearly, but does not see distant objects clearly because they are
focused too near the lens, in front of the retina. As depicted in Figure
30.20, the eyeball is too long or the surface of the cornea is too
curved. A remedy is to wear corrective lenses that diverge the rays
from distant objects so that they focus on the retina instead of in
front of it.
• Problem-Solving Exercises in
Physics 15-2
• PresentationEXPRESS
• Interactive Textbook
• Next-Time Question 30-3
30.8 Some Defects
......
Astigmatism Astigmatism of the eye is a defect that results when
the cornea is curved more in one direction than the other, somewhat
like the side of a barrel. Because of this defect, the eye does not form
sharp images. The remedy is cylindrical corrective lenses that have
more curvature in one direction than in another.
CONCEPT
CHECK
of Lenses
Key Term
aberration
Name and describe the three common
vision problems.
discover!
MATERIALS
30.8 Some Defects of Lenses
No lens gives a perfect image. The distortions in an image are
called aberrations. By combining lenses in certain ways, aberrations can be minimized. For this reason, most optical instruments use
compound lenses, each consisting of several simple lenses, instead of
single lenses. Two types of aberration are spherical aberration
and chromatic aberration.
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discover!
paper or cardboard
EXPECTED OUTCOME When the
page is viewed through the
pinhole, the print will be seen
more clearly. When the light
is bright, the pupil (i.e., the
aperture) is smaller.
Someone who can’t
quite read the small print in
a telephone book without his
or her glasses should squint
to reduce the size of the
“aperture” in the eyes.
THINK
Can a Pinhole Improve Your Vision?
1. Poke a tiny hole in a piece of paper or cardboard.
2. Hold the pinhole in front of your eye and close to this
page. Can you see the print clearly?
3. Why is bright light needed?
4. Think What advice do you have for someone who wears
glasses and misplaces them, and can’t see the small print
in a telephone book?
CHAPTER 30
LENSES
615
615
Demonstration
Send a wide beam of white
light through a converging
lens. Make sure that the beam
goes through the edges as
well as the center of the lens.
At the focal point, a circle of
unfocused light is formed due
to the spherical aberration.
Using a diaphragm, show
how the focus is improved
by limiting the aperture. (If
a diaphragm is not available,
use paper or cardboard with
holes of different sizes.) If you
look carefully near the focus,
you’ll note that different
colors focus at different
points.
Aberrations Spherical aberration results when light passes through
the edges of a lens, as in Figure 30.21a, and focuses at a slightly different place from light passing through the center of the lens. This can
be remedied by covering the edges of a lens, as with a diaphragm in a
camera. Spherical aberration is corrected in good optical instruments
by a combination of lenses.
Chromatic aberration is the result of the different speeds of light
of various colors and hence the different refractions they undergo, as
shown in Figure 30.21b. In a simple lens red light and blue light bend
by different amounts (as in a prism), so they do not come to focus in
the same place. Achromatic lenses, which combine simple lenses of
different kinds of glass, correct this defect.
FIGURE 30.21 a. Spherical aberration
occurs when light passes
through the edges of a lens.
b. Chromatic aberration
occurs because different
colors of light travel at different speeds.
In the eye, vision is sharpest when the pupil is smallest because
light then passes through only the center of the eye’s lens, where
spherical and chromatic aberrations are minimal. Also, light bends
the least through the center of a lens, so minimal focusing is required
for a sharp image. You see better in bright light because your pupils
are smaller.
......
Methods for Correcting Vision An alternative to wearing eyeglasses for correcting vision is contact lenses. A more recent option
is LASIK (acronym for laser-assisted in-situ keratomileusis), the procedure of reshaping the cornea using pulses from a laser. Another
recent procedure is PRK (photorefractive keratectomy). Still another
is IntraLase, where intraocular lenses are implanted in the eye like a
contact lens, a procedure of choice for extremely nearsighted or farsighted people and for those who can’t have laser surgery. The wearing of eyeglasses and contact lenses may soon be a thing of the past.
Two types of
CHECK aberration are
spherical aberration and
chromatic aberration.
CONCEPT
......
CONCEPT Name the types of aberrations that can occur in
CHECK
images formed by lenses.
Teaching Resources
think!
• Reading and Study
Workbook
Why is chromatic aberration a problem for lenses but not for mirrors?
Answer: 30.8
• PresentationEXPRESS
• Interactive Textbook
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616
REVIEW
30 REVIEW
Concept Summary
•
•
•
•
•
•
•
•
••••••
A lens forms an image by bending rays of
light that pass through it.
The type of image formed by a lens
depends on the shape of the lens and
the position of the object.
The size and location of the object, its
distance from the center of the lens, and
the focal length of the lens are used to
construct a ray diagram.
A converging lens forms either a real or
a virtual image. A diverging lens always
forms a virtual image.
Optical instruments that use lenses include the camera, the telescope (and binoculars), and the compound microscope.
The main parts of the eye are the cornea,
the iris, the lens, and the retina.
Three common vision problems are
farsightedness, nearsightedness, and
astigmatism.
Two types of aberrations are spherical
aberration and chromatic aberration.
Key Terms
For: Self-Assessment
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Teaching Resources
• TeacherEXPRESS
• Virtual Physics Lab 27
think! Answers
30.2 Both Jamie and his cat and the virtual image
of Jamie and his cat are “objects” for the lens
of the camera that took this photograph.
Since the objects are at different distances
from the camera lens, their respective images
are at different distances with respect to
the film in the camera. So only one can be
brought into focus.
30.4 The object should be (a) at one focal length
from the lens (at the focal point) (see
Figure 30.10); (b) and (c) within one focal
length of the lens (see Figure 30.9); (d) at two
focal lengths from the lens (see Figure 30.10);
(e) between one and two focal lengths from
the lens (see Figure 30.10).
30.8 Different frequencies travel at different speeds
in a transparent medium, and therefore
refract at different angles. This produces
chromatic aberration. Light reflection, on the
other hand, has nothing to do with the frequency of light. One color reflects the same as
any other.
••••••
lens (p. 603)
converging lens
(p. 603)
convex lens (p. 603)
diverging lens
(p. 603)
concave lens (p. 603)
principal axis
(p. 604)
focal point (p. 604)
focal plane (p. 604)
focal length (p. 604)
real image (p. 605)
ray diagram (p. 606)
eyepiece (p. 611)
objective lens (p. 612)
cornea (p. 612)
iris (p. 612)
pupil (p. 612)
retina (p. 612)
farsighted (p. 614)
nearsighted (p. 615)
astigmatism (p. 615)
aberration (p. 615)
CHAPTER 30
30
CHAPTER
LENSES
LENSES
617
617
ASSESS
Check Concepts
1. A converging lens is thickest
in the middle; a diverging lens
is thinnest in the middle.
2. The focal point is a single
point on the principal axis;
the focal plane is an area
perpendicular to the principal
axis.
30 ASSESS
Check Concepts
(continued)
••••••
Section 30.1
3. Only a real image can be
projected onto a screen.
1. Distinguish between a converging lens
and a diverging lens.
4. Parallel to the principal axis;
through the focal point;
through center of the lens
2. Distinguish between the focal point and
focal plane of a lens.
5. Any two
6. To both
7. Converging lenses form
either real or virtual images,
depending on where the
object is with respect to the
focal length of the lens.
Section 30.2
3. Distinguish between a virtual image and
a real image.
8. What types of images are formed by diverging lenses?
Section 30.5
9. Explain what is meant by saying that in
a telescope one looks at the image of an
image.
10. What is the function of the eyepiece in
an astronomical telecsope?
11. What type of lenses are used in a compound microscope?
Section 30.6
8. Diverging lenses always
form virtual images that are
reduced and right-side up.
12. Which instrument—a telescope, a compound microscope, or a camera—is most
similar to the eye?
9. The eyepiece forms an image
of the image formed by the
objective lens.
13. Why do you not normally notice a blind
spot when you look at your surroundings?
10. For the viewer to look at the
real image of the objective
lens
11. Converging lenses
12. A camera
13. One eye fills in the blind spot
of the other.
14. Farsighted—image
falls behind the retina;
nearsighted—image falls in
front of the retina
15. The cornea is curved like a
barrel; vision can be corrected
with a cylindrical lens.
16. Spherical—light that passes
through the lens’s edge
focuses poorly; combine
lenses; chromatic—different
colors focus at different
places; combine lenses of
different kinds of glass
618
Section 30.3
4. There are three convenient rays commonly used in ray diagrams to estimate the
position of an image. Describe these three
rays in terms of their orientation with
respect to the principal axis and focal
points.
Section 30.7
14. Distinguish between farsighted and
nearsighted vision.
5. How many of the rays in Question 4 are
necessary for estimating the position of
an image?
6. Do ray diagrams apply only to converging lenses, or to diverging lenses also?
Section 30.4
7. What types of images are formed by converging lenses?
618
15. What is astigmatism, and how can it be
corrected?
Section 30.8
16. Distinguish between spherical aberration
and chromatic aberration, and cite a remedy
for each.
Think and Rank
17. B, C, D, A
18. C = B, A
19. C, B, A
Think and Explain
20. It will only be dimmer! The
full image is still present.
Think and Rank
••••••
Rank each of the following sets of scenarios in
order of the quantity or property involved. List
them from left to right. If scenarios have equal
rankings, then separate them with an equal sign.
(e.g., A ⫽ B)
19. Here Percy is in front of a diverging lens.
Virtual images are seen by viewing from the
right side of the lens. For object positions A,
B, and C, rank the sizes of the virtual images
from largest to smallest.
24. It can focus sunlight energy
onto a flammable material
and start a fire.
Think and Explain
••••••
20. When you cover the top half of a camera
lens, what effect does this have on the pictures taken?
18. Depending on the location of Percy relative to the focal point of the converging lens
(only one of the symmetrical focal points is
shown here), the image may be real or virtual. The size of the image varies for object
positions A, B, and C. Rank the image sizes
from largest to smallest. (You may want to
draw ray diagrams on a separate piece of
paper.)
22. a. The object must be
between the lens and its focal
point.
b. A diverging lens cannot
produce a real image.
23. If you can project an image
onto a screen, it is a real
image.
17. Percy stands at different distances from a
lens with a focal length of 30 cm. Rank the
image distance from farthest to Percy to
closest to Percy.
(A) Object is at 10 cm.
(B) Object is at 35 cm.
(C) Object is at 60 cm.
(D)Object is at 90 cm.
21. It will only be dimmer! The
full image is still present.
25. It is located one focal length
from the film or chip.
26. No, because the image is
behind the mirror.
21. What will happen to the image projected
onto a screen by a lens when you cover most
of the lens?
22. a. What condition must exist for a converging lens to produce a virtual image?
b. What condition must exist for a diverging
lens to produce a real image?
23. How could you demonstrate that an
image was indeed a real image?
24. Why do you suppose that a magnifying
glass has often been called a “burning glass”?
25. In terms of focal length, how far is the
camera lens from the film or chip when very
distant objects are being photographed?
26. Can you photograph yourself in a mirror and focus the camera on both your
image and the mirror frame? Explain.
CHAPTER 30
CHAPTER 30
LENSES
LENSES
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27. You should set your focus for
4 m, since your image is as far
behind the mirror as you are
in front.
28. Check students’ diagrams.
29. Moon maps are upside-down
views of the moon to match
with the upside-down image
that moon watchers see in a
telescope.
30. Yes; your brain re-inverts the
images.
31. Greater change in speed when
light travels from air to glass
32. Greater amount of refraction
when light travels from air to
glass
30 ASSESS
(continued)
27. If you take a photograph of your image
in a plane mirror, how many meters away
should you set your focus if you are 2 m
in front of the mirror?
28. Copy the three drawings in the figure.
Then use ray diagrams to find the image of
each arrow.
34. A whale’s eye uses hydraulics to move the
lens of its eye closer or farther from the
retina. When a whale dives after having had
a look around in the air, in which direction
should the lens be moved?
34. Farther from the retina;
refraction is less, so the
distance must be greater.
35. Focal-length variations in birds and reptiles are accomplished by eye muscles that
change lens thickness and curvature. For
near vision, should the lens be made thicker
and more curved or thinner and less curved?
35. Thicker and more curved
so that the focal length is
less than the distance to the
retina.
36. Would telescopes and microscopes magnify if light had the same speed in glass as in
air? Explain.
33. Less
36. No; magnification depends
on refraction, which in turn
depends on speed changes.
37. The “nonwettable” leg of the
insect depresses and curves
the surface of the water.
This effectively produces a
lens that directs light away
from its course to form a
bright ring around a darker
region that then appears as a
shadow.
38. Chromatic aberration of the
lens; the edge of the lens acts
as a prism.
39. Sharpness (but dimmer)
29. Maps of the moon are actually upside
down. Why is this so?
30. The real image produced by a converging
lens is inverted. Our eyes have converging
lenses. Does this mean the images you see
are upside down on your retinas? Explain.
31. In which case does light undergo the greater
change in speed—traveling in air and entering a glass lens, or traveling in water and
entering a glass lens?
32. In which case is refraction greater, light in
water entering a glass lens, or light in air
entering a glass lens?
33. From water to glass, the change in the speed
of light is less than from air to glass. Does
this mean a magnifying glass submerged in
water will magnify more or less than in air?
620
37. If you have ever watched a water strider
or other insect upon the surface of water,
you may have noticed a large shadow cast by
the contact point where the thin legs touch
the water surface. Then around the shadow
is a bright ring. What accounts for this?
620
38. What is responsible for the rainbowcolored fringe commonly seen at the edges
of a spot of white light from the beam of a
slide projector?
39. Waves overlap very little in the image of a
pinhole camera. Does this feature contribute to sharpness or to a blurry image?
Activities
40. The two surfaces of the lenses
of eyeglasses have different
curvatures.
Activities
••••••
40. Look at the reflection of overhead lights
from the two surfaces of eyeglasses, and you
will see two fascinatingly different images.
Why are they different?
41. Note the shapes of light spots that reach
the ground in the shade of a tree. Most of
them are circular, or elliptical if the sun is
low in the sky. Interestingly, the spots of
light are images of something very special
to all who live on Earth. Identify this special
something.
42. Determine the magnification power of a
lens by focusing on the lines of a ruled piece
of paper. Count the spaces between the lines
that fit into one magnified space, and you
have the magnification power of the lens.
For example, if three spaces fit into one
magnified space, then the magnification
power of the lens is 3. Describe how you can
do the same with binoculars and a distant
brick wall.
43. Make a pinhole camera, as illustrated
in the figure. Cut out one end of a small
cardboard box, and cover the end with
tissue paper. Make a clean-cut pinhole at
the other end. Aim the camera at a bright
object in a darkened room, and you will see
an upside-down image on the translucent
tissue paper. In a dark, windowless room,
if you replace the tissue paper with unexposed photographic film, cover the back so
it is light-tight, and cover the pinhole with
a removable flap, you will be ready to take
a picture.
41. The spots are “pinhole”
images of the sun that
occur when the openings
between the leaves are small
compared with the distance
to the ground below. At
the time of a partial solar
eclipse, the spots appear as
crescents, just like the sun
itself.
42. Hold the binoculars so that
only one eye looks at the
bricks through the eyepiece
while the other looks directly
at the bricks. The number
of bricks, as seen with the
unaided eye, that will fit into
one magnified brick gives the
magnification power of the
instrument.
43. Check the construction of
your students’ cameras.
Exposure times differ, depending mostly on
the kind of film and the amount of light.
Try different exposure times, starting with
about 3 seconds. Also try boxes of various
lengths. You’ll find everything in focus in
your photographs, but the pictures will not
have clear-cut, sharp outlines. The principal
difference between your pinhole camera
and a commercial one is the glass lens,
which is larger than the pinhole and therefore admits more light in less time.
Teaching Resources
More Problem-Solving Practice
Appendix F
CHAPTER 30
CHAPTER 30
LENSES
LENSES
621
621
• Computer Test Bank
• Chapter and Unit Tests
621