PHYSICS BY INQUIRY Instructor’s Guide Light and Optics Lillian C. McDermott
and the
Physics Education Group at the University of Washington
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Part A: Plane mirrors and images
In Part A of Light and Optics, students construct a model that accounts for the formation of
images in plane mirrors. It is recommended that students work through at least the first few
sections of the Light and Color module before starting the Light and Optics module.
Section 1. Introduction to reflection
The main purpose of this section is to familiarize students with the behavior of light when
incident on a mirrored surface. There is also a brief introduction to the conditions necessary to
see an object. For students who have worked through Light and Color, this section provides a
brief review.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 1.1
“First surface” mirrors are
preferable. A first surface
mirror has the reflective
surface on the front. A
“second surface” mirror has
glass or other transparent
material in front of the
reflective surface. To test the
mirror, place your finger
against it. If your finger seems
to be touching its image, then
the mirror is a first surface
mirror; a gap indicates it is a
second surface mirror. In
either case, measurements
must be made relative to the
reflective surface.
Clear plastic ruler (each student can be asked to supply his or
her own); black construction paper; scissors; mirrors; wooden
blocks to hold mirrors upright; butcher paper; and light box (see
Appendix IV).
Experiment 1.2
Protractor
Experiment 1.3
Construction paper in various colors including red; flashlight;
tape; various materials of different types of surfaces (e.g.,
sandpaper, foil, shiny paper, black velvet, etc.).
Experiment 1.5
Index cards, nails, single bulb electric circuit (#14 bulb
connected to 1 or 2 C or D cells in series).
Experiment 1.7
Medium plane mirror (roughly 8" x 10"), with a support so that
it can stand vertically on a table; something to cover the mirror;
dowel that can stand upright.
Discussion of the experiments and exercises
Experiment 1.1
Students explore how a light beam interacts with a mirror. To
be able to “aim” a beam of light using mirrors, students must
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have a good understand of how a beam of light is reflected.
Many students will develop a rule for reflection based on this
experiment; others will not do so until Experiment 1.2.
Experiment 1.2
✔ Checkout
In this experiment, students construct a rule for reflection.
Note: Many students will decide to measure the angle between
the beam and the mirror. The conventional angle of incidence,
measured relative to the normal, is introduced in Section 5;
there is no need to introduce it now. Also, rays are not
introduced until Section 2; in this section, students should be
encouraged to think about beams of light, not just the edges of
the beam or the center of the beam.
Suggested questions:
Why does it make sense to refer to the light as a “beam”?
What rule have you formulated to predict the path of a reflected
beam of light?
What angles are you referencing in your rule? Where are they
on your diagrams?
Show me how you would use a mirror to direct the light from
the box so that it “hits the mark” on your first attempt.
Experiment 1.3
Part E works best in a very
dark room.
✔ Checkout
In Experiment 1.2 in the Light and Color module, students
investigate reflection by non-mirrored surfaces. In this
experiment in Light and Optics, students investigate reflection
from mirrored surfaces as well. They are asked to compare and
contrast the behavior of light when it is reflected by mirrored
and non-mirrored surfaces. Many students are surprised by the
differences in behavior. For example, some students expect to
see a bright spot where the beam strikes the mirror, just as they
would if the beam were shone on a non-mirrored surface. In a
checkout, it is worthwhile to ask students to describe what they
actually observed. (Note: If the mirror is dirty, students may
see a spot where the beam strikes the mirror.) It is worthwhile
to cycle back to these differences later in the module. Students
often have a tendency to treat all surfaces, both mirrored and
non-mirrored, to reflect like mirrored surfaces.
Suggested questions:
What is the origin of the color that you see on the white sheet of
paper? How can you explain its presence on the white paper?
How does what you see when light shines on a piece of rough
construction paper compare with what you see when light
shines on a piece of smooth paper of the same color? How can
you account for the differences?
Exercise 1.4
Children often have ideas about light that are different from a
physicist’s model. Some believe that they can see because of
something coming from their eye rather than something that
reaches their eye. Others believe that in order to see an object,
the object must be illuminated, and then they must simply look
toward the object. They do not realize that light must (in the
case of a non-luminous object) be reflected by the object and
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then reach their eye. We have also seen these difficulties in
college students prior to formal instruction. These difficulties
may also resurface later in the module, for example, when
students are drawing ray diagrams to determine which observer
can see an image.
Not all students will realize that the student statement in the
experiment is incomplete. They should be led to articulate that
in order to see an object, three steps are necessary (1) there
must be an unobstructed straight-line path between the object
and their eye, (2) either the object must emit light or light must
be reflected by the object, and (3) the light from the object must
reach their eye. Since light moves so quickly, some students
may have difficulty thinking about light moving; however, they
should be able to think about a “source” of light (the object) and
a “receiver” of light (the observer’s eye).
If students are having difficulty with these concepts, refer them
to Experiments 1.1 and 1.3 of Light and Color.
✔ Checkout
Suggested question:
Using diagrams, show what has to happen in order for a person
to see a specific object (It is helpful to use a local landmark,
building or a real object in the classroom). The approach can
be similar to that of writing an operational definition.
Experiment 1.5
In part A, some students may have difficulty in determining
where to put their eye to see the bulb in the mirror. In part B,
some students will be surprised to see that the path that light
takes to their eye is the same for the nail, a non-luminous
source, as it was for the luminous source, the lighted bulb. If
students have difficulty in seeing the nail, try putting a piece of
white paper behind the nail.
In part C, some students may move the index card so much that
they are not able to see the image of the nail in the mirror.
Exercise 1.6
Students apply the ideas developed in Exercise 1.2 and
Experiment 1.5. (i.e., In order to see an object in a mirror, light
must follow a straight-line path from the object to the mirror,
then a straight line path from the mirror to the observer, while
obeying the law of reflection when the light strikes the mirror.)
Experiment 1.7
See the end of this section for a
description of the
demonstration.
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Exercise 1.8
This exercise checks student understanding of ray diagrams by
giving them a more complicated situation than they have seen
before. It is often helpful for students to use colored pencils in
making their diagrams.
The diagram below indicates the region in which the student
would stand to see the entire pencil. Students should be able to
account for why, in the overlap region, they will also be able to
view the middle portion of the pencil. An example of
acceptable reasoning would be, “In this region (between the
rays from the tip of the pencil), an observer could see the image
of the tip of the pencil. In this other region (between the rays
from the eraser), an observer could see the image of the eraser.
In this region, where the first two regions overlap, an observer
could see both the image of the tip of the pencil and the image
of the eraser, as well as the images of all points in between.”
A good question to challenge the stronger students is, “It looks
like the lines that define the region where you can see the entire
pencil converge to a point somewhere away from the mirror.
What would you see if you stood at that point and looked at the
mirror?” This question has elicited some very interesting ideas
from students.
✔ Checkout
Suggested question:
Select a variety of points on the diagram and ask what an
observer at that point would see when looking at the mirror.
Demonstration for Experiment 1.7
Set up
Place two chairs in front of a table and a covered mirror as shown in the perspective view at left
below. Cover the mirror with paper or cloth. A top view diagram is shown at right below.
Top view
Perspective view
mirror
dowel
student #1
#1
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Demonstration
Run this demonstration for two students at a time. The students should sit in the chairs. Ask
them to predict which of them will be able to see the dowel in the mirror when the mirror is
uncovered. Each student should write down his or her own prediction before discussing.
Some students will not use the same reasoning for both observers. If the students have different
predictions, they still may be able to come to a correct conclusion if allowed to discuss their ideas
on their own.
Finally, uncover the mirror, and let the students check their predictions.
Discussion
Some students will incorrectly predict that an observer will be able to see the image of the dowel
in the mirror if a straight line can be drawn from the student’s eye through the dowel to the
mirror. For example, some students have drawn diagrams like the one below and incorrectly
predicted that student 1 would not be able to see the dowel, but student 2 would.
mirror
dowel
student #1
student #2
Mirror
Pencil
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Section 2. Image formation in a plane mirror
This section introduces the idea of an image. In order to understand why one speaks of the
location of the image in a plane mirror as being behind the mirror, students must have a method
for locating an inaccessible object. The first method introduced in this section is based on
parallax. The second method is based on determining the line of sight to the image from several
locations, and then looking for the intersection of those lines of sight. Finally, the term ray
tracing is introduced as a technique to determine image location.
Students often state that the image is on the surface of the mirror. Several experiments in this
section are designed to elicit and address that difficulty. Note that students who have studied
mirrors before may know that the image of an object in a plane mirror is behind the mirror. For
these students, the purpose of some of the experiments may not be clear. It can help to tell these
students that a common prediction is that the image is on the mirror surface. They should be
encouraged reflect on how the experiments can help students who have this incorrect idea.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 2.5
Pieces of corrugated cardboard (exact size not important, but
they should be at least as large as a piece of paper, i.e., 9" x
12"); pins (straight or T).
Experiment 2.10
Half-silvered mirror; pairs of matched cylinders (e.g., two
batteries or cans).
Experiment 2.11
Full-length mirror mounted on a vertical surface (optional).
Discussion of the experiments and exercises
Experiment 2.1
This experiment illustrates parallax. Occasionally, a student
will be able to place a finger on top of the paper easily (without
moving his or her head). In such a case, check to be sure that
the student is closing one eye, and that the student’s open eye is
really at table level and not slightly above.
Some students may realize early on that they must move their
head to a new location in order to locate the paper accurately.
Those students should be encouraged to discuss that idea.
Other students may not immediately come up with a method for
locating the paper. Rather than explaining the answer to them,
have them move on to the next experiment in which a method is
introduced. Experiment 2.2 introduces the concept of parallax
and Experiment 2.3 requires the student to relate what they
have learned about parallax to this situation.
Experiment 2.2
Students continue to examine parallax. In part B, students
begin to articulate the idea that near objects appear to move
opposite to the direction of their eye and objects that are farther
away appear to ‘follow’ their eye.
Part C illustrates that the effects of parallax are decrease as two
objects are brought closer to one another. In order for the
parallax between two objects to disappear, the objects must be
at the same location, or one directly above the other.
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Experiment 2.3
Part A gives the students practice in applying parallax. This
experiment attempts to deepen student understanding of why
there is an apparent change in the relative location of the pencil
when they look at the pencil from different locations.
Students who were unable to develop a strategy in
Experiment 2.1 should now be able to locate the piece of paper.
All students should now be able to determine whether their
finger is in front of or behind the object they are trying to
locate. The method of parallax will be used throughout the rest
of Light and Optics, so check students’ techniques carefully.
Different students may develop different criteria for how to
determine which object is farther from them (e.g., they may
focus on which object appears to follow them, or on which
object appears to move more, or on which object appears to
move faster). We have found that in simple situations, a variety
of criteria will work. However, in situations where the apparent
size of the image does not give correct cues about the image
location (e.g., when the image appears larger than the object,
yet is actually farther away), many students have difficulties.
We have found that most students have success if they
concentrate on which object appears to follow them. For
example, if they start with the two objects in line, when they
move to the right, the farther object will be on the right.
Alternatively, if they concentrate on their finger, as in
Experiment 2.1, if they move right and their finger is on the
right, they can conclude that their finger is farther from them
than the paper. Conversely, if they move right and their finger
is on the left, they can conclude that their finger is closer to
them than the paper.
Many students will talk about the objects moving, when it is
actually an apparent motion of the objects. Students should be
aware that it is only an apparent motion of the objects.
✔ Checkout
Suggested question:
Using two different sized objects, ask the students to identify
which of the objects is being held farther away and to explain
how they know.
Experiment 2.4
Students are asked to indicate the location of the image of a nail
in a mirror. Many students will not give the correct answer.
For some students, this question will not even make sense: they
may not believe that the image has a location. Others will say
the image is on the surface of the mirror and the location
depends on where one holds one’s head. Part A of this
experiment is intended to force students to think about what the
term “the location of the image” means and to elicit these ideas.
In part B, students are led to use parallax to determine the
location of the image of an object in a plane mirror. This
experiment is intended to establish that the image is behind the
mirror. The student is then led to see that all observers who can
see an image of the nail can agree on the location of the image.
Some students who are able to use parallax to determine the
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location of the image of the nail will find it disconcerting
because there is nothing at the image location. With these
students, it may be appropriate to discuss the difference
between something actually being located at the image location,
and something only appearing to be located at that location.
Often students are misled into believing that the image changes
location when the observer’s location changes. Students
believe that the line of sight to the image of the nail intersects
the mirror at different locations depending on the observer’s
position. In part C, student 1’s explanation is an example of a
common reason students give for why they believe that the
image does move and is located on the surface of the mirror.
This exercise helps students to reconsider the possibility that
the image does not have a definite location.
✔ Checkout
Suggested questions:
Where does student 1 believe the image is located?
How can you use the student’s observations in part C to
conclude that the image appears behind the mirror?
Experiment 2.5
In this experiment, students use a second technique to
determine the location of an image. This method is used to
motivate the use of ray tracing.
In part A, students see how they can use intersecting lines of
sight to determine the location of an object. Most students will
find this easy, but the experience lays the groundwork for the
more complicated situation in part B: using intersecting lines of
sight to determine the location of an image.
Students need to be careful when marking lines of sight. Some
will state that the technique doesn’t work if three lines of sight
do not intersect at a single point. It may be necessary to discuss
issues that affect the accuracy of drawing a line of sight.
In part B, some students may say that because they know the
image is as far behind the mirror as the object is in front of it,
they only need one ray. Those students are not using the ray
diagram alone to determine their answer. They should be lead
to see that with their method, no rays are necessary. Their
technique works for plane mirrors only; the technique
developed in the module is more general.
Students may insist that a single ray gives no information about
the image location. They should be led to see that the image
must lie somewhere along the line that reaches the eye. One
could ask, “Could the image be here or here?” while pointing to
locations behind the mirror that are not on the extension of the
reflected ray. Most students readily say no, to which the
instructor can respond “Oh, so you do know something about
the image location from just that one ray.” This is often a
sufficient prompt to get them to articulate the correct reasoning.
Other students may need to be referred back to Experiment 1.5.
In part C, students determine the location of an image of a nail
in a mirror for several nail locations. After students have done
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this several times, they should be able to state that the image is
as far behind the mirror as the nail is in front of the mirror.
Some students believe that there is no image when the object is
off to the side of the mirror. Their incorrect predictions are
sometimes confirmed if they do not check a sufficiently wide
range of observer locations.
Experiment 2.6
This experiment develops ray tracing as a technique to
determine the location of an image. In part A, students use the
lines of sight that they drew in the preceding experiment to the
image to determine the entire path of the light from the
observer. This is difficult for some students.
In part B, students make an analogy between two situations:
looking at the image of an object in a mirror and looking at an
object through a hole in a wall. Students should see that the
nail behind the wall corresponds to the image in the mirror, and
the hole in the wall corresponds to the mirror. In part C, it may
be helpful for some students to cover up all but the reflected
rays that reach the observer—not all students will see that the
rays that reach the observer are the same in the two situations.
Many students do not realize that their eye cannot tell whether
light comes directly from an object or whether it is reflected by
a mirror and only appears to come from the image location.
In part D, students develop the technique of ray tracing to
determine the image location.
✔ Checkout
It is important to ask a student what information a single ray
gives about the image location. Also, make sure that students
are using dashed lines for extensions of rays and that the
students are using arrow heads on rays.
Exercise 2.7
Students should now be able to prove that the image of an
object in a plane mirror is located as far behind the mirror as the
object is in front. Some students will find this very difficult,
and not all students will recognize that it is useful to draw a ray
that strikes the mirror at normal incidence.
Exercise 2.8
This exercise develops the ideas necessary to determine the
location of an extended object.
Exercise 2.9
This exercise provides practice in drawing a ray diagram for an
extended object.
Experiment 2.10
Students now consider the image of an object that has an
appreciable diameter. Some will have difficulty in
differentiating between size and apparent size. Some may not
realize that these are two different concepts. Part A is designed
to elicit these ideas; part B helps student confront these
differences.
In part B, in order to determine that the size of the image is the
same as the size of the object, the student must compare the size
of the image to the size of the second cylinder. Then knowing
that the second cylinder is the same size as the object cylinder,
the student can arrive at a comparison between the size of the
object cylinder and its image.
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✔ Checkout
Suggested questions:
How did you come to your decision regarding the image size?
What would you have observed if the image and object were not
the same size?
Experiment 2.11
Students who have not explicitly thought about this task before
often believe that the farther away from the mirror they are, the
more of themselves they will see. The diagrams students draw
at this point may indicate how they are thinking about the role
of the mirror. Some students may draw a diagram as shown at
right, indicating that the mirror is “looking at” the student.
Some students may draw sloppy diagrams (i.e., they do not
obey the law of reflection) to support their incorrect predictions.
Others may draw a diagram like that shown below, indicating
some remaining difficulty with the role of the eye in viewing an
image in a plane mirror; these students may be thinking of the
mirror as “containing” the image.
Others may draw a mirror that is as the same height as the
distance from the top of their shoulders to the top of their head.
Once they start drawing their ray diagrams to show how much
of themselves they can see, they usually realize that they can
see more than just their head and shoulders, but have difficulty
figuring out how to adjust the size and location of the mirror.
This is a more difficult task than determining how much of
themselves they could see in a given mirror. Students may have
difficulty determining where light from their shoulders (or the
tops of their heads must strike the mirror in order to strike their
eyes. Some students can verbalize this and explain that when
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the light hits the mirror, the angles that the rays make with the
mirror must be the same, but not know where to go from there.
At this point, asking the student where else they have seen
equal angles should remind them of similar triangles. Often,
this is a sufficient hint. However, it may be necessary to help
some students draw a side view diagram of a “flat” person on
graph paper. Typically, drawing a diagram so that it is easy to
determine the “half-way” point between shoulders and eyes and
between the top of the head and eyes gets the student started.
In part B, make sure that students draw the ray diagram
necessary to determine the minimum size mirror necessary to
see themselves in a mirror. Check that students differentiate
between the size of their image and the apparent size of their
image. They should understand that although the size of their
image does not change as they move closer to or farther from
the mirror, the apparent size of their image does change.
Research has shown that many students believe that they will
see more of their image if they back away from the mirror.
This may be in part because students often stand near a mirror
when looking at a part of their body (such as their face)
whereas they typically move farther away from a mirror when
they want to see their entire image. This difficulty may also be
related to the common experience of looking at one’s image in
a bathroom mirror where there is commonly a sink or counter
just below the mirror. In this situation, one can see more of
oneself as one backs away from the mirror.
In part C, it is essential that the mirror be vertical. If a fulllength mirror is not available, you might also try using a smaller
mirror or you might be able to get a decent reflection off of a
piece of glass, such as a display case or window.
Our experience has shown that some students have difficulty
believing the results of this experiment. Even when given a
mirror, students will say that they see more of themselves in the
mirror as they move farther from the mirror. It may help if
students close one eye.
Part D and Exercise 2.12 are designed to help students realize
that looking at their own image is a special situation: they are
acting as both observer and as the object. Some students
incorrectly generalize the results from part B (a mirror half their
height is necessary to see their entire image) to apply to all
mirror images (a mirror half the “size” of the object is
necessary to see its entire image, independent of observer
location). Students may also want to check their answers to this
part using the same mirrors as in part C.
✔ Checkout
Suggested questions:
What other predictions are you able to make about changes in
the image that occur when you move either closer to or farther
away from the mirror? Are you able to see more, less, or the
same amount of the room in which you are standing if your
position is changed?
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Exercise 2.12
This exercise is designed to help students realize that looking at
their own image is a special situation. Additionally, it provides
another chance for the students to differentiate between size and
apparent size.
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Section 3. Multiple images
The exercises in this section were designed to further develop an understanding of image
formation. Students are led to see how multiple reflections are responsible for multiple images.
This section is optional; subsequent sections do not depend on it.
Some mathematics is required for this section, notably in Experiment 3.6. Students should know
that there are 360 degrees in a full circle.
At the end of the section, students for whom the mathematics is less challenging could be asked
to discuss the progression of images as the mirrors are closed. As the angle between the mirrors
is decreased, additional images form and appear to move behind the mirrors. Students could be
asked to describe this movement and determine the angles at which special things happen in that
progression and justify their description with ray diagrams.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 3.2
Polar graph paper; masking tape and colored markers or Post-it
notes in two different colors.
Discussion of the experiments and exercises
Experiment 3.1
During the course of their explorations in this experiment,
students develop a qualitative understanding of multiple images
formed by two plane mirrors.
Check to be sure that students recognize that they must change
their viewing location to ensure that they find all the images.
This will be important later when they count the number of
images formed by two mirrors intersecting at various angles.
Students should observe that when images “overlap” (i.e., have
the same location), the images may be identical or may differ
from each other. The term “mirror image” or perverted image
is introduced at the end of this section.
Some students may decide that, when there is more than one
image, the number of images is always even. They may decide
that overlapping images are still separate images. It may be
worthwhile to help those students recognize that one can
consider both the number of images and the number of image
locations. There can be an odd number of image locations.
Some students may want to understand their observations more
thoroughly. They should be encouraged, even though many of
their observations will be developed in more detail later in this
section. As always, the module should be regarded as one way
of exploring a phenomenon, but not the only or best way.
Experiment 3.2
In part A, students predict the location of the image of a line
that intersects a mirror. Some students will confuse the line
itself with a ray in a ray diagram. In part B, students repeat part
A, but with a mirror replacing the line; part A sets the stage for
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interpreting the observations in part B.
Students should find that they can see an image of the second
mirror by looking in the first mirror. The analogy to part A is
made by considering the line in part A as having been replaced
by the second mirror. The image of the second mirror appears
to have the same location as the image of the original line.
However, because the second mirror is itself a mirror, there
appears to be an image of the first mirror behind the second.
The tape on the mirrors is intended to aid students in connecting
the various images to the original mirrors. Make sure that the
mirrors can be easily distinguished.
In part D, if students choose an angle for their mirrors such that
the mirrors and all their images appear evenly spaced about a
circle, have them discuss the angles for a more general case.
Some students may claim that all the angles are always equal.
For these students, suggest that they put their mirrors on a sheet
of polar graph paper with the “hinge” of the mirrors on the
center of the paper. This will allow the students to “measure”
the angle between the mirrors. (This works best if the length of
the mirrors is less that the radius of the graph paper.)
In later experiments, students discover that for certain angles
between the mirrors, the images of an object placed along the
bisector of that angle appear evenly spaced around the
circumference of a circle centered at the hinge of the mirrors.
When the mirrors are placed at one of those angles, a pair of
images overlaps, appearing to form a single image. Those
angles are the same as the angles discovered in this experiment,
for which all the images of the mirrors appear evenly spaced.
In part E, the idea of an “image of an image” is introduced. The
different markings on the two mirrors should help students
identify the images.
Experiment 3.3
In part A, the students apply the idea of an “image of an image”
to predict both the number of images and their locations in two
simple situations. If students do not hold their mirrors
carefully, students’ correct predictions may appear to be
incorrect.
Students’ descriptions of how to use the idea of an “image of an
image” should be very clear. It should include some sort of
check that the image-that-appears-to-be-an-object is on the
shiny side of the mirror if there is to be another image of it.
✔ Checkout
Experiment 3.4
Ask students to determine the number of images in a new
arrangement of 2 mirrors.
In this experiment, students study qualitatively how changing
the angle between two mirrors affects the images of an object
that lies along the bisector of the angle between the mirrors.
In part A, students see that as the angle between the mirrors
decreases, the number of images increases.
In part B, some students may choose to characterize the angle
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between the mirrors for a given number of images by a range of
angles. Other students may decide to record the angles for
which the object and its images appear evenly spaced. Either
method is appropriate at this point.
Some students may decide that there is no way to place the
mirrors in order to have an odd number of images. They may
claim that at certain angles, two images overlap so as to appear
to be a single image. As a result, those students may not mark
those angles on their paper.
At this point, some students may discover the mathematical
formula relating the angle between the mirrors and the number
of image locations. For students who do not, Experiment 3.6 is
intended to help.
The term central image is introduced in part C. Students should
find that only when there is a central image does there appear to
be an odd number of image locations. Some students may not
recognize that there are other angles for which the images
appear evenly spaced around the hinge between the mirrors.
✔ Checkout
Experiment 3.5
In the first diagram in part A, the angle between the mirrors is
intended to be such that the object and its four images are
evenly spaced around a circle centered on the hinge of the
mirrors. For the second diagram, the object and its three
images are evenly spaced.
Parts B and C illustrate the relationship between the locations of
the images of the mirrors and the locations of the images of the
object for the diagrams in part A. An understanding of this
relationship will help students in the following exercise.
Experiment 3.6
In this experiment, students determine the mathematical
relationship between the number of image locations and the
angle between the mirrors.
For an object placed along the bisector between two mirrors,
there are specific angles for which there is an odd number of
image locations; however, there is a range of angles for which
the number of image locations is even. In this experiment,
students must decide on a criterion for choosing a particular
angle that can be used to characterize the angle between the
mirrors when the number of image locations is even.
Allow students to struggle with the question of which angles to
select for measurement. This is especially appropriate in
courses for pre-service or in-service K-12 teachers.) As the
students try to decide what criteria to use to choose discrete
values for the angles, they are forced to observe carefully what
happens to the images as the angle between the mirrors is
changed. After considering various possibilities, they may
eventually decide to measure the appropriate angles. Even if
they begin by measuring other angles, they learn something
about the process of science. A class discussion afterwards can
be useful as students try to explain their reasoning for
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measuring the various angles they chose.
In a class preparing students for other physics classes, there
may not be time to allow students to struggle with this problem.
In that case, you may wish to have a class discussion before
students begin this experiment in order to ensure that students
make the appropriate measurements.
Sometimes recognition of the appropriate angle to measure
leads immediately to the discovery of the desired mathematical
relation. In that case, students could be encouraged to make
predictions about the angle for a particular number of images,
and then check their predictions.
Students may be able to describe verbally the relationship
between the angle between the mirrors and the number of image
locations, but have difficulty in expressing the relationship
mathematically. The idea that one variable can be used to
represent the number of image locations and another variable to
represent the angle between the mirrors may not come naturally
to all students. Students should be taken through the reasoning
leading to an equation as carefully as they are led through the
reasoning in other portions of the module. Have students check
their relationships for specific cases.
✔ Checkout
Experiment 3.7
The last two experiments in
this section deal with “mirror
images” or perverted images,
that is, images that appear
different from the object.
These experiments may be
considered an optional part of
this section.
In this exercise, students use ray diagrams to understand the
formation of images in the cases of two and three evenly spaced
images. Students should recognize that each image is formed
by a particular number of reflections from the mirrors.
Some students will have difficulty in using ray tracing to
determine the location of the “third” image in the three-image
case. The following strategy has proved helpful. The student
should determine a line of sight to the difficult third image for a
particular eye location. Given that part of the path, the student
should be able to determine how light had to strike the mirror in
order that it was reflected in that way. The student should then
be able to determine the rest of the path as well as be able to
choose another ray that will prove useful in determining the
location of the image.
Experiment 3.8
In this experiment, students’ attention is directed to the fact that
the object can differ from one of its images.
Experiment 3.9
In this experiment, students explore mirror images in more
detail. Students should recognize that perverted images are
associated with an odd number of reflections. In addition, the
central image is not always a perverted image.
✔ Checkout
Suggested question:
Determine the angles at which one first sees two, three, four
images.
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Part B: Lenses, curved mirrors, and images
Section 4. Introduction to refraction
This section illustrates the phenomenon of refraction. Students develop familiarity with the
change in direction of a beam of light as it passes from one medium to another. Students do not
make measurements of refraction until Section 5.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 4.1
Beakers, various liquids (e.g., vegetable oil, corn syrup, sugar
water, salt water), food coloring (optional).
Experiment 4.2
Containers with straight sides.
Experiment 4.4
Pieces of glass, both thin and thick (e.g., microscope slides and
pieces of window glass).
Experiment 4.9
Prisms, red and blue acetates.
Discussion of the experiments and exercises
Experiment 4.1
This is an open-ended activity in which students explore the
effect of beakers of water and various other liquids on a beam
of light. Students should be encouraged to continue their
explorations in an attempt to answer any questions that occur to
them while working through this experiment. Additional
questions are suggested in the latter part of the experiment.
These may help the students to direct their observations.
Note: Not all students fill the beakers to a level that is higher
than the level of the slits. Unexpected effects can occur if light
goes through the beaker above the level of the water. Students
notice that the beam spreads out horizontally, but many forget
that it also spreads out vertically. If the bulb is high enough
(relative to the slit), it is possible to get a beam that strikes the
paper and appears to go straight through the beaker. If the
students see unexpected results, they should try masking off the
part of the beaker above the level of the water to ensure that the
light does indeed pass through the water in the beaker.
If students believe that the light bends at the center of the water
container or that it follows a curved path through the water,
have food coloring available to put in the water; this may help
make the beam visible in the water. A drop of milk added to the
water will also make the beam visible.
Provide various liquids such as vegetable oil, corn syrup, and
salt water. Make sure that students use control of variables in
designing their experiment to compare the effects of different
liquids. Oil and water may be mixed in a single beaker for easy
comparison of their effects.
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In part C, there is a variety of experiments that students could
design to determine whether it is the glass from which the
beaker is made or the liquid in the beaker that is responsible for
the bend in the beam. For example, students might shine the
light down onto the top of the water. Students should also be
encouraged to explore other ways to answer that question, such
as testing an empty beaker, or thinking about what happens
when a different liquid is used.
Some students may believe that it is the amount of water along
the path that determines the amount of the bending.
Experiment 4.2
Students use containers with straight sides to continue their
explorations of the behavior of light in passing from one
medium to another. Most students will recognize that their
observations are similar to those of the previous experiments.
Some students will see the behavior in this case as very
different since there are more reflected beams.
Not all students will recognize at this time that light bends away
from the surface in passing from air to water and toward the
surface in passing from water to air. That idea will be revisited
in Exercise 4.6.
Some students may notice that for certain orientations of the
container relative to the beam, light will not pass from water to
air. That effect (total internal refraction) should be
acknowledged as an interesting observation but need not be
named at this time.
✔ Checkout
Suggested questions:
What conclusions are you able to draw after comparing the
behavior of light as it passes through containers that vary in
shape?
What differences did you notice when the light passed from
water to air and from air to water?
Exercise 4.3
Experiment 4.4
Students identify beams as “incident” and “transmitted.” Some
students have difficulty accepting that a beam can be
considered both a transmitted and an incident beam, depending
on the interface that one is considering.
Students see that glass does affect a beam of light, however, a
thinner piece of glass has a smaller effect on a beam of light
than does a thicker piece of glass. Some students may need
guidance to realize that it may be useful to compare situations
in which there is a large bend in the beam rather than a small
bend. Others may not use control of variables in designing their
experiments.
Exercise 4.5
Students summarize their findings about how a beam of light
bends when passing from air to water and from water to air.
Students may find this summary useful in Exercise 4.6.
Exercise 4.6
In part A, students’ diagrams should be qualitatively correct.
There are a variety of errors that students can make. Some
students will incorrectly draw a bend in a ray that makes a right
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angle with the surface. Others will show the refracted that
bends too much or the wrong direction.
In part B, some students will need help to see that they can first
draw a tangent to a curved surface, then draw a normal to the
tangent. Some students will need to be encouraged to draw the
normal to the beaker at additional points before they see that
lines normal to a circle intersect at the center of the circle, thus
a radius of a circle is a normal to the circle.
In parts C and D, students formally summarize their
observations in terms of light bending toward or away from the
normal. Students should see that the results are the same
whether the surface is curved or flat.
✔ Checkout
Suggested questions:
What influence, if any, does the shape of a surface have on the
direction light bends?
How does light bend when passing from air to water? From
water to air?
What experiments did you perform in order to determine these
generalizations? How did you control for variables in these
experiments?
Experiment 4.7
✔ Checkout
Students see that a path that light takes is reversible. If they
know only the path that light takes, it is not possible to
determine in which direction the light moved.
Suggested questions:
What experiments did you conduct to draw your conclusions
about the reversibility of a light ray? How did you control for
variables?
What conclusion(s) are you able to draw from your
experiments?
Exercise 4.8
Experiment 4.9
Some students will not realize that they should show the beam
bending the same amount in all three cases because the beam is
incident in the same way in all three cases. Students should
now be able to relate this to why the thicker piece of glass had
the larger effect on the beam in Experiment 4.4. Some students
may not realize that the results of Experiment 4.7 are applicable
and necessary here.
Students observe that the amount of bending is (slightly)
dependent on the color of the light. In part B, some students
may need to be reminded to use control of variables in their
experiment. Some students may incorrectly think of the prism
as adding color to the light rather than separating the light into
different colors. These students should be referred to the
appropriate experiments from Light and Color.
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Section 5. Law of refraction: Snell’s law
In this section, students study refraction quantitatively. Students make the measurements
necessary to see that the relationship between the angle of incidence and angle of refraction is not
linear; rather the relationship between the sines of those angles is linear.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 5.1
Exercise 5.7
Semi-cylindrical dishes (refraction tanks).
Graph paper, 5 squares/inch (students can provide).
Discussion of the experiments and exercises
Experiment 5.1
In part A, students become familiar with the effect of a semicylindrical dish of water on a beam of light. In parts B and C,
students are directed to look for particular orientations of the
dish relative to the beam that produce bending at (1) one and
only one side of the dish, (2) both sides of the dish, and
(3) neither side of the dish. This lays the groundwork for how
these dishes are used in making measurements of refraction.
In parts D and E, students observe total internal reflection.
Experiment 5.2
✔ Checkout
Some students may decide that there is a critical angle both for
light passing from water to air and from air to water. Ask these
students what they mean by “critical angle.” A good question
to ask students during a checkout is, “How would you expect
the critical angle for oil to compare with the critical angle for
air?” or even “Would you expect there to be a critical angle for
oil?”
Suggested questions:
How do you operationally define angle of incidence and angle
of reflection?
What are you able to conclude from the experiments you
performed in Experiment 5.1?
What can you conclude about total internal reflection?
Experiment 5.3
This experiment is preparation for making measurements of
refraction. The students see that in order for the beam to bend
only at the flat side of the dish, the beam must strike the dish at
the center of the flat side of the dish. Additionally, students see
that as the angle of incidence increases, the angle of refraction
also increases. Some students may incorrectly say that the
angle of refraction decreases as the angle of incidence increases
because the angle of refraction is less than the angle of
incidence. They may have misinterpreted this question as, “Is
the angle of refraction greater than, less than, or equal to the
angle of incidence?”
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Experiment 5.4
In part A, students see that there is not a simple relationship
between the angle of refraction and the angle of incidence, that
is, they are not directly proportional.
When checking students out on the experiment, go over the data
with them. Try to get the students to look at their data by
asking them questions such as: Which angle is larger: the
angle of incidence or the angle of refraction? Is that angle
always larger? For what angles of incidence do you get the
largest bend in the beam? For what angle of incidence do you
get the smallest bend in the beam? Have the students go from
their table to a ray diagram; some students will incorrectly draw
the refracted ray on the wrong side of the normal. Other
students will forget to measure angles relative to the normal.
Experiment 5.5
In this experiment, students develop a technique that can be
used to make measurements of refraction. Students will likely
struggle with many parts of this experiment. In part A, it may
be useful to first ask which direction each of the observers
would have to look to see the vertical mark at the center of the
dish. Then one could ask which direction the observer would
have to look to see the pin, if it lines up with the mark. Finally,
ask what would that imply about the path that light takes from
the pin to the observer. (Only one of these paths is qualitatively
correct.) In part B, some students may have difficulties seeing
the connections between the path that the beam of light took in
Experiment 5.4, bending only once, at the flat surface of the
dish, and the path of light from a pin through the dish to an
observer that bends only once, at the flat surface of the dish.
In part C, students’ methods should be something like the
following: Put the first pin at a point corresponding to the angle
of incidence for which you desire to measure the corresponding
angle of refraction. Look at the pin through the dish, and move
your head until the bottom of the pin (viewed through the
liquid) and the vertical mark appear to line up. From this
location, stick a second pin on the closer (curved) side of the
dish so that the second pin also appears to line up with the
bottom of the first pin and the vertical mark on the dish. Light
from the first pin that strikes the flat side of the dish will bend
at the flat side of the dish, then go straight through the curved
side of the dish to the second pin.
✔ Checkout
Suggested questions:
What prediction would you make for the angle of refraction
when the angle of incidence is equal to _______?
What did you have to consider in making this prediction? What
observations did you make while performing your experiments
that led you to this consideration?
Experiment 5.6
In this experiment, students generalize their procedure from
Experiment 5.5 so that they can make measurements of
refraction for light passing from water to air. In part A, some
students will have difficulty explaining why their method can
be used to make measurements for light passing from water to
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air when the “source” of light is in air, not water. Students
should see both similarities and differences between their data
for light passing from water to air and from air to water. For
example, the bend is greater for larger angles of incidence than
for smaller angles of incidence whether the light is passing from
water to air or vice versa. However, light bends toward the
normal when passing from air to water and away from the
normal when passing from water to air. Thus, the angle of
refraction is smaller than the angle of incidence for light
passing from air to water, and the angle of refraction is greater
than the angle of incidence for light passing from water to air.
Additionally, total internal reflection only occurs when light in
water is incident on air, not the other way around.
✔ Checkout
Suggested questions:
How do your results from Experiments 5.4 and 5.6 compare?
What can you conclude from these results?
Exercise 5.7
This exercise motivates the need to look for a more complicated
relationship between the angle of incidence and the angle of
refraction than a linear relationship. On the basis of their
results from Experiment 5.4, (i.e., that the angle of refraction
does not double when the angle of incidence doubles), some
students will suspect that the graph of θi versus θr will not be a
straight line. Other students will try to draw a straight line
through their data even though the points lie on a definite curve.
These students should be led to see that there is a trend in their
data that suggests that they should not draw a straight line
through the data. However, for small angles, it is reasonable to
do so; make sure that the students plot all of their data.
✔ Checkout
Suggested questions:
What can you determine from the graph of your data?
Is this what you predicted? What factors did you consider in
making your prediction? What additional factors should you
have taken into consideration?
Exercise 5.8
Make sure that students plot the correct variable on the correct
axis, otherwise the slope of their graph in part A will not be the
index of refraction of water with respect to air. In a graph of
sin qi versus sin qr, sin qi should be on the vertical (or y-axis)
and sin qr should be on the horizontal (or x-axis). If students
have done Kinematics, they can be reminded of how they
plotted x vs t, v vs t, and a vs t graphs.
Some students may have difficulty seeing that the slopes of the
two graphs are inverses of one another. If so, it may help to
have students label each angle as “in air” or “in water” as
appropriate. Talk with the student about reversibility and what
that implies about how the two sets of data are related.
Students will have a second chance to think about these issues
in the following experiment.
✔ Checkout
Suggested questions:
How do the slopes on the two graphs compare?
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What can you infer from the two graphs?
Experiment 5.9
✔ Checkout
Students determine the index of refraction of a material other
than water. Additionally, students describe the relationship
between the index of refraction for light passing from one
material to a second and the index of refraction for light passing
from the second material to the first.
Suggested questions:
What summarizing statements are you able to make as a result
of completing the experiments in Section 5? What evidence do
you have to support each of these statements?
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Section 6. Examples of refraction in everyday life
In this section, students begin to generalize their procedures for ray tracing to account for
phenomenon in everyday life. Students identify image location with the apparent location of the
object as viewed through a beaker of water. This is valuable and challenging even for students
who have already studied lenses in a traditional course.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 6.2
Modeling clay.
Experiment 6.3
Drawing compass (students can provide).
Discussion of the experiments and exercises
Experiment 6.1
Students see that water can affect the apparent location of an
object, and they draw ray diagrams to account for their
observations. Many students will have difficulty determining
what perspective drawing (e.g., top view, side view) will be
most helpful in accounting for their observations.
Experiment 6.2
In part A, some students will incorrectly say that the bottom of
the pin appears to be located where it actually is, and support
this with a single ray drawn straight from the pin to the
observer. Let them find, on their own in part B, that this
prediction is incorrect. A good question to ask, once students
have recognized their mistake, is “What can you tell from a
single ray about where an object appears to be located?” Some
students will forget to use dashed lines to draw extensions of
rays, that is, to show whence light appears to come.
In part B, some students will not think to use parallax to
compare the location of the top of the pin (in air) and the
apparent location of the bottom of the pin (in water). Instead,
they will try to use parallax to determine where the pin appears
to be located.
Note: The term image location is not introduced until after this
experiment. We have found that students do not always
understand what is meant by image location, so we chose to
wait to introduce the term.
In part C, some students will realize that if the pin is taller than
the plastic, they use parallax to compare the location of the top
part of the pin with the location of the part of the pin that is
above the water, yet “in” the plastic.
In part D, many students will be surprised that they can see the
bottom of the pin in two different places.
✔ Checkout
Suggested questions:
Ask students if they had any surprises while making the
observations.
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What ideas might you use to try to explain your observations?
Experiment 6.3
Part A gives students another chance (in a slightly more
complicated situation) to use ray tracing to determine the
location of the image of an object in a container of water.
Some students might bend their rays so much that they predict a
real image in front of the beaker, which is not what one actually
observes. With these students in particular, it is useful to discuss
that they are only drawing a qualitatively correct ray diagram—they
do not know exactly how much to bend each ray. It is useful to
realize that there are some things that we can predict correctly
using a qualitatively correct ray diagram, and that there are also
limitations. If we desired, we could use Snell’s law to draw a
quantitatively correct ray diagram and actually predict precisely
where the image would be located. Ask the students what they
would predict if they didn’t bend the rays as much. (With some
students, it is necessary to repeat this several times. It can also
be useful to ask whether they observed a larger bend for a larger
angle of incidence or for a smaller angle of incidence before
asking them what they would predict if the rays didn’t bend as
much as they had drawn.)
Research has shown that many students incorrectly use apparent
size as an indicator of image location. For example, some
students believe that if the image appears larger (or wider) than
the object, then the image must be closer to them than the
object. Some students realize that they are making this
inference; others implicitly make this inference without
realizing that they are doing so, and they may even deny doing
so. This causes many students difficulty when they are trying
to use parallax to determine the location of an image: they may
unknowingly use the cues they get from apparent size to
determine the image location rather than using the cues they are
getting from parallax. We have seen that this is a persistent
difficulty and, for the majority of students, it must be addressed
more than once and in different contexts before it is eliminated.
The dialog between student 1 and student 2 was included to
elicit this difficulty.
Student 3’s comment provides a chance for students to
distinguish object and image and to realize that light from the
object is bent at the change of medium and it only appears to
come from somewhere other than whence it actually comes.
In part C, students investigate how the location of the object
within the beaker affects the image location. This foreshadows
the section on lenses.
✔ Checkout
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Section 7. Image formation by convex lenses
This section provides an introduction to lenses. Students observe that when an object is viewed
through a lens, its apparent size and location can be affected. Ray diagrams involving lenses are
introduced in Section 8. The terms real image and virtual image are defined in this section.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 7.2
Double convex lenses of two different focal lengths and
diameters (e.g., one lens of focal length 50 mm and diameter
38 mm, and a second lens of focal length 100 mm and diameter
50 mm. The experiments are written assuming that the primary
lens that the students use (i.e., the lens with the larger diameter)
has a focal length of about 100 mm).
Experiment 7.4
Additional convex lenses (e.g., focal lengths of 150 mm,
200 mm, and 300 mm).
Discussion of the experiments and exercises
Exercise 7.1
Experiment 7.2
These introductory activities lead into the discussion of lenses.
Students see that a variety of factors affects to what extent a
piece of material, such as glass, can redirect the light. (Isn’t
there a flaw in the reasoning in this part of the curriculum?? -KW)
In part A, students explore the behavior of a convex lens by
looking through the lens at objects around the room. They
should recognize that there are a number of factors that
influence what is seen through the lens. These include the
relative locations of the eye, object, and lens. This portion of
the experiment is intended to be a brief open-ended activity.
In part B, without prompting, not all students will notice that
the coin can appear inverted or erect. In addition, students may
not notice that the object may appear to be a different size when
viewed through the lens. Some students may notice that the
observer location can affect the apparent size of the object as
viewed through the lens.
In part C, students explore the effect of a convex lens while
keeping the distance from their eye to the lens fixed. Some
students will find this easier if their partner holds the lens a
fixed distance from the object. Some students will place their
eye too close to the lens to be able to focus on the image when
it is in front of the lens.
In part D, students explore the effect of a convex lens while
keeping the object to eye distance fixed. As the lens is brought
closer to the eye, the image will become blurry and it will
become difficult to focus on it.
Experiment 7.3
This experiment motivates the idea that a lens forms the image
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of an object and that the image location is different from the
object location.
In part A, some students may be misled by the apparent size of
the nail when viewed through the lens and say that it appears to
be farther from their eye than the nail since it appears smaller.
(See also comments for 6.3.) The goal in part A is for the
students to get their ideas down, to get the students to make a
clear commitment about how they are determining their
answers. If their predictions in part A are incorrect, they will
find out about it in part B.
Students who had incorrectly decided in part A that the image is
farther from the observer than the object may have difficulties
using parallax to determine the image location. Allow time for
students to struggle with this problem before helping them
understand how to apply parallax to this situation. It may be
helpful to have students describe in words what their
observations are and how they are interpreting them (in terms of
using parallax). Additionally, it can be helpful to have them
use parallax to determine whether the image or the lens is
farther from them.
Some students, who incorrectly think that the image of the nail
is farther from the observer than the object may end up looking
at the image of the object nail and the image of the second nail.
It may require some time for students to recognize that the
second nail must be placed in front of the lens.
Students may have difficulty with this part of the experiment if
they try to match the apparent relative motions of the image and
reference nail over a large range of viewing angles. When the
image is too far “off center,” the image may distort. Direct
student attention to this fact and lead them to see that this
implies they should move their head over only a small range of
angles when attempting to locate the image.
In part C, students observe that an object placed near the lens
has an image that is farther behind the lens than the object.
Because the image appears larger than the object appears
without the lens, some students may say that the image is closer
to their eye than the object. Using apparent size as an indicator
of image location is a persistent difficulty. Do not be surprised
if this difficulty continues to surface even after this exercise.
Some students may try to come up with a rule that apparent size
can be used as a clue to image location. For example: If the
image looks bigger, it must be farther away, rather than closer,
as you might expect. If a student tries to come up with such a
rule, it can be useful to ask the student to look for a counter
example (e.g., Can you find an object location for which the
image and the object appear to be the same size? In that case, is
the image closer to you, farther from you, or the same distance
away from you as the object? Does your rule work in that
case?).
✔ Checkout
Ask students to describe their observations and interpret them.
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Suggested questions:
Can you find an object location for which the image and the
object appear to be the same size? In that case, is the image
closer to you, farther from you, or the same distance away from
you as the object? Does your rule work in that case?
Experiment 7.4
Students see that, for all of the lenses, a clear inverted image of
the distant object appears on the sheet of paper. To achieve a
clear image, the distance that the sheet of paper must be held
from the lens depends on the lens. In the text that follows this
experiment, this distance is defined as the focal length. If
possible, suggest that the students look at images of objects that
are outside. Students seem to enjoy especially looking at
images of moving objects (e.g., moving people or cars).
Experiment 7.5
Students measure the focal length for a variety of lenses. The
students should see that there is a focal point on each side of the
lens, and the focal length is the same for both sides of the lens,
thus a single symbol, ƒ, may be used to denote the focal length.
Experiment 7.6
In this experiment, students make observations of the image for
a wide range of object locations. It is intended in this
experiment that the students see the general changes that occur
in the image as the object location is varied rather than getting
bogged down in the quantitative aspects. In Experiment 9.1,
students do a more quantitative version of this experiment.
In this experiment, a long filament bulb may be used instead of
a #14 bulb. A long filament bulb has the advantage that it can
be plugged in, eliminating the need for keeping charged
batteries on hand. Additionally, its image on a screen is very
clearly related to the object. However long filament bulbs have
the drawback of being blindingly bright. Students will probably
only want the bulbs on when they are using them to see the
image on the screen. (A power strip may be useful in this
situation, providing a switch of sorts.)
Students may become impatient when they observe very little
change in the location of the image as they move the object
toward the lens. Be sure they have taken enough data to be able
to discuss how the image location changes as an object is
brought toward the lens.
✔ Checkout
Be sure to check students’ summaries in part D. Also (in parts
B and C) make sure that students differentiate between the
apparent size of the image, as viewed through the lens, and the
actual size of the image, as projected on a screen. Keep in mind
that the observer location can affect whether the image appears
larger than, smaller than, or the same size as the object. Also
check students’ conclusions about the range of validity of the
two different methods for determining image location.
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Section 8. Image formation and ray diagrams
By exploring the behavior of a convex lens, students are led to develop the appropriate ray
diagrams. Connections to the idea of refraction are made.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 8.10
Long filament bulb (and socket).
Discussion of the experiments and exercises
Exercise 8.1
Research has shown that many students put undue emphasis on
principal rays. By having the students draw many rays instead,
we hope to alleviate some of these difficulties. If students are
having difficulty with part A, have them consider the case of a
point source (essentially a #14 bulb) that produces an image on
a screen as in Experiment 7.6.
Exercise 8.2
Some students will not spontaneously realize that rays from a
point on a distant object can be regarded as parallel when they
reach the lens. Some students will have this difficulty because
they will try to show the distant object on their diagram. In
addition to making the connection that the rays converge at the
image location, we want students to realize that rays from point
P, which is on the principal axis, converge at the focal point of
the lens.
In part B, students should see that rays from a second point on a
distant object are parallel to one another, but are not parallel to
the first set of rays that they drew. Some students may have
heard that “rays from a distant object are (essentially) parallel.”
While this is true for a distant point object, it is not true for a
distant extended object. This may be difficult for some students
to accept.
Experiment 8.3
This checks student understanding that rays can be traced in
either direction, as discussed in Section 4. Some students will
have trouble making this prediction and may need to be
reminded of their results from that section. This result will be
used in the development of the principal rays.
Exercise 8.4
In this exercise, students apply their knowledge of refraction
and their results from previous exercises to justify one of the
principal rays for a thin lens: the ray that passes through the
center of the lens is essentially undeviated.
✔ Checkout
Suggested question:
Consider student’s statement: ”I think that rays from all distant
objects are parallel”. Do you agree or disagree with the
student?
Exercise 8.5
Students are led to see that the image of a point on an object can
be located easily by using three special rays, which will be
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called principal rays.
Note: After instruction, students often think of these three rays
as critical for image formation; if any one of the rays is
blocked, students then predict that the image will not be
formed. Part of this exercise and the next begin to address that
difficulty.
In part A, some students will not realize that they can apply
what they have seen in Exercise 8.2, Experiment 8.3, and
Exercise 8.4 to determine the continuation of each of the rays
shown. It is important to have students explain, in their own
words, how they decided to draw the continuation of each of the
rays. It can also be helpful to ask the students which
experiments they have done that support their answers.
Part B checks student understanding of what is meant by image
location. As in Exercise 8.1, students should realize that all
light from a point on an object that passes through the lens will
converge at (or appear to have come from) the corresponding
image point.
In part C, students draw a ray diagram for a point that is not the
top of the object. This reinforces that idea that for each point
on the object there is a unique image point and that to determine
the location of the image of an extended object, one must
determine the location of more than one point on the object.
In part D, some students will have difficulty because the
principal rays “merge” into one. Some students will need to be
lead to think of looking at a limiting process of a point that
approaches the principal axis.
✔ Checkout
In a checkout, make sure to have the students describe, in their
own words, how to draw each of the three principal rays. Also,
check their answers to and reasoning for part D.
Suggested questions:
How did you use your model of light in developing of the
principal rays idea?
Is the following statement true or false: “For the light coming
from the object to converge at the corresponding image point,
the light must take the path of one of the principal rays”?
Exercise 8.6
Research has shown that some students believe that a complete
image will not be formed if part of the object is “above” the
lens or if one or more of the principal rays are blocked.
Students should realize that principal rays are a convenient tool
for drawing ray diagrams, but principal rays are not essential
for the formation of an image.
Exercise 8.7
Part A provides practice in using principal rays to determine the
location of an extended object. Students will need to draw
additional rays in order to answer correctly parts B–D.
In part E, students are required to distinguish between apparent
size of the image (which depends on observer location) and
actual size of the image (which does not depend on observer
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location). If students have difficulty believing that there is a
difference, students should set this up and check their results.
Students can measure the actual size of the image if it is
projected onto a screen. Students can then remove the screen
and observe that the image of the pencil (with the lens in place)
may appear larger than or smaller than the pencil itself (with the
lens removed). The apparent size of the image depends on
observer location: if the observer is sufficiently far from the
lens, the image can actually appear the same size as the object
or even smaller than the object. Students should be encouraged
to account for this. Be careful that students set up the apparatus
so that the image is actually smaller than the object. (In the
diagram, the object is approximately 2.5ƒ from the lens.)
✔ Checkout
In a checkout, it is good to ask a student about observers at
additional points, shown in the diagram below. We have seen
that many students incorrectly believe that observers at these
locations can see the image. It is useful to have students
explain why they believe that an observer could see an image.
A useful first question for students who believe that the
observer at A or B could see the image is, “Which direction
would the observer look to see the image?” Some students,
who believe that the observer at point A can see the image, are
simply failing to distinguish between image and object. Other
students don’t think about the direction that the light is moving,
and forget that the light must enter the observer’s eye in order
for the observer to see the image. Other students will say that
the observer at B should look in the direction of the light that is
reaching the observer (that is, away from the image location).
These students have not realized that not only must light from
the object reach the observer, but additionally, light from a
single point must diverge at the observer’s eye. For these
students, it is useful to probe more deeply and ask, “Where
would this image be located?” When students use the two rays
to determine the image location, most will recognize their
difficulty.
Exercise 8.8
In this exercise, students extend the procedure developed in
Exercise 8.5 to use ray tracing to determine the location of a
real image formed to a convex lens to include the case in which
the image is virtual. Expect some students to have difficulty
with one of the three principal rays. Make sure that students
start good habits of using dashed lines for extensions of rays to
show from where light appears to come.
Exercise 8.9
Students are given practice in using ray diagrams to determine
the location of the image when the object is placed at various
positions along the principal axis. In drawing a large number of
diagrams, students reinforce their skill at drawing and
interpreting ray diagrams. Additionally, they gain insight about
how the image location is affected by changing the object
location. In this exercise, students are expected to be able to
tell from a ray diagram whether the image is real or virtual.
This may be difficult for some students. Some students will
need to review the definitions of real and virtual images.
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Some students may draw ray diagrams in which the rays stop at
the image, especially for a real image. They should be led to
see that the rays do not stop at the image location, but continue
past that point.
Experiment 8.10
In this experiment, students are asked to predict the effect on an
image of blocking off part of the lens. Research has shown that
often students will consider the three principal rays as critical in
image formation. This experiment is designed to elicit and
confront that idea.
In part A, where the top half of the lens is covered by a mask,
students will often predict that either the top or bottom half of
the image will disappear. In giving these responses, students
may be thinking of the image as actually entering the lens and
being inverted inside. Thus if the paper is placed in front of the
lens, it has not yet inverted, so the top of the image is blocked.
However if the paper is placed after the lens, the image has
already inverted, and now it is the bottom of the image that is
blocked. It is essential that a long filament bulb be used in this
experiment.
Part B tests student understanding of image formation by a lens.
Some students may say that only the part of the bulb in line
with the hole will form an image. We have seen many students
draw only rays from a long-filament bulb that either go straight
toward the lens or are emitted perpendicular to the bulb, rather
than treating each point on the long filament as a point source
of light.
In part C, students check their predictions and, if necessary,
draw revised ray diagrams to illustrate their observations.
Some students feel so strongly about their predictions that they
do not actually check their predictions.
Note: Different results are obtained if one covers half of the
object, rather than half of the lens. One could ask the stronger
student what would happen to the image on the screen if the top
half of the object were covered. As a final test of
understanding, one could ask students about how covering half
of the lens would affect what they see if they are viewing the
image directly, that is, without a screen.
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Section 9. Image formation and the thin lens equation
The main purpose of this section is to develop an algebraic representation for the relationships
among the distance of an object from a lens, the distance of the image from a lens, and the focal
length of the lens.
The algebraic sign convention used in this module for object and image distance and for the focal
length of a convex lens is given in the text at the beginning of this section.
Equipment (first use) None
Discussion of the experiments and exercises
Experiment 9.1
The first part of this experiment is the quantitative complement
to Experiment 7.6. Here students make quantitative
observations of the image for a variety of object locations. In
this experiment, students develop the Newtonian form of the
thin lens equation. The more common form of thin lens
equation, the Gaussian form, is developed in Exercise 9.2.
Students with weaker mathematical backgrounds may have
difficulty with part B of this experiment.
✔ Checkout
Ask students to describe the experiments and observations they
made in order to develop the thin lens equation. Check their
reasoning.
Exercise 9.2
Some students may have difficulty with part A, which is one of
the more mathematical parts of this module.
In part B, students may try to use a single data point rather than
the entire graph to determine the focal length. Other students
may have difficulty seeing how to determine the focal length of
the lens from their graph. A good place to start is to have the
students write down the equation that describes their graph in
point-slope form. Then have the students rearrange the
equation so that it looks as much as possible like the Gaussian
form of the thin lens equation. By making a correspondence
between different parts of the two equations, students should
then be able determine which feature of the graph to use to
determine the focal length of the lens.
Exercise 9.3
Students apply the thin lens equation to a variety of object
locations. Students are forced to interpret negative values of s'.
Exercise 9.4
In part A, some students may incorrectly believe that they
cannot determine the image location by using an equation when
the equation yields a negative value for s'. Others may not
know how to interpret the results of the equation for s = ƒ.
If students have not written
operational definitions
previously, it will be necessary
to refer them to the discussion
of operational definitions in
Properties of Matter.
✔ Checkout
Suggested questions:
Which feature of the graph did you use to determine the focal
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length of the lens?
In Experiment 9.3, how did you interpret negative value of s’?
In Experiment 9.4, how did you interpret the results of the
equation for s’=f?
Experiment 9.5
Students should realize that they would see a clear, crisp image
of the bulb on a piece of paper placed at the location of the
image, which is essentially at the focal point for a bulb 2 m
away. Research has shown that after traditional instruction,
some students believe if the piece of paper is moved from this
location, they will see an image that is still in focus, but that is a
different size from when the screen is at the image location.
Not all students have realized one of the implications of the thin
lens equation: for each object location, there is a unique image
location.
Research has also shown that after traditional instruction, some
students believe that the purpose of a lens is to invert the image.
Some students will believe that there will still be an image on
the screen after the lens is removed, but the image will not be
inverted.
Exercise 9.6
Students derive the equation for the magnification of an image
in the case of a real, inverted image produced by a convex lens.
Experiment 9.7
Students interpret magnification in the case of an object placed
closer to a convex lens than one of the focal points. Some
students incorrectly believe that the magnification tells them
whether the image will appear larger or smaller than the object
would if the lens were removed. This exercise gives students
additional practice in distinguishing between size and apparent
size.
✔ Checkout
Suggested questions:
According to your knowledge of thin lenses so far, what is the
purpose of a thin lens?
What happens to an image of an object after the lens is
removed?
How did you interpret magnification in the case of an object
placed closer to a convex lens than to one of the focal points.
What observations you made in the experiment supports the
idea that there is a difference between size and apparent size?
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Section 10. Image formation by concave lenses
The main purpose of this section is to study images formed by concave lenses. Students also
draw ray diagrams to predict image locations and investigate whether the thin lens equation can
also be applied to concave lenses.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 10.1
Double concave lenses of two different focal lengths and
diameters (e.g., one lens of focal length 100 mm and diameter
38 mm, and a second lens of focal length 200 mm and diameter
50 mm). The experiments are written assuming that the
primary lens that the students use (i.e., the lens with the larger
diameter) has a focal length of about 100 mm.
Experiment 10.4
Additional concave lenses (e.g., focal lengths of 50 mm and
150 mm).
Discussion of the experiments and exercises
Experiment 10.1
This experiment parallels Experiment 7.2. Here, students
explore the behavior of concave lenses. At this point, some
students will begin to see some of the differences between the
images formed by concave and convex lenses. In Experiment
10.3, students are formally asked to compare and contrast the
behavior of the two types of lenses.
Experiment 10.2
This experiment parallels Experiment 7.3. Students use the
method of parallax to determine the location of the image for an
object placed (1) outside the focal point of the lens, and
(2) inside the focal point of the lens. Some students may still
fall into the trap of thinking that the apparent size of the image
gives information about the image location.
Experiment 10.3
Students compare and contrast the types of images that can be
formed by concave and convex lenses.
✔ Checkout
Suggested question:
What are the differences and similarities in image formation by
concave and convex lenses?
Experiment 10.4
Students see that the image of a distant object formed by a
concave lens is virtual, motivating the need for an alternative
method for determining the focal length of a concave lens.
Experiment 10.5
This experiment parallels Experiment 7.5. Here, students
determine the focal length of a variety of concave lenses.
The algebraic sign convention
for the focal length of a lens is
introduced in the text following
Experiment 10.5.
Exercise 10.6
This exercise parallels Exercise 8.1. Since students often put
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undue emphasis on principal rays, we begin by having students
draw many rays from a single point on an object that pass
through the lens.
Exercise 10.7
The concept of principal rays for a concave lens is developed in
this exercise. In part A, some students will incorrectly try to
continue a ray that comes in parallel to the principal axis
through the focal point on the other side of the lens, just as they
would for a converging lens. If students are having difficulty,
have them first draw a ray diagram for a distant point on the
principal axis of the lens. In part D, most students will use the
image location to help them draw the third principal ray; it is
unlikely that many students will see that they combine the idea
of reversibility and the principal ray that they drew in part A to
draw the third principal ray. Part E reinforces the idea that the
principal rays are only a few of the infinitely many rays that
may be drawn from one point on the object, and it provides a
check that students understand what is meant by image location.
✔ Checkout
In a checkout, ask students to describe in their own words how
to draw each of the principal rays. Additionally, one could ask
them how the principal ray that they drew in part C is similar to
the principal ray that they drew in part A.
Suggested questions:
Ask students to describe in their own words how to draw each
of the principal rays. Additionally, ask them how the principal
ray that they drew in part C is similar to the principal ray that
they drew in part A.
Exercise 10.8
This exercise extends Exercise 10.7; students use ray tracing to
determine the location of the image of an extended object.
✔ Checkout
Check the reasoning students use in drawing their ray diagrams.
Exercise 10.9
✔ Checkout
Experiment 10.10
Exercise 10.11
Experiment 10.12
Similar to Exercise 8.6, this provides a check that students do
not believe that all three principal rays are necessary to
determine the location of the image.
Ask students if they understand the purpose of the exercise.
This experiment parallels Experiment 7.6. Students make
qualitative observations of the image produced by a concave
lens for a wide range of object locations. In part B, students
should keep in mind that the observer location can affect
whether the image appears larger than, smaller than, or the
same size as the object. Experiment 10.12 is a more
quantitative version of this experiment.
Students are given practice in using ray diagrams to determine
the location of the image when the object is placed at various
positions along the principal axis. In drawing a large number of
diagrams, students reinforce their skill at drawing and
interpreting ray diagrams. Additionally, they gain insight about
how the image location is affected by changing the object
location. This exercise parallels Exercise 8.9.
In this experiment, students determine the image location for a
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variety of object locations and determine that the thin lens
equation can also be used for concave lenses. Be sure to check
carefully students’ reasoning about their choice of sign
conventions.
✔ Checkout
Experiment 10.13
Check students’ reasoning about their choice of sign
conventions.
Students apply the thin lens equation to four different object
locations and check that their answers agree with their
observations.
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Section 11. Image formation by curved mirrors
In this section, students investigate images formed by convex and concave mirrors.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 11.1
Concave mirrors of two different focal lengths and diameters
(e.g., one mirror of focal length 15 cm and diameter 5 cm, and a
second mirror of focal length 7 cm and diameter 7.5 cm).
Experiment 11.4
Additional concave mirrors (e.g., focal lengths of 20 cm and
30 cm).
Experiment 11.8
Convex mirrors of two different focal lengths and diameters
(e.g., one mirror of focal length 20 cm and diameter 5 cm, and a
second mirror of focal length 5 cm and diameter 3.75 cm);
additional convex mirrors (e.g., focal lengths of 10 cm and
15 cm).
Discussion of the experiments and exercises
Experiment 11.1
Students investigate the images formed by concave mirrors.
This experiment parallels Experiments 7.2 and 10.1.
Experiment 11.2
Students begin to draw ray diagrams to account for images
formed by a concave mirror. This exercise parallels Exercises
8.1 and 10.6.
Exercise 11.3
The principal rays for a concave mirror are developed in this
exercise. In part A, some students will need guidance to see
that they can extend what they developed about focal points in
the context of lenses to the context of curved mirrors. In a
checkout, make sure that students can define focal point in this
context.
Some students may try to use the law of reflection to draw all of
the reflected rays. While this would work in theory, in practice
curved mirrors that have a well-defined focal point use only a
small portion of the sphere of which they are a part; otherwise,
there is not a well-defined focal point. This is discussed in
more detail in Experiment 11.6.
In part B, students see that there is a fourth principal ray for a
curved mirror. Students can use the law of reflection to draw
the reflected ray. Alternatively, once they have located the
image, they can use the image location as a guide to draw the
reflected ray.
✔ Checkout
Suggested questions:
How did you use ideas developed about focal points in the
context of lenses in the context of curved mirrors?
How did you define focal point in this context?
Experiment 11.4
For this experiment, label the mirrors that the students will use
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The algebraic sign convention
for object and image distance
for a curved mirror follows
Experiment 11.4.
according to radius of curvature. It is important to have a wide
range of radii of curvature mirrors in order to determine the
relationship between focal length and radius of curvature.
Students should be able to explain the difference between
radius of curvature and radius of the mirror.
In the following experiment, students will find that the thin lens
equation can also be applied to concave mirrors, given an
appropriate algebraic sign convention. After that experiment,
some students may wish to return to this experiment to
determine the exact relationship between radius of curvature of
a mirror and its focal length. Hint: Students should consider
the case for which the object and image distances are equal.
Experiment 11.5
In this experiment, students explore whether the thin lens
equation can also be used for concave mirrors. For a few object
locations, students determine the corresponding image location
and check whether the equation is valid.
Experiment 11.6
Students investigate spherical aberration in concave mirrors.
In part A, some students will believe that they must have drawn
the reflected rays incorrectly since the reflected rays do not all
pass through the same point.
In part B, different answers would be acceptable. Some
students may say that the image would be blurry or fuzzy, since
rays from a single point on an object do not all meet at a single
well-defined point. Others may realize that, in this case, the
image location could depend on observer location; that is, that
locally, the rays from a point on the object could appear to
come from a well-defined location, but rays that reach a second
observer at a different location could appear to come from a
different well-defined location. In either case, students should
be able to use their diagram from part A to see that if a smaller
portion of the mirror near the principal axis is used, the focal
point would be better defined.
Experiment 11.7
In order for part A of this experiment to work well, students
must not only draw reflected rays carefully, but must also
carefully draw a parabola.
In part B, students should realize that the focal point of a
spherical mirror is not well defined for a large portion of a
spherical mirror. Some students will be able to relate their
responses here to their results from Exercise 11.6.
Experiment 11.8
The algebraic sign convention
for the focal length of a curved
mirror follows Experiment
11.8.
Experiment 11.9
Experiment 11.10
In part A, students repeat the first four experiments and
exercises using convex mirrors instead of concave mirrors.
In part B, students compare and contrast their findings using the
two types of curved mirrors. This provides an important
summary of their observations to date.
Students investigate whether or not the thin lens equation can
be applied to convex mirrors. This parallels Experiment 11.5.
This experiment parallels Experiment 8.10. It provides students
a chance to revisit certain ideas in a different context.
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McDermott & P.E.G., U.Wash.
L&O
Instructor’s guide
42
Section 12. Applications of geometrical optics
The main purpose of this section is to make connections between the ideas developed in this
module and the behavior of various optical instruments and optical phenomena.
Equipment (first use)
Unless otherwise specified, each group will need one set of the following:
Experiment 12.1
Cardboard tubing, small plane mirrors (e.g., 1.5" x 1.5").
Experiment 12.9
Transparent sphere, approximately 1" in diameter.
Experiment 12.11
Optical fiber, large plastic funnel, bucket (or sink in dark
room).
Discussion of the experiments and exercises
Experiment 12.1
Students design and construct a periscope.
Experiment 12.2
Students determine what type of mirror is best suited for use as
a rear-view mirror. Some students will already know that a
plane mirror is typically used inside the car, near the driver, and
that a curved mirror is typically used on the passenger-side rearview mirror. These students should be encouraged to consider
the advantages of using a plane mirror for the inside rear view
mirror and the advantages of using a curved mirror for the
passenger-side rear-view mirror.
Experiment 12.3
Students investigate the use of a convex lens as a magnifying
glass. Some students may not realize that a magnifying glass
typically is used to create an erect image. Some students may
still incorrectly think that because the image appears larger than
the object would without the lens, the image is closer to them
than the object.
✔ Checkout
Suggested questions:
What type of mirror is best suited for use as a rear-view
mirror?
What are the advantages of using a plane mirror for the inside
rear view mirror and the advantages of using a curved mirror
for the passenger-side rear-view mirror?
The warning that appears on a curved rear-view mirror is
typically, “Objects are closer than they appear.” Strictly
speaking, is this statement correct?
Exercise 12.4
Experiment 12.5
Students consider a simple physical model for a camera, which
provides a nice context in which to apply many of the concepts
developed in Part B of this module. In part A, some students
may need to be referred to the text that precedes part A.
The role of the eye is finally discussed in this experiment.
Students investigate farsightedness and nearsightedness, and
how to correct for each. In part B, some students will not see
Instructor’s Guide for Physics by Inquiry, 1st Edition
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McDermott & P.E.G., U.Wash.
Instructor’s guide L&O
43
that they need to keep the distance between the lens and the
image the same in the “close object” and “distant object” cases.
Experiment 12.6
Students are lead to build a simple telescope. This telescope is
different from many common telescopes in that the image
produced by the first lens is not located “at infinity.”
In part C, some students will have difficulties drawing a ray
diagram for the combination of the two lenses. The principal
rays for the first lens will probably not be the principal rays for
the second lens; some students will need guidance to see that
they can draw additional rays that are principal rays for the
second lens. Some students will draw these rays starting at the
location of the image produced by the first lens. Encourage
these students to show, if possible, the entire path of light from
the object through the first lens and then through the second
lens.
Experiment 12.7
✔ Checkout
In this experiment, students construct a simple microscope. If
students are having difficulty with this experiment, it may be
helpful to go over Experiment 12.6 at this point. In a checkout,
have students compare and contrast (1) the design of a
microscope and a telescope, and (2) the situations in which one
would use a microscope and a telescope.
Suggested questions:
Check the ray diagram students draw for the combination of
two lenses in constructing a telescope.
Compare and contrast (1) the design of a microscope and a
telescope, and (2) the situations in which one would use a
microscope and a telescope.
Experiment 12.8
Students consider what type of mirror would be most
appropriate for use in a headlight. Some students will have
seen headlights and know what type of mirror is used, but they
may not understand the reasons behind the choice. Some
students may not have ever thought about why a mirror is used.
Experiment 12.9
In this experiment, students study a simple model for a rainbow.
Many students will not have noticed that they only see a
rainbow when the sun is behind them. Here, we are trying to
motivate that rainbows could be produced by light that is
refracted and reflected by water droplets in the sky. We are not
attempting to address some of the more complicated issues
involved in the creation of rainbows.
Exercise 12.10
Experiment 12.11
If possible, perform part C in a
very dark room that contains a
sink.
In this experiment, students study chromatic aberration.
In this experiment, students study fiber optics. Some students
will believe that fiber optics works only for very thin fibers.
Part C of this experiment is designed to address this
misconception.
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Copyright © John Wiley & Sons, Inc.
McDermott & P.E.G., U.Wash.
L&O
Instructor’s guide
44
Appendix: Information regarding special equipment
Section 1
Materials required for each light box: 1 3-gallon ice cream container (from Baskin Robbins,
Tastee Freeze, etc.), 1 ceramic lamp socket (bottom should be covered so that no electrical wires
are exposed); 6 feet of electrical wire (two strand wrapped), 1 electrical plug, 10 brass brads (1"
length, 3/8" or 1 cm diameter head), 1 200-W clear bulb.
Assorted other materials: black construction paper, scissors, single edge razor blade or sharp
knife, screwdriver, cardboard or other surface on which to cut.
8 1/2"
4"
2"
1/2" sill
ESS Source
A. The ice cream cartons must be cut and “telescoped” first, because they are too tall. In the
finished box, the bulb should be between 1" and 1-1/2" above the table, as in the ESS light
source. The amount by which the ice cream carton will need to be shortened varies
depending on the bulb and the bulb socket used.
The diagram below illustrates how to telescope the light box. First, make a cut about 2" from
the top of the box (the closed end of the box). Then make incisions in each part of the box at
regular intervals as shown in the middle illustration. The depth of the incisions should be
such that when the two parts of the box are interwoven as shown in the illustration at far
right, the bulb is about 1" above the table.
2"
1"
B. To cut the mask openings, make as a pattern, a rectangle 2" x 4". Make four equally spaced
openings around the box by tracing around the pattern on the carton. Leave a “sill” under
each opening of about 1/2". This will give strength to the opening.
Instructor’s Guide for Physics by Inquiry, 1st Edition
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McDermott & P.E.G., U.Wash.
Instructor’s guide L&O
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C. Fasten the electrical wire and plug to the socket (see staff).
D. Attach the socket to the carton so that the bulb is centered in the box (see staff).
E. Cut ventilation holes in the top of the box (triangles/squares/circles).
F. Make four masks, each with a different pattern of slits.
Attach brads, one on either side of each of the openings, to hold the masks.
Instructor’s Guide for Physics by Inquiry, 1st Edition
Copyright © John Wiley & Sons, Inc.
McDermott & P.E.G., U.Wash.