Unit 4 Symmetry and Scaling
Using Mirrors and Lenses
In this workshop participants will be introduced to the concept of image formation
by mirrors and lenses. The images produced by flat mirrors will be analyzed in some
depth but there will only a brief introduction to images by convex mirrors. Likewise
there will only be a short experience with lenses in order to establish the concept of
image formation and the fact that images occur in a specific location. Mirrors and
lenses are optical devices that produce images by reflecting or refracting the light
rays that strike them.
The science background involves both the manner in which light behaves and also
the specific manner that mirrors and lenses act on the light. It is important to
realize that light obeys the following simple rules: (1) light travels and (2) light
travels in straight lines. The first rule is important because you really can’t see light,
you just detect the fact that light has entered your eyes. The second rule is basically
a human experience, namely, when you look at something your experience tells you
that the object is exactly in the direction you are looking. In other words when you
“see something” it is in a specific place because light enters your eyes “as if” it came
from that place. This allows us to understand the concept of image formation by
lenses and mirrors. The images have a definite location and can be determined by
locating the place where light rays intersect.
Lab: Lenses and Images
A converging lens forms a real image when the object (a light bulb) is at a distance
from the lens. It is called a real image because light rays “really” intersect at a point
where the image is formed. In this lab the gaol is to find the exact location of the
image and the scaling and symmetry properties it has relative to the object.
Grade Level:
5-8
Materials:
Light bulb in a moveable socket
Converging lenses
Wax paper
Procedure:
1. Place a light bulb in a portable socket at a central location in the classroom.
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Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
2. Have students look through a converging lenses trying to find the image of the
light bulb as they move their arm back and forth. Where is the image of the light
bulb as you focus in the bulb? What properties does it have? For example, is it
right side up or upside down? Is bigger or smaller than the real light bulb?
3.
Patterns in Nature
Put a piece of wax paper between the converging lens and the light bulb. Locate
the image of the light bulb on the wax paper.
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Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002
Discussion:
The image viewed through this kind of lens is called a real image. The wax paper
enables you to see the exact location of the image. It is important to realize from
this that any image will have an exact location even if some of the properties differ
from this experiment with converging lenses. The principles of this type of image
formation are similar and can be applied to the way that the human eye or slide
projector works.
Lab: Flat Mirrors and Images
Flat mirrors reflect light and form images. These images are located at the point
where the reflected rays intersect. If the light rays don’t actually reach the point of
intersection the image is called an “imaginary” or “virtual” image. Visually locating
this image generally is an intriguing experience.
Grade Level:
5-8
Materials:
Flat Mirror
Soda Can
Procedure: Part 1
1. Place a flat mirror vertical on a
table top.
Using light rays to locate image formed by a flat mirror
Flat Mirror
2. Place a soda can in front of the
mirror. Where is the image of
the soda can?
Discussion:
The image is behind the mirror. It
can be located at the same distance
behind the mirror as the object is in
front of the mirror. The size of the
image is the same size as the object.
There is a one-to-one size
relationship between the object and
the image. The light ray does not
actually reach the point of
intersection where the image would
form.
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Procedure: Part 2
1 Fold a piece of paper in half. In bold print write a word on the front of one
folded side. Hold the folded paper in front of you with the word facing the
mirror.
Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
Patterns in Nature
2. Discuss what is seen. Is the image reversed?
3. Repeat the procedure but using an arrow drawn horizontally on a piece of folded
paper. Lay the paper down in front of the mirror with the arrow side up.
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Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002
4. Discuss what is seen. Is this image reversed? Be sure to find a satisfactory
conclusion to your answer for questions 2 and 4.
Discussion:
The image is not reversed. Why does a person want to think that a reversal has taken
place? One view of the image is simple relating what the word looks like in the mirror
to our normal perception or reading English words from right to left. Recall how the
letter on the front of an ambulance are arranged. Why? After viewing the word with
the paper folded, lift up the flap and look at the word through the paper. Compare
the position of each letter on the paper to the position of the letter in the mirror.
Demonstration: Candle Burning Under Water?
This is a concrete example of the concept that the image formed by a flat mirror is
located behind the mirror.
Grade Level:
5-8
Materials:
Candle
16” x 16” pane of glass
250 ml beaker of water
Procedure:
1. Vertically set up a pane of glass on a table top.
2. Set a candle 10 cm from the front of the glass.
3. Set the beaker behind the glass at an equal
distance.
4. Light the candle. Turn off the classroom lights.
Discussion:
The image of the candle is located behind the glass at the same place as the beaker.
Light never gets to the image: it is an imaginary image.
Demonstration: Full Length Mirror
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Grade Level:
5-8
Materials:
Full length mirror
Procedure:
1. What size would you need for a full length mirror?
Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
2. Set up a full length mirror against the wall and
have a student stand in front of the mirror with his
of her whole body image reflected in the mirror.
3. Mark on the mirror the top of the student’s head
and the bottom of the student’s feet.
Patterns in Nature
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Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002
Discussion:
The size of the image behind the mirror should be discussed. Have the student
discuss what is happening when the student backs up away from the mirror. Does the
size of the mirror needed depend on the distance a person stands from the mirror?
Lab: Corner Mirror: Two Mirrors at Right Angles
When more that one mirror is used there will be multiple image formations that occur
because light may reflect more than once before entering the eye.
Grade Level:
5-8
Materials:
Two flat mirror tiles
Soda can
Procedure:
1. Vertically orient two mirror tiles on a table to
create a 90° angle.
2.
Place a soda can in the center of the two mirrors
about 12 cm from the mirrors.
3.
Discuss with the students what they see.
Discussion:
How many soda cans do you see? Explain that you get a double reflection of the
image. Explain how light rays will reflect twice when producing the image behind the
corner of the mirror.
Demonstration: Box of Mirrors
Grade Level:
5-8
Materials:
Six flat mirror tiles
Soda can
Procedure: Part 1
1. Vertically orient two mirror tiles parallel to each other.
2. Place a third mirror tile between the two vertical mirror tiles to keep them parallel
and for use in the second part of this demonstration.
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3. Place a soda can equidistant between the two mirrors.
Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
Patterns in Nature
4. Discuss what is seen.
Discussion:
When the two mirrors are parallel the multiple images that extend to infinity are seen.
The scaling is still one-to-one but the images will seem smaller because they are
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Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002
getting further behind the mirrors.
Procedure: Part 2
1. Add two mirrors perpendicular to the vertical mirror tiles to form an open box of
five mirror tiles.
2. Place a soda can in the middle of the box.
3. Discuss what is seen.
Discussion
With the mirrors forming a square around the box, the images will extend off to
infinity in a plane.
Procedure: Part 3
1. Add a mirror tile to the top of the box. THE
TOP MIRROR SOLD BE ORIENTED SLIGHTLY OFF
CENTER SO THAT IT DOESN’T FALL INTO THE
BOX. Enough room should be left at one
corner to enable students to peer into the box
of mirrors.
2. Discuss what is seen.
Discussion
When the box is complete with the top mirror in
place, a three dimensional display of images extending to infinity will be seen.
Lab: Convex Mirrors
Grade Level:
5-8
Materials:
Convexed mirrors (silver ornament balls)
Procedure: Part 1
1 Hold a convexed mirror (ornament ball) in front of your face. Observe the image.
2.
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Discuss the image produced from this type of mirror. Is it right side up or upside
down? Is it bigger or smaller? Real or Virtual?
Discussion:
Convex mirrors also form virtual images but the scaling is different than flat mirrors.
The images are smaller. That smaller scale coupled with human experience that
smaller means distant leads to the warning on side mirrors of automobiles that
“objects in the mirror may be closer than they appear!”
Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
Patterns in Nature
Procedure: Part 2
1. Hold an ornament ball in each hand and move the two balls towards each other.
2
Observe how the number of images and the size of the images seems to change as
the balls are brought closer together until they touch.
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Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002
3.
Is there a type of zoom effect noticed while bringing the two balls together?
Discussion:
The images in convex mirrors are smaller than the object. Also they images are
located a short distance behind the mirror. Consequently, when two spheres are
brought towards each other, there will be an apparent zooming effect of these images
as they get closer and closer to a single point behind the mirror. This point is called
the focal point.
Demonstration: Tetrahedron of Ornament Balls
Grade Level:
5-8
Materials:
Four silver ornament balls
Flashlight
Three paper cups
Procedure:
1. Cut the bottom half inch off the paper cups.
Place three of the ornament balls on the
cutoff bottoms and arrange in a triangular
shape on the desktop. Place the fourth
ornament ball on top of the three arranged
balls.
2.
Shine a flashlight and/or laser onto one of the openings between the spheres.
3.
Have individual students look into the openings and observe what they see.
Discussion:
When the spheres form a tetrahedron and light is shined into the openings, the points
on the mirrors that the light rays reflect will form the outline of the Sierpinski
Triangle, one of the most well known fractal shapes. One can also observe the
multiple images produced in this setup.
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Sunshine State
Standards
SC.H.1.3.5
SC.H.1.3.7
Patterns in Nature
38
Unit 4
Developed through the National Science Foundation Project Pattern Exploration: Integrating Mathematics and Science for the Middle Grades, 2002