“Object in Mirror are closer than
they appear!”
– Why?
MIRRORS & LENSES
REFLECTION & REFRACTION
Concepts of Physics
Mr. Kuffer
Name:
How Big Should a "Full Length"
Mirror Be?
(Plane Mirror Reflection)
Group:
Class Period:
You can buy mirrors in all sorts of shapes and lengths. When you look in your bathroom
mirror, you probably can't see all of yourself. For you to be able to see all of yourself, how
big of a mirror do you really need? You just learned about where you can see images in
mirrors. Now you will explore how much you can see in a mirror.
Materials: 12" x 12" mirror tile, stickies, meter stick, wall.
1. Imagine attaching the flat mirror to the wall so the top of the mirror is at a height that allows you
to see the top of your head even with the top of the mirror. Imagine starting about 3 feet in front
of the mirror and walking backward further and further away from the mirror. Predict whether
you will continue to see the exact same amount of your body in the mirror, less and less of
yourself, or more and more of yourself as you move further back.
2. Test your prediction by doing the experiment. Have one lab partner hold the mirror flat against
the wall. Adjust the vertical height of the mirror on the wall so that the person looking in the
mirror sees the top of his or her head exactly at the top of the mirror. When you move backward
to a new position, the person holding the mirror on the wall may need to move the mirror slightly
up or down so that you see the top of your head exactly at the top of the mirror again. Describe
what you observed. Let each member of the group try the experiment.
3. What is the minimum size of a flat mirror mounted on the wall that would just barely enable you
to see your entire body in it, from the top of your head to the bottom of your feet? (Hint:
Michael Jordan is 6'7" tall, but he does not need a mirror that is 6'7" long in order to see his full
height.) Write your prediction below and explain your reasoning.
4. Try the experiment. The top mirror should be positioned so you can just see the top of your
head in the top of the mirror. (Instead of using several mirrors, you can use just one mirror, mark
the top of your head on the wall with tape, slide the mirror down the wall until you see the tips of
your toes, and mark the wall with tape. (you should be able to see exactly from the top of your
head to the bottom of your feet.) Use tape to mark the portion of one of the mirrors that you
need to see all of yourself. Use the meter stick to make the measurement of the vertical size of
mirror needed.
Make sure each lab partner has the opportunity to try the experiment. Measure the heights of each
person and compare these measurements with the mirror heights needed for each person.
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Record your data and conclusions below.
Group Member
Actual height
Minimum height of
Mirror needed
5. What general relationship does there seem to be between a person’s actual height and the
minimum size of a mirror needed for the person to see her entire image at one time in the
mirror? Is this what you had predicted?
6. Mr. K will use the simulator to construct a ray diagram
for this situation. The picture to the right shows what
you will see when you open the simulator. For
simplicity, we have represented the “person” as a stick
figure with an eye at the top of his head. Three point
sources are shown, one at the top, one in the middle
of his body, and one at the bottom. A mirror is placed
against the wall. Change the mirror to its minimum
height so this person could just “see” his entire body.
(You can change the length of this mirror by selecting
it and dragging its handles, and you can change its
vertical position on the wall. Use the tape measure
tool to measure the height of the person and the
mirror.) Drag out light rays from each of the point
sources and show that the reflected rays can enter the
eye.
7. With the simulator, try moving the “person” further from the mirror, or closer to the mirror, and
see if the results change.
8. Imagine that all you had was the original 12 inch mirror tile. Figure out at least one way (more if
possible) that you could use this mirror to see more of yourself than you could when it was
mounted on the wall. Try it, and describe each successful method below.
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Extra Practice – Ray Diagrams
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Images in Concave and Convex Mirrors
Object
Three Steps to Determine Image Location and Size
1. Draw a ray of light parallel to the principle axis. This line
always reflects through the focal point.
2. Draw a ray of light through the focal point. This line always
reflects parallel to the principle axis.
3. Draw a ray of light through the center of curvature. This
ray always reflects back on itself.
Terms:
Principle axis – The axis perpendicular to the curved mirror at the center of
curvature.
Center of Curvature – radius of sphere along the principle axis
Focal Point – point where parallel light rays converge from a mirror.
Concave mirror - A mirror with an inward curve.
Convex mirror - A mirror with an outward curve.
Convergent point – the point where light converges (or crosses).
Virtual Image – image is created where backward extension lines converge.
Real Image – image is created where light actually converges.
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Object
Object
Object
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Looking into Water
(Refraction)
Part I: What happens to light when looking at objects under water?
1. Suppose you and some other physics students are on a lake that has unfortunately had some
trash thrown into it by unthinking tourists. As physics students you have been asked to go
out in a boat and retrieve the pieces of trash from the lake.
Since we cannot exactly duplicate this situation, we would like for you to consider a slight
variation. Instead of a lake, there is a fish tank. A small object hanging from a wire at one end
of the tank represents the underwater piece of trash (the target). A glass or plastic tube is
mounted in a clamp above the fish tank so the bottom end of the tube is above the water line.
(See figure below.) You can aim this tube to point in any direction that you wish. There is also a
long rod that can be made to slide down the tube.
If you wanted to “spear” the piece of trash with the rod, predict where the tube should be
aimed so that when the rod slides down the tube it will enter the water and hit the piece of
trash (target). (Assume the rod does not bend when entering the water, but continues in the
direction in which it was heading.) Should you aim the tube directly at the target, above the
target, or below the target? Draw on the diagram below to assist in explaining your thinking.
What is your prediction? Explain why.
2. Assume that as “high tech” physics students you also have available a new kind of laser.
When this laser beam hits a piece of trash, it turns the trash into food for the fish in the
lake.
Instead of a rod, let’s put a laser beam at the end of the glass tube so that it can be aimed
directly down the tube. Predict where we should aim the tube, if we wanted the laser beam of
light to hit the target. Should we aim the tube above the target, at the target, or below the
target? In the diagram below, draw how you think the light would behave as it leaves the end of
the tube.
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What idea or ideas do you have about the behavior of light that would support your prediction?
3. Discuss your predictions and ideas with other members of your group. Write down
predictions/ideas/diagrams that differ from yours
4. With those at your table, try to reach a consensus on a best set of predictions for how the
tube should be aimed with the rod, and with the laser beam. Be prepared to share your
thoughts with the class. (document your thoughts below)
5. Listen carefully to and note the predictions, drawings and explanations offered by other
members of the class. Summarize those that differ from your own, and seem particularly
interesting or useful to you. Do you want to change your mind as a result of listening to the
other predictions and explanations?
6. How should the laser beam be aimed to hit the target?
7. Participate in a whole class discussion to make sense of these observations. Your instructor
will help the class summarize its initial ideas about these demonstrations. List those initial
ideas below, and place an asterisk (*) next to those that make the most sense to you at the
present time.
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Why are Objects Not Where They Seem to be?
In the Elicitation activity you considered whether an object under water was actually
located where it appeared to be. In the last activity you discovered how light behaves
when traveling between air and water. Now you will have an opportunity to consider how
light plays a role in causing objects to appear displaced when seen under water.
Materials: 2 styrofoam cups, marker, and water
1. A small dot is placed inside the cup. There is a hole toward the top of the cup opposite the
black dot. Angle the cup so you can see the dot through the hole.
Dot
2. Return to the empty cup and position your eye (as before) so you can just barely see the
coin over the edge of the cup. Lower your eye slightly so you can no longer see the dot
(because your view is blocked by the edge of the cup).
3. Your partner will now fill the cup with water. What do you observe? Explain
You should observe that the dot suddenly comes into view! Have each group member observe
the effect for himself or herself. (You will need to keep emptying the cup.)
4. Below is a diagram of the dot at the bottom of the cup of water, and the observer's eye
looking in. Assume the observer can now see the coin. Draw two light rays leaving the dot
and show how they must behave in order to enter the observer's eye. Also show on the
diagram approximately where the observer "thinks" the dot is seen. Below the diagram
write a few sentences to explain your diagram (on next page)
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Dot
Explain here:
5. Below are three pictures of a person looking through a tube into a tank of water. An object
hangs by a string from the far end of the tank. In which of the three pictures is it most
likely that the person can actually see the object through the tube?
Why?
6. Instead of looking through the tube, suppose the person wants to shoot a beam of light (like
a laser beam) through the tube and hit the target. In which of the pictures below is it most
likely that the light beam (moving in the direction of the arrow) can enter the water and hit
the target?
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How did you decide?
7. Check your answers to the two previous questions with at least two other groups. Did the
other group(s) have the same answer, or different ones? Do you want to change your mind?
8. Based on the evidence you gathered in this experiment you may wish to address the
following three questions:
Question #1: How does light change direction when traveling from air into a transparent
solid or liquid?
Question #2: How does light change direction when traveling from a transparent solid or
liquid into air?
Question #3: When looking into, or though, a transparent liquid or solid, why do objects
appear at a different location?
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What Happens to Light Traveling Between Air
and a Transparent Material?
When you look into a fish tank, it may seem that the fish are very near. Yet if you look
at a different angle, the fish look far away. Like the target in the previous activity, it
can be tricky to determine where something really is in water. How does a different
material affect how light travels? In this activity you will investigate what happens to a
beam of light when it travels from air into water, and then what happens when the beam
travels the other way, from inside the water out into the air. You will also explore what
happens when light travels between air and other transparent materials.
Part I: Light going from air into a transparent material
1. Consider a beam of light being aimed at the surface between air and water. See the picture
below. A dashed line is shown representing a line drawn perpendicular to the surface through
the point where the beam enters the water. (This is called a "normal" or perpendicular line.)
When the beam enters the water, do you predict it will continue in a straight line, bend
towards the normal, or bend away from the normal? How did you decide?
Your prediction and reason:
2. You can test your prediction with the simulator. Mr. Kuffer will provide a demonstration to
check your prediction.
3. Would you say that when traveling from air into water the beam travels in a straight line,
bends towards the normal, or bends away from the normal?
4. Before you perform further experiments, we want to introduce some ‘new terminology’ that
scientists use to describe how light behaves when it changes its direction. Recall that we
have discussed Snell’s Law. You found that the angle the reflected light made with the
surface was the same as the angle that the incoming light made with the surface. This
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relationship can be stated in a slightly different way, by defining the normal (or
perpendicular) to the surface, the incident angle and the reflected angle. See the following
figure. Your observation that angles A and B are equal also implies that the Reflected angle
equals the Incident angle.
Scientists use the term “refraction” to refer to the bending or changing of direction of
light when it travels from one transparent medium into another (like from air into water).
They define the Refracted Angle as shown in the figure below:
INSERT REFRACTION DIAGRAM HERE!!!
LABEL ANGLES AND THE NORMAL LINE!!!!
5. In the situation you have seen with the simulator, the light beam struck the water at a
certain incident angle, and the beam made a certain refracted angle in the water. Consider
the sequence of pictures shown below. From left to right, the incident angle increases from
zero to larger and larger values. Predict what would happen to the refracted angle. Would it
also increase, stay the same, or decrease?
COMPLETE EACH OF THE DIAGRAMS BELOW BY ADDING A NORMAL LINE, ANGLE OF
INCIDENCE, ANGLE OF REFRACTION, AND THE BEAM.
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p
i
c
s
How did you decide?
6. Mr. Kuffer will return to the simulator to test your prediction.
(Draw your observation for each of the four diagrams above)
7. Summarize your findings. As you have seen, when light travels from air into water, the light
bends towards the normal. As the incident angle increases, does the refracted angle
increase, remain the same or decrease?
8. There is another way of interpreting your findings. Instead of describing what happens to
the light in terms of the refracted angle, you could also describe your findings in terms of
how much the light actually bends (or changes direction) when entering the water. Look
again at your sequence of pictures from the simulator. As the incident angle increases, does
the amount of bending increase, decrease or remain the same?
9. Is there a special value of the incident angle when the light goes straight into the water
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without bending at all (that is, have a refracted angle of zero degrees? If so, what is it?
10. As you know, there are many different transparent materials besides water. Does the
refracted angle depend on the material into which light is going? For example, instead of
water, suppose the beam of light was going into glass, or into solid diamond (!). For the three
pictures below, predict how the refracted angle of light might compare. The incident angle
is the same in all three cases. How did you decide?
11. The simulator can be used to test your prediction because you can change the medium.
Return to the simulator. Aim the beam so it enters the water with an incident angle close to
the one shown in the pictures above. Then draw it in the space below.
Mr. Kuffer will change the media. Draw your observations above
12. What relationship have you identified? Explain.
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Part II: Light going from a transparent material into air
1. So far you have explored what happens when light goes from air into a transparent material.
Now we want you to consider the reverse situation, light going from the transparent
material out into the air. Consider the situation shown in the picture below. Predict whether
the light will continue in a straight line out into the air, will bend towards the normal in the
air, or will bend away from the normal in the air. How did you decide?
Your prediction and reason:
2. Draw you observation below.
Comparison:
3. In the previous part of this activity you investigated what happened to the refracted angle
as you changed the incident angle when light was traveling from air into water. Does light
behave the same way when it travels from water into air? Draw it below!
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p
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Rules for Ray-Diagramming
Converging Lens with an Object outside the focal point
Step One: Draw ray 1 from the top of the object, parallel with the principle axis until you
hit the middle of the lens. Once the ray hits the middle of the lens bend the ray down
through focal point 2.
Step Two: Draw ray 2 directly through the center of the lens with no bending.
Step Three: Draw ray 3 directly through focal point 1 until you hit the middle of the lens.
Once the ray hits the middle of the lens, bend the ray and continue the line parallel with
the principle axis. Where the three intersect is where the inverted image is formed.
Converging Lens with an Object inside the Focal Point (Magnifying Glass)
Step One: Draw ray 1 parallel to the principle axis until you hit the middle of the lens.
Once the ray hits the middle of the lens, bend the ray down through focal point 2. Then
extend the line back past the object like it is below.
Step Two: Draw ray 2 through the middle of the lens then extend that ray back past the
object like it is below. Where the two lines intersect is where the image is formed and
magnified.
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Diverging Lens with an Object
Step One: Draw ray 1 parallel to the principle axis until you hit the middle of the lens.
Once the ray hits the middle of the lens, the ray bends up and out so that when you
extend the ray back, it would hit focal point 1.
Step Two: Draw the ray 2 so that it is directed toward focal point 2. When the ray hits
the middle of the lens it bends so it continues forward parallel to the principle axis. Then
you extend the ray back towards the object.
Step Three: Draw ray 3 right through the middle of the lens without any bending. Where
the three intersect is where the upright image is formed. See below.
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You Try!
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Lens / Mirror Equation
All features of the image can be found mathematically. You can use geometry to relate
the focal length of the mirror, ƒ, to the distance from the object to the mirror, do, and to
the distance from the image to the mirror, di. The equation for this is called the
lens/mirror equation:
1
ƒ
1
di
1
do
Another useful equation is the definition of magnification. Magnification, m, is the ratio of
the size of the image, hi, to the size of the object, ho.
m = hi / ho
By using similar triangles in a ray diagram, you obtain the following.
m = -di / do
Lens / Mirror Equation
All features of the image can be found mathematically. You can use geometry to relate
the focal length of the mirror, ƒ, to the distance from the object to the mirror, do, and to
the distance from the image to the mirror, di. The equation for this is called the
lens/mirror equation:
1
ƒ
1
di
1
do
Another useful equation is the definition of magnification. Magnification, m, is the ratio of
the size of the image, hi, to the size of the object, ho.
m = hi / ho
By using similar triangles in a ray diagram, you obtain the following.
m = -di / do
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