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Optics
Revised 04/09 A. Tomasch
Pre-Lab Question
Why can you see your reflection in the mirror?
EXPLORATION
Exploration Materials
1 ray box
1 box optical materials
-slit screen
-flat/concave/convex mirror
1 clear ruler
Definitions
A convex lens or mirror is thicker in the center than at its edges.
A concave lens or mirror is thinner at the center than at its edges.
You will find diagrams illustrating convex and concave lenses and mirrors at
the end of this worksheet.
1. Plug in the ray box and insert the slit screen into the front of it so that only one
narrow beam is emitted. Place a piece of white paper beneath the emitted light from
the ray box to more easily see the beams of light. You are going to deduce the
“Law of Reflection” from your observations of rays reflected by mirrors of different
shapes.
Place the flat mirror in the path of the light ray and observe what happens. Rotate
the flat mirror slightly and observe how varying the angle of incidence for the
incident ray of light striking the mirror affects the angle at which the ray is reflected
from the mirror surface. Draw diagrams showing the incident ray of light, the mirror
and the reflected ray of light for two different angles of incidence.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
2. Insert the concave mirror and observe what happens. Rotate the concave mirror
slightly and see what different angles of incidence do to the angle of reflection. Draw
ray diagrams to represent how two different light rays reflect off a concave mirror.
3. Insert the convex mirror and observe what happens. Rotate the convex mirror
slightly and see what different angles of incidence do to the reflection. Draw ray
diagrams to represent how two different light rays reflect off a convex mirror.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
4. How are reflections from the different mirrors similar? Based on your
observations, how are the angles made by incident and reflected rays of light related
to each other? Does this depend on how the mirror is oriented?
Based on your observations, define a “law of reflection” stating the relationship
between the direction of incident and reflected rays of light at a mirror’s surface.
it the same law for flat and curved mirrors?
Is
(Hint: Define the direction angles for incident and reflected light rays with respect
to the direction perpendicular to the mirror surface (called the normal direction) at
the point where the incident beam strikes the mirror. Sketching in a line to indicate
the normal direction in your ray diagrams may help guide your analysis).
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
Testing the law of Reflection
5. Change the slit screen so you have 5 narrow beams. Before placing the mirror
back in the path, look at the imaging paper under the beam. The 5 beams should be
parallel, but they may be diverging (spreading out) or converging (narrowing
together). If the beams are not parallel, slide the ray box casing until they are.
Place the flat mirror in the path and observe what happens. Rotate the flat mirror
slightly and see what different angles of incidence do to the reflection. Draw a ray
diagram. Does this agree with your law of reflection? Explain and indicate the
relationship between the directions of incident and reflected rays in your diagram.
6. Place the concave mirror in the path and observe what happens. Rotate the
mirror slightly and see what different angles of incidence do to the reflection. Draw a
diagram. Does this agree with your law of reflection? Explain.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
7. Place the convex mirror in the path and observe what happens. Rotate the mirror
slightly and see what different angles of incidence do to the reflection. Draw a
diagram. Does this agree with your law of reflection? Explain.
Challenge Work:
1. Sometimes a watch can reflect light onto other people’s faces. What is happening,
and what is usually the source of the incident light?
2. If you owned a fashionable boutique, would you install slightly concave or convex
mirrors to make your customers think they were skinnier? Explain.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
Everyday Applications
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Household mirrors
Lighthouses
Indoor lighting
Art
Optical illusions-amusement galleries
APPLICATION
Materials
1 ray box
Optical materials
-slit screen
-lenses: thin and thick convex,
concave, prism, trapezoid,
hollow concave and square
1 clear ruler
1. You’ve observed reflection, but there is another important optical phenomenon
called refraction. When a ray of light passes from one material to another, its
direction will change depending upon the optical properties of the two materials and
the angle at which the ray is incident at the boundary.
Start with the rectangular part of the trapezoid. Place the rectangle, clear side up, in
the path of 5 parallel beams so the length of the rectangle is perfectly
perpendicular to the incoming light rays. Draw the incoming and outgoing rays.
What does the plastic do to direction of light rays as they pass through?
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
2. Rotate the rectangle slightly (about 5º). Observe what happens. Draw a diagram
of the incoming and outgoing rays as well as the refracted rays inside the plastic
rectangle.
Is your description of plastic’s impact on the direction of the light rays the same as
before the block was rotated? How does the direction of the light rays change
relative to the normal at the surface of the plastic as it passes into the plastic block?
Which is larger, the angle outside the plastic or inside the plastic, both with respect
to the normal at the plastic surface?
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
3. Place the prism in the path of the ray box as shown below so that it intercepts a
single ray of light. Make the prism perfectly perpendicular to the path of the ray.
(Hint: look at the reflected beam.)
Figure 1: Ray Box and Prism
What do you observe? Draw a diagram and explain your observations. Compare this
result to a mirror.
4. Rotate the prism clockwise slightly and sketch the resulting pattern below.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
5. Place a convex lens in the path of 3 parallel beams. Make the flat face perfectly
perpendicular to the beam paths. Mark with a pencil where the three beams focus,
and do not disturb the lens or ray box position.
Insert between the slit card and the ray box two color filters, one for each outside
beam leaving the center beam as white light. Observe and draw where and if the
beams converge. Explain this effect. How is this related to what you observed for
light passing through the prism?
6. Lens Shape
Does the shape of a lens impact refraction? Use the thick convex lens to see how a
convex lens interacts with the light rays. Draw a diagram, including the path of the
beams inside the convex lens.
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Record how far away the focal point, where all the rays converge, is from the center
of the lens. This distance is called the focal length of the converging, convex lens.
Focal Length (cm)
7. How will the focal length of the thin convex lens compare to the thick convex
lens?
Insert the thin convex lens in the path of the beams and record how far away the
focal point is from the center of this lens.
Focal Length (cm)
Compare the focal lengths for the thin and thick convex lenses. How does the
thickness of the lens affect the focal length? Compare the focusing property of a
convex lens to what you observed for concave and convex mirrors—which type of
mirror focuses light in the same way as the convex lens?
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
Challenge Work:
1. How does a concave lens interact with the beams? Draw a ray diagram of the
concave lens in the beam path. Where is the focal point of the concave lens?
(Hint: Trace a line through each ray emerging from the concave lens and find where
all the lines meet).
Summary:
1. The law of reflection states that the angle of reflection is equal to the
angle of incidence for a reflected ray of light. The angles are defined with
respect to the direction perpendicular to the reflecting surface called the
normal.
2. Concave mirrors focus rays so that they converge at a common focal point
in front of the mirror. Convex mirrors produce diverging rays with a focal
point (the origin of all the diverging rays) behind the mirror.
3. The speed of light in a material such as glass, water or plastic is slower
than it is in vacuum. The ratio of (speed of light in vacuum)/(speed of light
in matter) is called the refractive index of the material.
4. The direction of a light ray changes as it enters a material with a higher
refractive index such that its angle with the normal decreases. This is
how lenses change the direction of light rays.
5. Convex lenses produce converging rays brought to a common focal point.
Concave lenses produce diverging rays.
6. The speed of light, and hence the index of refraction, is different in optical
materials such as glass or plastic for different wavelengths of light. This
effect is called dispersion.
7. Blue light (short wavelength) is refracted (bent toward the normal) more
than red light (long wavelength). This is how a prism separates white light
into its component colors.
8. The dispersion of the glass or plastic material used to construct a converging
(convex) lens causes the different colors of light to have different focal
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lengths (blue light has a shorter focal length than red light). This causes
lenses to exhibit chromatic aberration, where rings of color appear around
the image focused by the lens. For this reason, lenses are coated with
additional layers of different clear material with different refractive indices to
correct for this effect and bring all colors to a common focus.
Reflection
A wave is reflected when it is incident upon a material that redirects it outward.
Reflected waves are redirected according to the law of reflection: the angle of
incidence is equal to the angle of reflection. The angles of incidence and reflection
are defined with respect to the direction normal (perpendicular) to the mirror surface
as shown below.
The law of reflection holds for each of type of mirror, but the result it produces is
different for each. The plane mirror creates an actual-size virtual image of the object
which appears to be behind the mirror. Concave mirrors make incident plane waves
diverge, and convex mirrors cause incident plane waves to converge. Both of these
contribute to the distorted images of faces and bodies you see in carnival mirrors
which often have both convex and concave regions on the same mirror.
Figure 2: Plane Mirror
Figure 3: Concave (Converging) Mirror
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Figure 4: Convex (Diverging) Mirror
Figure 5: Convex (Converging) Lens
Figure 6: Concave (Diverging) Lens
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109