Chapter 13
Section 1 Characteristics of
Light
Objectives
• Identify the components of the electromagnetic
spectrum.
• Calculate the frequency or wavelength of
electromagnetic radiation.
• Recognize that light has a finite speed.
• Describe how the brightness of a light source is
affected by distance.
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Chapter 13
Section 1 Characteristics of
Light
Electromagnetic Waves
• An electromagnetic wave is a wave that consists of
oscillating electric and magnetic fields, which radiate
outward from the source at the speed of light.
• Light is a form of electromagnetic radiation.
• The electromagnetic spectrum includes more than
visible light.
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Chapter 13
Section 1 Characteristics of
Light
The Electromagnetic Spectrum
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Chapter 13
Section 1 Characteristics of
Light
Electromagnetic Waves, continued
• Electromagnetic waves vary depending on frequency
and wavelength.
• All electromagnetic waves move at the speed of light.
The speed of light, c, equals
c = 3.00  108 m/s
• Wave Speed Equation
c = f
speed of light = frequency  wavelength
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Chapter 13
Section 1 Characteristics of
Light
Electromagnetic Waves, continued
• Illuminance decreases as the square of the distance
from the source.
• The rate at which light is emitted from a source is
called the luminous flux and is measured in lumens
(lm).
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Chapter 13
Section 2 Flat Mirrors
Objectives
• Distinguish between specular and diffuse reflection
of light.
• Apply the law of reflection for flat mirrors.
• Describe the nature of images formed by flat mirrors.
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Chapter 13
Section 2 Flat Mirrors
Reflection of Light
• Reflection is the change in direction of an
electromagnetic wave at a surface that causes it to
move away from the surface.
• The texture of a surface affects how it reflects light.
– Diffuse reflection is reflection from a rough, texture
surface such as paper or unpolished wood.
– Specular reflection is reflection from a smooth,
shiny surface such as a mirror or a water surface.
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Chapter 13
Section 2 Flat Mirrors
Reflection of Light, continued
• The angle of incidence is the the angle between a
ray that strikes a surface and the line perpendicular
to that surface at the point of contact.
• The angle of reflection is the angle formed by the
line perpendicular to a surface and the direction in
which a reflected ray moves.
• The angle of incidence and the angle of reflection are
always equal.
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Chapter 13
Section 2 Flat Mirrors
Flat Mirrors
• Flat mirrors form virtual images that are the same
distance from the mirror’s surface as the object is.
• The image formed by rays that appear to come from
the image point behind the mirror—but never really
do—is called a virtual image.
• A virtual image can never be displayed on a physical
surface.
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Chapter 13
Section 2 Flat Mirrors
Image Formation by a Flat Mirror
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Chapter 13
Section 3 Curved Mirrors
Objectives
• Calculate distances and focal lengths using the mirror
equation for concave and convex spherical mirrors.
• Draw ray diagrams to find the image distance and
magnification for concave and convex spherical
mirrors.
• Distinguish between real and virtual images.
• Describe how parabolic mirrors differ from spherical
mirrors.
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Chapter 13
Section 3 Curved Mirrors
Concave Spherical Mirrors
• A concave spherical mirror is a mirror whose
reflecting surface is a segment of the inside of a
sphere.
• Concave mirrors can be used to form real images.
• A real image is an image formed when rays of light
actually pass through a point on the image. Real
images can be projected onto a screen.
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Chapter 13
Section 3 Curved Mirrors
Image Formation by a Concave Spherical Mirror
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Chapter 13
Section 3 Curved Mirrors
Concave Spherical Mirrors, continued
• The Mirror Equation relates object distance (p),
image distance (q), and focal length (f) of a spherical
mirror.
1 1 1
+ =
p q f
1
1
1
+
=
object distance image distance focal length
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Chapter 13
Section 3 Curved Mirrors
Concave Spherical Mirrors, continued
• The Equation for Magnification relates image height
or distance to object height or distance, respectively.
h'
q
=–
h
p
image height
image distance
magnification =
=–
object height
object distance
M=
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Chapter 13
Section 3 Curved Mirrors
Concave Spherical Mirrors, continued
• Ray diagrams can be used for checking values
calculated from the mirror and magnification
equations for concave spherical mirrors.
• Concave mirrors can produce both real and virtual
images.
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Chapter 13
Section 3 Curved Mirrors
Sample Problem
Imaging with Concave Mirrors
A concave spherical mirror has a focal length of
10.0 cm. Locate the image of a pencil that is
placed upright 30.0 cm from the mirror. Find the
magnification of the image. Draw a ray diagram to
confirm your answer.
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Imaging with Concave Mirrors
1. Determine the sign and magnitude of the focal
length and object size.
f = +10.0 cm
p = +30.0 cm
The mirror is concave, so f is positive. The object is
in front of the mirror, so p is positive.
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Imaging with Concave Mirrors
2. Draw a ray diagram using the rules for drawing
reference rays.
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Imaging with Concave Mirrors
3. Use the mirror equation to relate the object and
image distances to the focal length.
1 1 1
+ =
p q f
4. Use the magnification equation in terms of object
and image distances.
q
M=–
p
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
5. Rearrange the equation to isolate the image
distance, and calculate. Subtract the reciprocal of
the object distance from the reciprocal of the focal
length to obtain an expression for the unknown
image distance.
1 1 1
= –
q f p
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Substitute the values for f and p into the mirror
equation and the magnification equation to find the
image distance and magnification.
1
1
1
0.100 0.033 0.067
=
–
=
–
=
q 10.0 cm 30.0 cm
cm
cm
cm
q = 15 cm
q
15 cm
M=– =–
= –0.50
p
30.0 cm
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
6. Evaluate your answer in terms of the image
location and size.
The image appears between the focal point (10.0
cm) and the center of curvature (20.0 cm), as
confirmed by the ray diagram. The image is smaller
than the object and inverted (–1 < M < 0), as is also
confirmed by the ray diagram. The image is
therefore real.
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Chapter 13
Section 3 Curved Mirrors
Convex Spherical Mirrors
• A convex spherical mirror is a mirror whose
reflecting surface is outward-curved segment of a
sphere.
• Light rays diverge upon reflection from a convex
mirror, forming a virtual image that is always smaller
than the object.
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Chapter 13
Section 3 Curved Mirrors
Image Formation by a Convex Spherical Mirror
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Chapter 13
Section 3 Curved Mirrors
Sample Problem
Convex Mirrors
An upright pencil is placed in front of a convex
spherical mirror with a focal length of 8.00 cm. An
erect image 2.50 cm tall is formed 4.44 cm behind
the mirror. Find the position of the object, the
magnification of the image, and the height of the
pencil.
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Convex Mirrors
Given:
Because the mirror is convex, the focal length is
negative. The image is behind the mirror, so q is
also negative.
f = –8.00 cm q = –4.44 cm h’ = 2.50 cm
Unknown:
p=? h=?
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Convex Mirrors
Diagram:
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Convex Mirrors
2. Plan
Choose an equation or situation: Use the mirror
equation and the magnification formula.
1 1 1
+ =
p q f
and
h'
q
M= =–
h
p
Rearrange the equation to isolate the unknown:
1 1 1
= –
p f q
and
p
h = – h'
q
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Convex Mirrors
3. Calculate
Substitute the values into the equation and solve:
1
1
1
=
–
p –8.00 cm –4.44 cm
1 –0.125 –0.225 0.100
=
–
=
p
cm
cm
cm
p = 10.0 cm
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Chapter 13
Section 3 Curved Mirrors
Sample Problem, continued
Convex Mirrors
3. Calculate, continued
Substitute the values for p and q to find the magnification of the image.
q
–4.44 cm
M=– =–
M = 0.444
p
10.0 cm
Substitute the values for p, q, and h’ to find the height
of the object.
p
10.0 cm
h = – h' = –
(2.50 cm)
q
–4.44 cm
h = 5.63 cm
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Chapter 13
Section 3 Curved Mirrors
Parabolic Mirrors
• Images created by spherical mirrors suffer from
spherical aberration.
• Spherical aberration occurs when parallel rays far
from the principal axis converge away from the
mirrors focal point.
• Parabolic mirrors eliminate spherical aberration. All
parallel rays converge at the focal point of a parabolic
mirror.
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Chapter 13
Section 3 Curved Mirrors
Spherical Aberration and Parabolic Mirrors
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Chapter 13
Section 4 Color and Polarization
Objectives
• Recognize how additive colors affect the color of
light.
• Recognize how pigments affect the color of reflected
light.
• Explain how linearly polarized light is formed and
detected.
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Chapter 13
Section 4 Color and Polarization
Color
• Additive primary colors produce white light when
combined.
• Light of different colors can be produced by adding
light consisting of the primary additive colors (red,
green, and blue).
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Chapter 13
Section 4 Color and Polarization
Color, continued
• Subtractive primary colors filter out all light when
combined.
• Pigments can be produced by combining subtractive
colors (magenta, yellow, and cyan).
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Chapter 13
Section 4 Color and Polarization
Polarization of Light Waves
• Linear polarization is the alignment of electromagnetic waves in such a way that the vibrations of
the electric fields in each of the waves are parallel to
each other.
• Light can be linearly polarized through transmission.
• The line along which light is polarized is called the
transmission axis of that substance.
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Chapter 13
Section 4 Color and Polarization
Linearly Polarized Light
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Chapter 13
Section 4 Color and Polarization
Aligned and Crossed Polarizing Filters
Aligned Filters
Crossed Filters
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Chapter 13
Section 4 Color and Polarization
Polarization of Light Waves
• Light can be polarized by reflection and scattering.
• At a particular angle, reflected light is polarized
horizontally.
• The sunlight scattered by air molecules is polarized
for an observer on Earth’s surface.
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