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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
c=(3 x108 m/s)• Light is a form of electromagnetic radiation.
• The electromagnetic spectrum includes more than
visible light.
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Electromagnetic Spectrum
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Section 1 Characteristics of
Light
Electromagnetic Waves, continued
• Electromagnetic waves vary depending on frequency and wavelength.
• Wave Speed Equation
c = flspeed of light = frequency wavelength
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Electromagnetic Waves
Section 1 Characteristics of
Light
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Section 1 Characteristics of
Light
• Huygens’ principle Waves can be approximated as rays.
• Lines drawn tangent to the crest (or trough) of a wave are called wave fronts.
• Rays are drawn normal (perpendicular to wave fronts)
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Section 1 Characteristics of
Light
• luminous flux (P)The rate at which light is emitted unit =lumens (lm).
• Illuminance (E) decreases as the square of the distance from the source. Another inverse square law 1/r2
• E=P/(4π r2)
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Section 2 Flat MirrorsReflection of Light
• Reflection =change in
direction of a wave at a
surface.
• The texture of a surface
affects how it reflects
light.
– Diffuse reflection
– Specular reflection
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• Opaque= does not transmit light
through the material. (reflected only)
• Translucent= Light passes through the
medium but is distorted.
• Transparent= material with no light
distortion.
• Transparent and translucent transmit
and reflect light at the same time.
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Section 2 Flat Mirrors
Reflection of Light, continued
• Normal= line perpendicular
to a surface.
• Angle of incidence θ
=angle between a ray
striking and the normal.
• Angle of reflection θ’
formed by the normal and
the reflected rays.
θ = θ’
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Chapter 13
Angle of Incidence and Angle of Reflection
Section 2 Flat Mirrors
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Section 2 Flat Mirrors
Chapter 13
Flat Mirrors Virtual Images
• Flat mirrors form virtual images =same distance from
the mirror’s surface as the object and is upright.
• image forms behind mirror
• A virtual image cannot be projected.
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Drawing ray diagrams1. Reflected light rays can be
extended behind the mirror.
2. Ray intersections represent
locations of image formation.
3. At least 2 rays must be drawn
for reference.
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Chapter 13
Image Formation by a Flat Mirror
Section 2 Flat Mirrors
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Chapter 13
Comparing Real and Virtual Images
Section 2 Flat Mirrors
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Section 3 Curved Mirrors
Chapter 13
Concave Spherical Mirrors
• A concave spherical mirror The reflecting surface
is on the inside of a sphere.
• Concave mirrors can be used to form real and virtual
images depending on the position of the object being
reflected.
• A real image is an image formed when rays of light
pass through a point on the image. Real images can
be projected onto a screen.
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Chapter 13
Image Formation by a Concave Spherical Mirror
Section 3 Curved Mirrors
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Section 3 Curved Mirrors
Chapter 13
Concave Spherical Mirrors, continued
• The Mirror Equation relates object distance (p),
image distance (q), and focal length (f) of a spherical
mirror.
1
p
1
q
1
f
1
object distance
1
image distance
1
focal length
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Section 3 Curved Mirrors
Chapter 13
Concave Spherical Mirrors, continued
• The Equation for Magnification relates image height
or distance to object height or distance, respectively.
'–
image height image distancemagnification = –
object height object distance
h qM
h p
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Chapter 13
Rules for Drawing Reference Rays for Mirrors
Section 3 Curved Mirrors
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Regular p 465 honors 605
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Chapter 13
Ray Tracing for a Concave Spherical Mirror
Section 3 Curved Mirrors
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Sign Convention
• + q= real image in front of mirror
• -q= virtual image behind the mirror
• +M= virtual image (upright)
• -M= real image inverted
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Section 3 Curved Mirrors
Chapter 13
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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• Succeed
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Section 3 Curved Mirrors
Chapter 13
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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Section 3 Curved Mirrors
Chapter 13
Sample Problem, continued
Imaging with Concave Mirrors
2. Draw a ray diagram using the rules for drawing
reference rays.
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Section 3 Curved Mirrors
Chapter 13
Sample Problem, continued
Imaging with Concave Mirrors
3. Use the mirror equation to relate the object and
image distances to the focal length.
–q
Mp
1
p
1
q
1
f
4. Use the magnification equation in terms of object
and image distances.
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Section 3 Curved Mirrors
Chapter 13
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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Section 3 Curved Mirrors
Chapter 13
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– –
10.0 cm 30.0 cm cm cm cm
15 cm
15 cm– – –0.50
30.0 cm
q
q
qM
p
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Section 3 Curved Mirrors
Chapter 13
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
Image Formation by a Convex Spherical Mirror
Section 3 Curved Mirrors
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Section 3 Curved Mirrors
Chapter 13
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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Section 3 Curved Mirrors
Chapter 13
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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Section 3 Curved Mirrors
Chapter 13
Sample Problem, continued
Convex Mirrors
2. Plan
Choose an equation or situation: Use the mirror
equation and the magnification formula.
1 1 1
– and – 'p
h hp f q q
1 1 1 '
and –h q
Mp q f h p
Rearrange the equation to isolate the unknown:
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Section 3 Curved Mirrors
Chapter 13
Sample Problem, continued
Convex Mirrors
3. Calculate
Substitute the values into the equation and solve:
1 1 1–
–8.00 cm –4.44 cm
1 –0.125 –0.225 0.100–
cm cm cm
10.0 cm
p
p
p
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Section 3 Curved Mirrors
Chapter 13
Sample Problem, continued
Convex Mirrors
3. Calculate, continued
Substitute the values for p and q to find the magnifi-cation of the image.
10.0 cm– ' – (2.50 cm)
–4.44 cm
5.63 cm
ph h
q
h
Substitute the values for p, q, and h’ to find the height of the object.
–4.44 cm
– – 0.44410.0 cm
qM M
p
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Chapter 13
Ray Tracing for a Convex Spherical Mirror
Section 3 Curved Mirrors
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Section 3 Curved Mirrors
Chapter 13
Parabolic Mirrors
• Images created by spherical mirrors suffer from
spherical aberration.
• parallel rays far from the principal axis converge
away from the mirrors focal point.
• Parabolic mirrors eliminate spherical aberration. All
rays converge at the focal point.
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Chapter 13
Spherical Aberration and Parabolic Mirrors
Section 3 Curved Mirrors
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Chapter 13
Reflecting Telescope
Section 3 Curved Mirrors
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Section 4 Color and Polarization
Chapter 13
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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Section 4 Color and Polarization
Chapter 13
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
Additive Color Mixing
Section 4 Color and Polarization
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Section 4 Color and Polarization
Chapter 13
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
Subtractive Color Mixing
Section 4 Color and Polarization
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Wavelength’s of visible spectrum
• Use nm remember 1X10-9
• Red = 700 nm
• Blue=450 nm
• Violet = 420 nm
• Why is the sky blue?
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Section 4 Color and Polarization
Chapter 13
Polarization of Light Waves
• Linear polarization is the alignment of electro-
magnetic 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
Linearly Polarized Light
Section 4 Color and Polarization
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Chapter 13
Aligned and Crossed Polarizing Filters
Section 4 Color and Polarization
Crossed FiltersAligned Filters
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Quantification of Polarization with two films
• Malus’s Law
• I2=I1 cos2θ
• Or
• I2=I1(cos θ)2
• I2=Light intensity passing through the second film
• I1 =Light intensity entering the first film.
• Θ=angle of separation between the films
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Section 4 Color and Polarization
Chapter 13
Polarization of Light Waves
• Light can also be polarized
by reflection and scattering.
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Chapter 13
Polarization by Reflection and Scattering
Section 4 Color and Polarization
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Multiple Choice
1. Which equation is correct for calculating the focal
point of a spherical mirror?
A. 1/f = 1/p – 1/q
B. 1/f = 1/p + 1/q
C. 1/p = 1/f + 1/q
D. 1/q = 1/f + 1/p
Standardized Test PrepChapter 13
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Multiple Choice, continued
1. Which equation is correct for calculating the focal
point of a spherical mirror?
A. 1/f = 1/p – 1/q
B. 1/f = 1/p + 1/q
C. 1/p = 1/f + 1/q
D. 1/q = 1/f + 1/p
Standardized Test PrepChapter 13
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Multiple Choice, continued
2. Which of the following statements is true about the
speeds of gamma rays and radio waves in a
vacuum?
F. Gamma rays travel faster than radio waves.
G. Radio rays travel faster than gamma rays.
H. Gamma rays and radio waves travel at the same
speed in a vacuum.
J. The speed of gamma rays and radio waves in a
vacuum depends on their frequencies.
Standardized Test PrepChapter 13
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Multiple Choice, continued
2. Which of the following statements is true about the
speeds of gamma rays and radio waves in a
vacuum?
F. Gamma rays travel faster than radio waves.
G. Radio rays travel faster than gamma rays.
H. Gamma rays and radio waves travel at the same
speed in a vacuum.
J. The speed of gamma rays and radio waves in a
vacuum depends on their frequencies.
Standardized Test PrepChapter 13
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Multiple Choice, continued
3. Which of the following correctly states the law of reflection?A. The angle between an incident ray of light and the normal to the mirror’s surface equals the angle between the mirror’s surface and the reflected light ray.
B. The angle between an incident ray of light and the mirror’s surface equals the angle between the normal to the mirror’s surface and the reflected light ray.
C. The angle between an incident ray of light and the normal to the mirror’s surface equals the angle between the normal and the reflected light ray.
D. The angle between an incident ray of light and the normal to the mirror’s surface is complementary to the angle between the normal and the reflected light ray.
Standardized Test PrepChapter 13
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Multiple Choice, continued
3. Which of the following correctly states the law of reflection?A. The angle between an incident ray of light and the normal to the mirror’s surface equals the angle between the mirror’s surface and the reflected light ray.
B. The angle between an incident ray of light and the mirror’s surface equals the angle between the normal to the mirror’s surface and the reflected light ray.
C. The angle between an incident ray of light and the normal to the mirror’s surface equals the angle between the normal and the reflected light ray.
D. The angle between an incident ray of light and the normal to the mirror’s surface is complementary to the angle between the normal and the reflected light ray.
Standardized Test PrepChapter 13
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Multiple Choice, continued
4. Which of the following processes does not linearly
polarize light?
F. scattering
G. transmission
H. refraction
J. reflection
Standardized Test PrepChapter 13
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Multiple Choice, continued
4. Which of the following processes does not linearly
polarize light?
F. scattering
G. transmission
H. refraction
J. reflection
Standardized Test PrepChapter 13
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Multiple Choice, continued
5. Which kind of mirror is
shown in the ray
diagram?
A. flat
B. convex
C. concave
D. Not enough
information is available
to draw a conclusion.
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
5. Which kind of mirror is
shown in the ray
diagram?
A. flat
B. convex
C. concave
D. Not enough
information is available
to draw a conclusion.
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
6. What is true of the
image formed by the
mirror?
F. virtual, upright, and diminished
G. real, inverted, and diminished
H. virtual, upright, and enlarged
J. real, inverted, and enlarged
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
6. What is true of the
image formed by the
mirror?
F. virtual, upright, and diminished
G. real, inverted, and diminished
H. virtual, upright, and enlarged
J. real, inverted, and enlarged
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
7. What is the focal length
of the mirror?
A. –10.0 cm
B. –4.30 cm
C. 4.30 cm
D. 10.0 cm
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
7. What is the focal length
of the mirror?
A. –10.0 cm
B. –4.30 cm
C. 4.30 cm
D. 10.0 cm
Standardized Test PrepChapter 13
Use the ray diagram below
to answer questions 5–7.
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Multiple Choice, continued
8. Which combination of primary additive colors will
produce magenta-colored light?
F. green and blue
G. red and blue
H. green and red
J. cyan and yellow
Standardized Test PrepChapter 13
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Multiple Choice, continued
8. Which combination of primary additive colors will
produce magenta-colored light?
F. green and blue
G. red and blue
H. green and red
J. cyan and yellow
Standardized Test PrepChapter 13
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Multiple Choice, continued
9. What is the frequency of an infrared wave that has a
vacuum wavelength of 5.5 µm?
A. 165 Hz
B. 5.5 1010 Hz
C. 5.5 1013 Hz
D. 5.5 1016 Hz
Standardized Test PrepChapter 13
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Multiple Choice, continued
9. What is the frequency of an infrared wave that has a
vacuum wavelength of 5.5 µm?
A. 165 Hz
B. 5.5 1010 Hz
C. 5.5 1013 Hz
D. 5.5 1016 Hz
Standardized Test PrepChapter 13
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Multiple Choice, continued
10. If the distance from a light source is increased by a
factor of 5, by how many times brighter does the light
appear?
F. 25
G. 5
H. 1/5
J. 1/25
Standardized Test PrepChapter 13
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Multiple Choice, continued
10. If the distance from a light source is increased by a
factor of 5, by how many times brighter does the light
appear?
F. 25
G. 5
H. 1/5
J. 1/25
Standardized Test PrepChapter 13
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Short Response
11. White light is passed through a filter that allows only
yellow, green, and blue light to pass through it. This
light is then shone on a piece of blue fabric and on a
piece of red fabric. Which colors do the two pieces of
fabric appear to have under this light?
Standardized Test PrepChapter 13
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Short Response, continued
11. White light is passed through a filter that allows only
yellow, green, and blue light to pass through it. This
light is then shone on a piece of blue fabric and on a
piece of red fabric. Which colors do the two pieces of
fabric appear to have under this light?
Answer:
The blue fabric appears blue. The red fabric
appears black.
Standardized Test PrepChapter 13
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Short Response, continued
12. The clothing department of a store has a mirror that consists of three flat mirrors, each arranged so that a person standing before the mirrors can see how an article of clothing looks from the side and back. Suppose a ray from a flashlight is shined on the mirror on the left. If the incident ray makes an angle of 65º with respect to the normal to the mirror’s surface, what will be the angle q of the ray reflected from the mirror on the right?
Standardized Test PrepChapter 13
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Short Response, continued
12. The clothing department of a store has a mirror that consists of three flat mirrors, each arranged so that a person standing before the mirrors can see how an article of clothing looks from the side and back. Suppose a ray from a flashlight is shined on the mirror on the left. If the incident ray makes an angle of 65º with respect to the normal to the mirror’s surface, what will be the angle q of the ray reflected from the mirror on the right?
Standardized Test PrepChapter 13
Answer: 65º
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Short Response, continued
13. X rays emitted from material around compact
massive stars, such as neutron stars or black holes,
serve to help locate and identify such objects. What
would be the wavelength of the X rays emitted from
material around such an object if the X rays have a
frequency of 5.0 1019 Hz?
Standardized Test PrepChapter 13
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Short Response, continued
13. X rays emitted from material around compact
massive stars, such as neutron stars or black holes,
serve to help locate and identify such objects. What
would be the wavelength of the X rays emitted from
material around such an object if the X rays have a
frequency of 5.0 1019 Hz?
Answer: 6.0 10–12 m = 6.0 pm
Standardized Test PrepChapter 13
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Extended Response
14. Explain how you can use a piece of polarizing
plastic to determine if light is linearly polarized.
Standardized Test PrepChapter 13
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Extended Response, continued
14. Explain how you can use a piece of polarizing
plastic to determine if light is linearly polarized.
Answer: Polarized light will pass through the plastic
when the transmission axis of the plastic is parallel
with the light’s plane of polarization. Rotating the
plastic 90º will prevent the polarized light from
passing through the plastic, so the plastic appears
dark. If light is not linearly polarized, rotating the
plastic 90º will have no effect on the light’s intensity.
Standardized Test PrepChapter 13
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Extended Response, continued
15. What is the distance
between the surface of
the mirror and the
image?
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
15. What is the distance
between the surface of
the mirror and the
image?
Answer: 15.0 cm
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
16. What is the focal
length of the mirror?
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
16. What is the focal
length of the mirror?
Answer: 10.0 cm
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
17. What is the
magnification of the
image?
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
17. What is the
magnification of the
image?
Answer: –0.500
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
18. If the candle is 12 cm
tall, what is the image
height?
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
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Extended Response, continued
18. If the candle is 12 cm
tall, what is the image
height?
Answer: –6.0 cm
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
ResourcesChapter menu
Extended Response, continued
19. Is the image real or
virtual? Is it upright or
inverted?
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
ResourcesChapter menu
Extended Response, continued
19. Is the image real or
virtual? Is it upright or
inverted?
Answer: real; inverted
Standardized Test PrepChapter 13
Use the ray diagram below to
answer questions 15–19.
A candle is placed 30.0 cm from
the reflecting surface of a
concave mirror. The radius of
curvature of the mirror is 20.0 cm.