• SICS 10e
`
`David Young
`Shane Stadler
`
`Louisiana State University
`
`WILEY
`
`Page 1
`
`

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`Main text: 9781118486894
`Main text binder ver.;ion: 9781118651889
`Volume 1:9781118836880
`Volume 2: 9781 I 18836873
`
`Printed in the United States of America
`
`109876543 2 1
`
`Page 2
`
`

`
`I Contents __
`
`llntroduction and Mathematical Concepts 1
`1.1
`The Nature of Physics 1
`1.2
`Units 1
`1.3
`The Role of Units in Problem Solving 3
`1.4
`Trigonometry 6
`1.5
`Scalars and Vectors 8
`1.6
`Vector Addition and Subtraction 10
`1.7
`The Components of a Vector 12
`1.8
`Addition of Vectors by Means of Components 15
`CONCEPT SUMMARY 18
`
`2 Kinematics in One Dimension 2s
`2.1
`Displacement 26
`2.2
`Speed and Velocity 27
`2.3
`Acceleration 29
`2.4
`Equations of Kinematics f or Constant Acceleration 33
`2.5
`Applications of the Equations of Kinematics 36
`2.6
`Freely Falling Bodies 40
`2.7 Graphical Analysis of Velocity and Acceleration 44
`CONCEPT SUMMARY 46
`
`3 Kinematics in Two Dimensions 54
`3.1
`Displacement. Velocity. and Acceleration 54
`3.2
`Equations of Kinematics in Two Dimensions 55
`3.3
`Projectile Motion 59
`3.4 Relative Velocity 67
`CONCEPT SUMMARY 71
`
`4 Forces and Newton's Laws of Motion 79
`4.1
`The Concepts of Force and Mass 79
`4.2 Newton's First Law of Motion 79
`4.3
`Newton's Second Law of Motion 81
`4.4
`The Vector Nature of Newton's Second Law
`of Motion 84
`4.5 Newton's Third Law of Motion 85
`4.6
`Types of Forces: An Overview 8 6
`4.7
`The Gravitational Force 87
`4.8
`The Normal Force 91
`4.9
`Static and Kinetic Frictional Forces 94
`4.10 The Tension Force 100
`4.11
`Equilibrium Applications of Newton's Laws
`of Motion 101
`4.12 Nonequilibrium Applications of Newton's Laws
`of Motion 105
`CONCEPT SUMMARY 110
`
`5 Dynamics of Uniform Circular Motion 121
`5.1
`Uniform Circular Motion 121
`5.2
`Centripetal Acceleration 122
`5.3
`Centripetal Force 125
`5.4
`Banked Curves 128
`5.5
`Satellites In Circular Orbits 129
`
`vi
`
`5.6
`Apparent Weightlessness and Artificial Gravity 133
`*5.7
`Vertical Circular Motion 135
`CONCEPT SUMMARY 136
`
`6 Work and Energy 142
`6.1 Work Done by a Constant Force 142
`6.2
`The Work-Energy Theorem and Kinetic Energy 145
`6.3 Gravitational Potential Energy 152
`6.4 Conservative Versus Nonconservative Forces 154
`6.5
`The Conservation of Mechanical Energy 156
`6.6
`Nonconservative Forces and the Work-Energy
`Theorem 159
`6.7
`Power 160
`6.8 Other Forms of Energy and the Conservation of
`Energy 162
`6.9 Work Done by a Variable Force 162
`CONCEPT SUMMARY 164
`
`7 Impulse and Momentum 173
`7.1
`The Impulse-Momentum Theorem 173
`7.2
`The Principle of Conservation of Linear Momentum 177
`7.3
`Collisions in One Dimension 182
`7.4 Collisions in Two Dimensions 187
`7.5
`Center of Mass 187
`CONCEPT SUMMARY 189
`
`8 Rotational Kinematics 197
`8.1
`Rotational Motion and Angular Displacement 197
`8.2
`Angular Velocity and Angular Acceleration 200
`8.3
`The Equations of Rotational Kinematics 202
`8.4
`Angular Variables and Tangential Variables 204
`8.5
`Centripetal Acceleration and Tangential
`Acceleration 206
`8.6 Rolling Motion 20 9
`*8.7
`The Vector Nature of Angular Variables 210
`CONCEPT SUMMARY 210
`
`9 Rotational Dynamics 21s
`9.1
`The Action of Forces and Torques on Rigid Objects 218
`9.2 Rigid Objects in Equilibrium 220
`9.3
`Center of Gravity 225
`9.4 Newton's Second Law for Rotational Motion About a
`Fixed Axis 230
`Rotational Work and Energy 236
`9.5
`9.6
`Angular Momentum 239
`CONCEPT SUMMARY 241
`
`10 Simple Harmonic Motion
`and Elasticity 2s1
`10.1
`The Ideal Spring and Simple Harmonic Motion 251
`10.2 Simple Harmonic Motion and the Reference Circle 255
`10.3 Energy and Simple Harmonic Motion 260
`
`Page 3
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`

`
`10.4 The Pendulum 263
`10.5 Damped Harmonic Motion 266
`10.6 Driven Harmonic Motion and Resonance 267
`10.7 Elastic Deformation 268
`10.8 Stress, Strain, and Hooke's Law 271
`CONCEPT SUMMARY 272
`
`11 Fluids 281
`11.1 Mass Density 281
`11.2 Pressure 282
`11.3 Pressure and Depth in a Static Fluid 284
`11.4 Pressure Gauges 287
`11.5 Pascal's Principle 288
`11.6 Archimedes' Principle 291
`11.7
`Fluids in Motion 295
`11.8
`The Equation of Continuity 297
`11.9 Bernoulli's Equation 299
`11.10 Applications of Bernoulli's Equation 301
`*11.11 Viscous Flow 304
`CONCEPT SUMMARY 306
`
`12 Temperature and Heat 316
`12.1 Common Temperature Scales 316
`12.2 The Kelvin Temperature Scale 317
`12.3 Thermometers 318
`12.4 Linear Thermal Expansion 320
`12.5 Volume Thermal Expansion 326
`12.6 Heat and Internal Energy 328
`12.7 Heat and Temperature Change: Specific Heat
`Capacity 328
`12.8 Heat and Phase Change: Latent Heat 331
`*12.9 Equilibrium Between Phases of Matter 336
`*12.10 Humidity 339
`CONCEPT SUMMARY 340
`13 The Transfer of Heat 348
`13.1 Convection 348
`13.2 Conduction 351
`13.3 Radiation 357
`13.4 Applications 361
`CONCEPT SUMMARY 362
`
`14 The Ideal Gas law and Kinetic
`Theory 367
`14.1 Molecular Mass, the Mole, and Avogadro's
`Number 367
`14.2 The Ideal Gas Law 370
`14.3 Kinetic Theory of Gases 375
`*14.4 Diffusion 379
`CONCEPT SUMMARY 382
`
`Contents
`
`vii
`
`15.4 Thermal Processes 391
`15.5 Thermal Processes Using an Ideal Gas 395
`15.6 Specific Heat Capacities 398
`15.7 The Second Law of Thermodynamics 399
`15.8 Heat Engines 400
`15.9 Carnot's Principle and the Carnot Engine 401
`15.10 Refrigerators, Air Conditioners, and Heat
`Pumps 404
`15.11 Entropy 408
`15.12 The Third Law of Thermodynamics 412
`CONCEPT SUMMARY 412
`
`16 Waves and Sound 422
`16.1 The Nature of Waves 422
`16.2 Periodic Waves 424
`16.3 The Speed of a Wave on a String 425
`*16.4 The Mathematical Description of a Wave 428
`16.5 The Nature of Sound 428
`16.6 The Speed of Sound 431
`16.7 Sound Intensity 435
`16.8 Decibels 437
`16.9 The Doppler Effect 439
`16.10 Applications of Sound in Medicine 444
`*16.11 The Sensitivity of the Human Ear 446
`CONCEPT SUMMARY 446
`17 The Principle of linear Superposition
`and Interference Phenomena 456
`17.1 The Principle of Linear Superposition 456
`17.2 Constructive and Destructive Interference of Sound
`Waves 457
`17.3 Diffraction 461
`17.4 Beats 463
`17.5 Transverse Standing Waves 465
`17.6
`Longitudinal Standing Waves 469
`*17.7 Complex Sound Waves 472
`CONCEPT SUMMARY 473
`18 Electric Forces and Electric Fields 481
`18.1 The Origin of Electricity 481
`18.2 Charged Objects and the Electric Force 482
`18.3 Conductors and Insulators 484
`18.4 Charging by Contact and by Induction 485
`18.5 Coulomb's Law 486
`18.6 The Electric Field 491
`18.7 Electric Field Lines 496
`18.8 The Electric Field Inside a Conductor: Shielding 499
`18.9 Gauss' Law 501
`*18.10 Copiers and Computer Printers 505
`CONCEPT SUMMARY 506
`
`15 Thermodynamics 388
`15.1
`Thermodynamic Systems and Their Surroundings 388
`15.2 The Zeroth Law of Thermodynamics 388
`15.3 The First Law of Thermodynamics 389
`
`19 Electric Potential Energy and the
`Electric Potential s14
`19.1 Potential Energy 514
`19.2 The Electric Potential Difference 515
`
`Page 4
`
`

`
`viii
`
`Contents
`
`19.3 The Electric Potential Difference Created by Point
`Charges 521
`19.4 Equipotential Surfaces and Their Relation to the
`Electric Field 525
`19.5 Capacitors and Dielectrics 528
`*19.6 Biomedical Applications of Electric Potential
`Differences 532
`CONCEPT SUMMARY 534
`
`20 Electric Circuits 541
`20.1 Electromotive Force and Current 541
`20.2 Ohm's law 543
`20.3 Resistance and Resistivity 544
`20.4 Electric Power 547
`20.5 Alternating Current 549
`20.6 Series Wiring 552
`20.7 Parallel Wiring 555
`20 .8 Circuits Wired Partially in Series and Partially in
`Parallel 559
`Internal Resistance 560
`20.9
`20.10 Kirchhoff's Rules 561
`20.11 The Measurement of Current and Voltage 564
`20.12 Capacitors in Series and in Parallel 566
`20.13 RC Circuits 568
`20.14 Safety and the Physiological Effects of
`Current 569
`CONCEPT SUMMARY 570
`
`21 Magnetic Forces and Magnetic
`Fields 5so
`21.1 Magnetic Fields 580
`21.2 The Force That a Magnetic Field Exerts on a Moving
`Charge 582
`21.3 The Motion of a Charged Particle in a Magnetic
`Field 585
`21.4 The Mass Spectrometer 589
`21.5 The Force on a Current in a Magnetic Field 590
`21.6 The Torque on a Current-Carrying Coil 592
`21.7 Magnetic Fields Produced by Currents 594
`21.8 Ampere's Law 601
`21.9 Magnetic Materials 602
`CONCEPT SUMMARY 605
`
`22 Electromagnetic Induction 615
`22.1
`Induced Emf and Induced Current 615
`22.2 Motional Emf 616
`22.3 Magnetic Flux 622
`22.4 Faraday's Law of Electromagnetic Induction 624
`22.5 Lenz's Law 627
`*22.6 Applications of Electromagnetic Induction to the
`Reproduction of Sound 630
`22.7 The Electric Generator 631
`22.8 Mutual Inductance and Self-Inductance 636
`22.9 Transformers 639
`CONCEPT SUMMARY 642
`
`23 Alternating Current Circuits 651
`23.1 Capacitors and Capacitive Reactance 651
`23.2
`Inductors and Inductive Reactance 653
`23.3 Circuits Containing Resistance. Capacitance. and
`Inductance 655
`23.4 Resonance in Electric Circuits 660
`23.5 Semiconductor Devices 662
`CONCEPT SUMMARY 667
`24 Electromagnetic Waves 673
`24.1 The Nature of Electromagnetic Waves 673
`24.2 The Electromagnetic Spectrum 6n
`24.3 The Speed of Light 679
`24.4 The Energy Carried by Electromagnetic Waves 681
`24.5 The Doppler Effect and Electromagnetic Waves 685
`24.6 Polarization 686
`CONCEPT SUMMARY 692
`25 The Reflection of Light: Mirrors 699
`25.1 Wave Fronts and Rays 699
`25.2 The Reflection of Light 100
`25.3 The Formation of Images by a Plane Mirror 701
`25.4 Spherical Mirrors 703
`25.5 The Formation of Images by Spherical Mirrors 706
`25.6 The Mirror Equation and the Magnification
`Equation 710
`CONCEPT SUMMARY 715
`26 The Refraction of Light: lenses and
`Optical Instruments 121
`26.1 The Index of Refraction 121
`26.2 Snell's Law and the Refraction of Light 722
`26.3 Total Internal Reflection 727
`26.4 Polarization and the Reflection and Refraction of
`Light 733
`26.5 The Dispersion of Light: Prisms and Rainbows 733
`26.6
`lenses 735
`26.7 The Formation of Images by lenses 736
`26.8 The Thin-Lens Equation and the Magnification
`Equation 739
`26.9 Lenses in Combination 742
`26.10 The Human Eye 744
`26.11 Angular Magnification and the Magnifying Glass 748
`26.12 The Compound Microscope 750
`26.13 The Telescope 751
`26.14 Lens Aberrations 753
`CONCEPT SUMMARY 754
`27 Interference and the Wave
`Nature of Light 766
`27.1 The Principle of Linear Superposition 766
`27.2 Young's Double-Slit Experiment 768
`Thin-Film Interference n1
`27 3
`27.4 The Michelson Interferometer n5
`27.5 Diffraction n6
`
`Page 5
`
`

`
`Contents
`
`ix
`
`27.6 Resolving Power 780
`27.7 The Diffraction Grating 785
`"27.8 Compact Discs, Digital Video Discs. and the Use of
`Interference 787
`27.9 X-Ray Diffraction 789
`CONCEPT SUMMARY 790
`28 Special Relativity 798
`28.1 Events and Inertial Reference Frames 798
`28.2 The Postulates of Special Relativity 799
`28.3 The Relativity of Time: Time Dilation 801
`28.4 The Relativity of Length: Length Contraction 805
`28.5 Relativistic Momentum 807
`28.6 The Equivalence of Mass and Energy 809
`28.7 The Relativistic Addition of Velocities 814
`CONCEPT SUMMARY 816
`
`29 Particles and Waves 822
`29.1 The Wave-Particle Duality 822
`29.2 Blackbody Radiation and Planck's Constant 823
`293 Photons and the Photoelectric Effect 824
`29.4 The Momentum of a Photon and the Compton
`Effect 830
`29.5 The De Broglie Wavelength and the Wave Nature of
`Matter 833
`29.6 The Heisenberg Uncertainty Principle 835
`CONCEPT SUMMARY 839
`30 The Nature of the Atom 844
`30.1 Rutherford Scattering and the Nuclear Atom 844
`30.2 Line Spectra 845
`30.3 The Bohr Model of the Hydrogen Atom 847
`30.4 De Broglie's Explanation of Bohr's Assumption About
`Angular Momentum 852
`30.5 The Quantum Mechanical Picture of the Hydrogen
`Atom 852
`30.6 The Pauli Exclusion Principle and the Periodic
`Table of the Elements 856
`30.7 X-Rays 859
`30.8 The Laser 863
`"30.9 Medical Applications of the Laser 865
`
`*30.10 Holography 867
`CONCEPT SUMMARY 869
`
`31 Nuclear Physics and Radioactivity 876
`31.1 Nuclear Structure 876
`31.2 The Strong Nuclear Force and the Stability of the
`Nucleus 878
`313 The Mass Defect of the Nucleus and Nuclear Binding
`Energy 879
`31.4 Radioactivity 882
`31.5 The Neutrino 887
`31.6 Radioactive Decay and Activity 888
`31.7 Radioactive Dating 891
`31.8 Radioactive Decay Series 895
`31.9 Radiation Detectors 895
`CONCEPT SUMMARY 897
`
`32 Ionizing Radiation, Nuclear Energy. and
`Elementary Particles 903
`32.1 Biological Effects of Ionizing Radiation 903
`Induced Nuclear Reactions 907
`32.2
`32.3 Nuclear Fission 909
`32.4 Nuclear Reactors 911
`32.5 Nuclear Fusion 912
`32.6 Elementary Particles 915
`32.7 Cosmology 920
`CONCEPT SUMMARY 923
`Appendixes A-1
`Appendix A Powers of Ten and Sdentific Notation A-1
`Appendix 8 Significant Figures A-1
`Appendix C Algebra A-2
`Appendix D Exponents and Logarithms A-3
`Appendix E Geometry and Trigonometry A-4
`Appendix F Selected Isotopes A-5
`Answers to Check Your Understanding A-9
`Answers to Odd-Numbered Problems A-16
`Index ,_,
`
`A list of The Physics of applications can be found on the showcase site: www.wiley.com/coUege/sdcutnell
`
`Page 6
`
`

`
`706
`
`Chapter 25 1 The Reflection of Light: Mirrors
`
`5. The photograph shows an experimental device
`at Sandia National Laboratories in New Mexico.
`This device is a mirror that focuses sunlight to
`heat sodium to a boil, which then heats helium gas
`in an engine. The engine does the work of driving
`a generator to produce electricity. The sodium unit
`and the engine are labeled in the photo. (a) What
`kind of mirror, concave or convex, is being used?
`(b) Where is the sodium unit located relative to
`the mirror? Express your answer in terms of the
`focal length of the mirror.
`6. Refer to Figure 25.14 and the related discussion
`about spherical aberration. To bring the top
`ray closer to the focal point F after reflection,
`describe how you would change the shape of the
`mirror. Would you open it up to produce a more
`gently curving shape or bring the top and bottom
`edges closer to the principal axis?
`
`Question 5
`
`25.5 I The Formation of Images by Spherical Mirrors
`As we have seen, some of the light rays emitted from an object in front of a mirror strike
`the mirror, reflect from it, and form an image. We can analyze the image produced by either
`concave or convex mirrors by using a graphkaJ method called ray tracing. This method is
`based on the law of reflection and the notion that a spherical mirror has a center of curva(cid:173)
`ture C and a focal point F. Ray tracing enables us to find the locarion of the image, as well
`as its size, by taking advantage of the following fact paraxial rays leave from a point on
`the object and intersect, or appear to intersect, at a corresponding point on the in1age after
`reflection.
`
`Concave Mirrors
`
`Three specific paraxial rays are especially convenient to use in the ray-tracing method.
`Figure 25.17 shows an object in front of a concave mirror, and these three rays leave from a
`point on the top of the object. The rays are labeled I, 2, and 3, and when tracing their paths,
`we use the following reasoning strategy.
`
`Reasoning Strategy Ray Tracing for a Concave Mirror
`Ray 1. This ray is initially parallel to the principal axis and. therefore, passes through tl1e focal
`point F after reflection from the mirror.
`Ray 2. This ray initially passes through the focal point F and is reflected paraHel to the principal
`axis. Ray 2 is analogous to ray l except iliat the reflected, rather tl1an the incident, ray is
`parallel to the principal axis.
`Ray 3. This ray travels along a line that passes tl1rough Lbe cenLer of curvature C and foUows a
`radius of the spherical mirror; as a resul4 the ray strikes the nmror perpendicularly and
`reflects back on itself.
`
`c
`
`Figure 25.17 The rays I abe led I, 2, and 3
`are useful in locating the image of an object
`placed in front of a concave spherical mirror.
`The object is represented as a vertical arrow.
`
`Page 7
`
`

`
`25.5 1 The Formation of Images by Spherical Mirrors
`
`707
`
`If rays 1, 2, and 3 are superimposed on a scale drawing, they converge at a point on the
`top of the image, as can be seen in Figure 25.18a.* Although three rays have been used here
`to locate the image, only two are really needed; the third ray is usually drawn to serve as
`a check. In a similar fashion, rays from all other points on the object locate corresponding
`points on the image, and the mirror forms a complete image of the object. If you were to
`place your eye as shown in the drawing, you would see an image that is larger and inverted
`relative to the object. The image is real because the light rays actually pass through the
`image.
`If the locations of the object and image in Figure 25.18a are interchanged, the situation
`in part b of the drawing results. The three rays in part b are the same as those in part a,
`except that the directions are reversed. These drawings illustrate the principle of reversibil(cid:173)
`ity, which states that If the direction of o light roy Is reversed, the light retraces Its orlglnol poth.
`This principle is quite general and is not restricted to reflection from mirrors. The image is
`real, and it is smaller and inverted relative to the object.
`When the object is placed between the focal point F and a concave mirror, as in
`Figure 25.19a, three rays can again be drawn to find the image. Now, however, ray 2
`does not go through the focal point on its way to the mirror, since the object is closer
`to the mirror than the focal point is. When projected backward, though, ray 2 appears
`to come from the focal point. Therefore, after reflection, ray 2 is directed parallel to
`the principal axis. In this case the three reflected rays diverge from each other and do
`not converge to a common point. However, when projected behind the mirror, the three
`rays appear to come from a common point; thus, a virtual image is formed. This virtual
`image is larger than the object and upright.
`The physics of makeup and shaving mirrors. Makeup and shaving mirrors are concave
`mirrors. When you place your face between the mirror and its focal point, you see an
`enlarged virtual image of yourself, as Figure 25.19b shows.
`
`~ Figure 25.18 (a) When an object is
`~~ placed between the focal point F and the
`center of curvature C of a concave mirror, a
`real image is formed. The image is enlarged
`and inverted relative to the object. (b) When
`the object is located beyond the center of
`curvature C, a real image is created that is
`reduced in size and inverted relative to the
`object.
`
`Problem-Solving Insight
`
`Figure 25.19 (a) When an object is located
`between a concave mirror and its focal point
`F, an enlarged, upright, and virtual image is
`produced. (b) A makeup mirror (or shaving
`mirror) is a concave mirror that functions in
`exactly this fashion, as this photograph shows.
`
`Virtua l
`image
`
`*In the drawings that follow. we assume that the rays are paraxial, although the distance between the rays and
`the principal axis is often exaggerated for clarity.
`
`(a)
`
`(b)
`
`Page 8
`
`

`
`708
`
`Chapter 25 1 The Reflection of Light: Mirrors
`
`Windshield
`
`I Combiner
`~ I
`
`(b)
`
`Virtual
`1mage 2
`
`c~~:v~------J
`
`m1rror
`
`'
`'
`
`' ' ' ' ' "
`
`Virtual
`image 1
`
`The physics of a head-up display for automobiles. Concave mirrors are also used
`in one method for displaying the speed of a car. The method presents a digital readout
`(e.g., "5 1 km/h") that the driver sees when looking directly through the windshield,
`as in Figure 25.20a. The advantage of the method, which is called a head-up display
`(HUD), is that the driver does not need to take his or her eyes off the road to monitor
`the speed. Figure 25.20b shows how one type of HUD works. Below the windshield is a
`readout device that displays the speed in digital form. This device is located between a
`concave mirror and its focal point. The arrangement is similar to the one in Figure 25.19a
`and produces a virtual, upright, and enlarged image of the speed readout (see virtual im(cid:173)
`age I in Figure 25.20b). Light rays that appear to come from this image strike the wind(cid:173)
`shield at a place where a so-called "combiner" is located. The purpose of the combiner
`is to combine the digital readout information with the field of view that the driver sees
`through the windshield. The combiner is virtually undetectable by the driver because it
`allows all colors except one to pass through it unaffected. The one exception is the color
`produced by the digital readout device. For this color, the combiner behaves as a plane
`mirror and reflects the light that appears to originate from image 1. Thus, the combiner
`produces image 2, which is what the driver sees. The location of image 2 is out above
`the front bumper. The driver can then read the speed with eyes focused just as they are
`to see the road.
`
`Convex Mirrors
`
`The ray-tracing procedure for determining the location and size of an image in a convex
`mirror is similar to that for a concave mirror. The same three rays are used. However,
`the focal point and center of curvature of a convex. mirror lie behind the mirror, not in
`front of it. Figure 25.21a shows the rays. When tracing their paths, we use the following
`reasoning strategy, which takes into account these locations of the focal point and center
`of curvature.
`
`(a)
`Figure 25.20 (a) A head-up display (HUD)
`presents the driver with a eli gila! readout
`of the car's speed in the field of view seen
`through the windshield. (b) One version of a
`HUD uses a concave mirror. (See the text for
`explanation.)
`
`Figure 25.21 (a) An object placed in front
`of a convex mirror always produces a vinual
`image behind the mirror; the image is reduced
`in size and is upright. (b) This chromed
`motorcycle helmet acts as a convex mirror and
`produces an image of other motorcycles and
`pedestrians.
`
`Object
`
`F
`
`image
`
`C
`
`(a)
`
`(b)
`
`Page 9
`
`

`
`25.5 1 The Formation of Images by Spherical Mirrors
`
`709
`
`Reasoning Strategy Ray Tracing for a Convex Mirror
`
`Ray 1. This ray is initially parallel to the principal axis and, therefore, appears to originate from
`the focal point F after reflection from the mirror.
`Ray 2. This ray beads toward F, emerging parallel to the principal axis after reflection. Ray 2 is
`analogous to ray 1, except that the reflected, rather than the incident, ray is parallel to the
`principal axis.
`Ray 3. This ray travels toward the center of curvature C; as a result, the ray strikes the mirror
`perpendicularly and reflects back on itself.
`
`The three rays in Figure 25.2 La appear
`to come from a point on a virtual image that
`is behind the mirror. The virtual image is
`diminished in size and upright, relati ve to
`the object. A convex mirror always forms a
`virtual image of the object, no matter where
`in front of the mirror the object is placed.
`Figure 25.21b shows an example of such an
`image.
`
`----~-=~--~=-_.----~~·' ,,
`',
`
`--+---=-"--~ ~::::::.::;~"1«---" ............... ------------
`
`Object
`
`F
`
`image
`
`C
`
`The physics of passenger-side automobile mirrors. Because of its shape, a convex
`mirror gives a wider field of view than do other types of mirrors. A mirror with a wide
`field of view is needed to give a driver a good rear view. Thus, the outside mirror on the
`passenger side is often a convex mirror. Printed on such a mirror is usually the warning
`"VEHICLES LN MIRROR ARE CLOSER THAN THEY APPEAR." The reason for the warning is that,
`as in Figure 25.2la, the virtual image is reduced in size and therefore looks smaller,
`just as a distant object would appear in a plane mirror. An unwary driver, thinking that
`the side-view mirror is a plane mirror, might incorrectly deduce from the small size of
`the image that the car behind is far enough away to ignore. Because of their wide field
`of view, convex mirrors are also used in stores for security purposes.
`
`(a)
`
`Check Your Understanding
`
`(The answers are given at the end of the book.)
`7. Concept Simulation 25.3 at www.wiley.com/coUege/cutneU allows you to explore the con(cid:173)
`cepts to which this question relates. rs it possible to use a convex mirror to produce an image
`that is larger than the object?
`8. (a) When you look at the back side of a shiny teaspoon held at arm's length, do you see
`yourself upright or upside down? (b) When you look at the other side of the spoon, do you see
`yourself upright or upside down? Assume in both cases that the distance between you and the
`spoon is greater than the focal length of the spoon.
`9. (a) Can the image formed by a concave mirror ever be projected directly onto a screen without
`the help of other mirrors or lenses? If :so, specify where the object should be placed relative to
`the mirror. (b) Repeat part (a) assuming that the mirror is convex.
`I 0. Suppose that you stand in front of a spherical mirror (concave or convex). Is it possible for
`your image to be (a) real and upright (b) virtual and inverted?
`II. An object is placed between the focal point and the center of curvature of a concave mirror.
`The object is then moved closer to the mirror, but still remains between the focal point and
`the center of curvature. Do the magnitudes of (a) the image distance and (b) the image height
`become larger or smaller?
`12. When you see the image of yourself formed by a mirror. it is because (1) light rays actually
`coming from a real image enter your eyes or (2) light rays appearing to come from a virtual
`image enter your eyes. If light rays from the image do not enter your eyes. you do not see
`yourself. Are there any places on the principal axis where you cartnot see yourself when you
`are standing in from of a mirror that is (a) convex (b) concave? If so. where are these places?
`Assume that you have only the one mirror to use.
`
`(b)
`Figure 25.21 (Repeated) (a) An object placed
`in front of a convex mirror always produces
`a virtual image behind the mirror; the io1age
`is reduced in size and is upright. (b) This
`chromed motorcycle helmet acts as a convex
`mirror and produces an image of other
`motOrcycles and pedestrians.
`
`Page 10
`
`

`
`710
`
`Chapter 25 1 The Reflection of light: Mirrors
`
`Object
`
`(a)
`
`(b)
`Figure 25.22 These diagrams are used
`to derive the mirror equation and the
`magnification equation. (a) The two colored
`triangles are similar triangles. (b) If the ray
`is close to the principal axis, the two colored
`regions are almost similar triangles.
`
`25.6 I The Mirror Equation and the Magnification Equation
`Ray diagrams drawn to scale are useful for determining the location and size of the image
`formed by a mirror. However, for an accurate description of the image, a more analytical
`technique is needed, so we will derive two equations, known as the m irror equation and
`the magnification equation. These equations are based on the law of reflection and provide
`relationships between:
`f = the focal length of the mirror
`do = the object distance, which is the distance between the object and the mirror
`d1 = the image distance, which is the distance between the image and the mirror
`m =the magnification of the mirror, which is the ratio of the height of the image to the
`height of the object.
`
`Concave Mirrors
`
`We begin our derivation of the mirror equation by referring to Figure 25.22a, which shows
`a ray leaving the top of the object and striking a concave mirror at the point where the
`principal axis intersects the mirror. Since the principal axis is perpendicular to the mirror,
`it is also the normal at this point of incidence. Therefore, the ray reflects at an equal angle
`and passes through the image. The two colored triangles are similar triangles because they
`have equal angles, so
`
`-h;
`
`d;
`
`where h., is the height of the object and h; is the height of the image. The minus sign appears
`on tlhe left in this equation because the image is inverted in Figure 25.22a. In part b another
`ray leaves the top of the object, this one passing through the focal point F, reflecting par(cid:173)
`allel to the principal axis, and then passing through the image. Provided the ray remains
`clos.e to the axis, the two colored areas can be considered to be similar triangles, with the
`result that
`
`do- J
`h0
`--=--
`f
`- h;
`Setting the two equations above equal to each other yields dJd1 = (d0 -
`this result gives the mirror equation:
`
`Mirror
`equation
`
`1
`1
`1
`-+- = (cid:173)
`d; J
`do
`
`f)/f Rearranging
`
`(25.3)
`
`We have derived this equation for a real image formed in front of a concave mirror. In
`this case, the image distance is a positive quantity, as are the object distance and the focal
`length. However, we have seen in the last section that a concave mirror can also form a vir(cid:173)
`tual image, if the object is located between the focal point and the mirror. Equation 25.3 can
`also be applied to such a situation, provided that we adopt the convention that d1 is negative
`for an image behind the mirror, as it is for a virtual in1age.
`In deriving the magnification equation, we remember that the magnification m of a
`mirror is the ratio of the image height to the object height: m = h;lh0 • If the image height
`is less than the object height, the magnitude of m is less than one, and if the image is
`larger than the object, the magnitude of m is greater than one. We have already shown
`that h0 / ( - h,) = dJd;, so it follows that
`
`Magnification
`equation
`
`d1
`Image height, h 1
`m = Object height, ho = -do
`
`(25.4)
`
`As Examples 3 and 4 show, the value of m is negative if the image is inverted and positive
`if the image is upright.
`
`Page 11
`
`

`
`25.6 I The Mirror Equation and the Magnification Equation
`
`7 11
`
`EXAMPLE 3 A Real image Formed by a Concave Mirror
`
`A 2.0-cm-high object is placed 7 .I 0 em from a concave mirror whose radius of curvature is
`10.20 em. Find (a) the location of the image and (b)