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University Physics Volume 3

Chapter 4

University Physics Volume 3Chapter 4
Table of contents
  1. Preface
  2. Optics
    1. 1 The Nature of Light
      1. Introduction
      2. 1.1 The Propagation of Light
      3. 1.2 The Law of Reflection
      4. 1.3 Refraction
      5. 1.4 Total Internal Reflection
      6. 1.5 Dispersion
      7. 1.6 Huygens’s Principle
      8. 1.7 Polarization
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Geometric Optics and Image Formation
      1. Introduction
      2. 2.1 Images Formed by Plane Mirrors
      3. 2.2 Spherical Mirrors
      4. 2.3 Images Formed by Refraction
      5. 2.4 Thin Lenses
      6. 2.5 The Eye
      7. 2.6 The Camera
      8. 2.7 The Simple Magnifier
      9. 2.8 Microscopes and Telescopes
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 3 Interference
      1. Introduction
      2. 3.1 Young's Double-Slit Interference
      3. 3.2 Mathematics of Interference
      4. 3.3 Multiple-Slit Interference
      5. 3.4 Interference in Thin Films
      6. 3.5 The Michelson Interferometer
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Diffraction
      1. Introduction
      2. 4.1 Single-Slit Diffraction
      3. 4.2 Intensity in Single-Slit Diffraction
      4. 4.3 Double-Slit Diffraction
      5. 4.4 Diffraction Gratings
      6. 4.5 Circular Apertures and Resolution
      7. 4.6 X-Ray Diffraction
      8. 4.7 Holography
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Modern Physics
    1. 5 Relativity
      1. Introduction
      2. 5.1 Invariance of Physical Laws
      3. 5.2 Relativity of Simultaneity
      4. 5.3 Time Dilation
      5. 5.4 Length Contraction
      6. 5.5 The Lorentz Transformation
      7. 5.6 Relativistic Velocity Transformation
      8. 5.7 Doppler Effect for Light
      9. 5.8 Relativistic Momentum
      10. 5.9 Relativistic Energy
      11. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    2. 6 Photons and Matter Waves
      1. Introduction
      2. 6.1 Blackbody Radiation
      3. 6.2 Photoelectric Effect
      4. 6.3 The Compton Effect
      5. 6.4 Bohr’s Model of the Hydrogen Atom
      6. 6.5 De Broglie’s Matter Waves
      7. 6.6 Wave-Particle Duality
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 7 Quantum Mechanics
      1. Introduction
      2. 7.1 Wave Functions
      3. 7.2 The Heisenberg Uncertainty Principle
      4. 7.3 The Schrӧdinger Equation
      5. 7.4 The Quantum Particle in a Box
      6. 7.5 The Quantum Harmonic Oscillator
      7. 7.6 The Quantum Tunneling of Particles through Potential Barriers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 8 Atomic Structure
      1. Introduction
      2. 8.1 The Hydrogen Atom
      3. 8.2 Orbital Magnetic Dipole Moment of the Electron
      4. 8.3 Electron Spin
      5. 8.4 The Exclusion Principle and the Periodic Table
      6. 8.5 Atomic Spectra and X-rays
      7. 8.6 Lasers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    5. 9 Condensed Matter Physics
      1. Introduction
      2. 9.1 Types of Molecular Bonds
      3. 9.2 Molecular Spectra
      4. 9.3 Bonding in Crystalline Solids
      5. 9.4 Free Electron Model of Metals
      6. 9.5 Band Theory of Solids
      7. 9.6 Semiconductors and Doping
      8. 9.7 Semiconductor Devices
      9. 9.8 Superconductivity
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 10 Nuclear Physics
      1. Introduction
      2. 10.1 Properties of Nuclei
      3. 10.2 Nuclear Binding Energy
      4. 10.3 Radioactive Decay
      5. 10.4 Nuclear Reactions
      6. 10.5 Fission
      7. 10.6 Nuclear Fusion
      8. 10.7 Medical Applications and Biological Effects of Nuclear Radiation
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 11 Particle Physics and Cosmology
      1. Introduction
      2. 11.1 Introduction to Particle Physics
      3. 11.2 Particle Conservation Laws
      4. 11.3 Quarks
      5. 11.4 Particle Accelerators and Detectors
      6. 11.5 The Standard Model
      7. 11.6 The Big Bang
      8. 11.7 Evolution of the Early Universe
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  12. Index

Check Your Understanding

4.1

17.8°17.8°, 37.7°37.7°, 66.4°66.4°; no

4.2

74.3°74.3°, 0.0083I00.0083I0

4.3

From dsinθ=mλdsinθ=mλ, the interference maximum occurs at 2.87°2.87° for m=20.m=20. From Equation 4.1, this is also the angle for the second diffraction minimum. (Note: Both equations use the index m but they refer to separate phenomena.)

4.4

3.332×10−6m3.332×10−6m or 300 lines per millimeter

4.5

8.4×10−4rad8.4×10−4rad, 3000 times broader than the Hubble Telescope

4.6

38.4°38.4° and 68.8°68.8°; Between θ=0°→90°θ=0°→90°, orders 1, 2, and 3, are all that exist.

Conceptual Questions

1.

The diffraction pattern becomes wider.

3.

Walkie-talkies use radio waves whose wavelengths are comparable to the size of the hill and are thus able to diffract around the hill. Visible wavelengths of the flashlight travel as rays at this size scale.

5.

The diffraction pattern becomes two-dimensional, with main fringes, which are now spots, running in perpendicular directions and fainter spots in intermediate directions.

7.

The parameter β=ϕ/2β=ϕ/2 is the arc angle shown in the phasor diagram in Figure 4.7. The phase difference between the first and last Huygens wavelet across the single slit is 2β2β and is related to the curvature of the arc that forms the resultant phasor that determines the light intensity.

9.

blue; The shorter wavelength of blue light results in a smaller angle for diffraction limit.

11.

No, these distances are three orders of magnitude smaller than the wavelength of visible light, so visible light makes a poor probe for atoms.

13.

UV wavelengths are much larger than lattice spacings in crystals such that there is no diffraction. The Bragg equation implies a value for sin⁡θ greater than unity, which has no solution.

15.

Image will appear at slightly different location and/or size when viewed using 10%10% shorter wavelength but at exactly half the wavelength, a higher-order interference reconstructs the original image, different color.

Problems

17.

a. 33.4°33.4°; b. no

19.

a. 1.35×10−6m1.35×10−6m; b. 69.9°69.9°

21.

750 nm

23.

2.4 mm, 4.7 mm

25.

a. 1.00λ;1.00λ; b. 50.0λ;50.0λ; c. 1000λ1000λ

27.

1.92 m

29.

45.1 ° 45.1 °

31.

I / I 0 = 2.2 × 10 −5 I / I 0 = 2.2 × 10 −5

33.

0.63 I 0 , 0.11 I 0 , 0.0067 I 0 , 0.0062 I 0 , 0.00088 I 0 0.63 I 0 , 0.11 I 0 , 0.0067 I 0 , 0.0062 I 0 , 0.00088 I 0

35.

0.200

37.

3

39.

9

41.

5.97 ° 5.97 °

43.

8.99 × 10 3 8.99 × 10 3

45.

707 nm

47.

a. 11.8°11.8°, 12.5°12.5°, 14.1°14.1°, 19.2°19.2°; b. 24.2°24.2°, 25.7°25.7°, 29.1°29.1°, 41.0°41.0°; c. Decreasing the number of lines per centimeter by a factor of x means that the angle for the x-order maximum is the same as the original angle for the first-order maximum.

49.

a. using λ=700nm,θ=5.0°;λ=700nm,θ=5.0°; b. using λ=460nm,θ=3.3°λ=460nm,θ=3.3°

51.

a. 26,300 lines/cm; b. yes; c. no

53.

1.13 × 10 −2 m 1.13 × 10 −2 m

55.

107 m

57.

a. 7.72×10−4rad;7.72×10−4rad; b. 23.2 m; c. 590 km

59.

a. 2.24×10−4rad;2.24×10−4rad; b. 5.81 km; c. 0.179 mm; d. can resolve details 0.2 mm apart at arm’s length

61.

2.9 μ m 2.9 μ m

63.

6.0 cm

65.

7.71 km

67.

1.0 m

69.

1.2 cm or closer

71.

no

73.

0.120 nm

75.

4.51 ° 4.51 °

77.

13.2 ° 13.2 °

Additional Problems

79.

a. 2.2 mm; b. 0.172°0.172°, second-order yellow and third-order violet coincide

81.

2.2 km

83.

1.3 cm

85.

a. 0.28 mm; b. 0.28 m; c. 280 m; d. 113 km

87.

33 m

89.

a. vertically; b. ±20°±20°, ±44°±44°; c. 0, ±31°±31°, ±60°±60°; d. 89 cm; e. 71 cm

91.

0.98 cm

93.

I / I 0 = 0.041 I / I 0 = 0.041

95.

340 nm

97.

a. 0.082 rad and 0.087 rad; b. 480 nm and 660 nm

99.

two orders

101.

yes and N/A

103.

600 nm

105.

a. 3.4×10−5°3.4×10−5°; b. 51°51°

107.

0.63 m

109.

1

111.

0.17 mW/cm2mW/cm2 for m=1m=1 only, no higher orders

113.

28.7 ° 28.7 °

115.

a. 42.3 nm; b. This wavelength is not in the visible spectrum. c. The number of slits in this diffraction grating is too large. Etching in integrated circuits can be done to a resolution of 50 nm, so slit separations of 400 nm are at the limit of what we can do today. This line spacing is too small to produce diffraction of light.

117.

a. 549 km; b. This is an unreasonably large telescope. c. Unreasonable to assume diffraction limit for optical telescopes unless in space due to atmospheric effects.

Challenge Problems

119.

a. I=0.00500I0,0.00335I0I=0.00500I0,0.00335I0; b. I=0.00500I0,0.00335I0I=0.00500I0,0.00335I0

121.

12,800

123.

1.58 × 10 −6 m 1.58 × 10 −6 m

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