Principles of Engineering Physics 1

Contents
Preface
Acknowledgment
1. Oscillations and Waves
	1.1 Introduction
		1.1.1 Parameters of an oscillatory system
	1.2 Simple Harmonic Oscillation (SHO)
		1.2.1 Energy of a simple harmonic oscillator
		1.2.2 Characteristics of SHO
	1.3 Damped Harmonic Oscillation (DHO)
		1.3.1 Damping of an oscillator
	1.4 Forced Vibrations
		1.4.1 Velocity of the forced harmonic oscillator
		1.4.2 Total energy of the forced harmonic oscillator
		1.4.3 Power of the forced harmonic oscillator
	1.5 Displacement Resonance
		1.5.1 Resonant amplitude
		1.5.2 Sharpness of resonance
		1.5.3 Quality factor of a forced harmonic oscillator
		1.5.4 Examples of resonance
	1.6 Coupled Oscillators
		1.6.1 Experiment on a two-body coupled oscillator
	1.7 Analogy of Mechanical and Electrical Oscillations
	1.8 Wave as a Periodic Variation Quantity in Space and Time
		1.8.1 Wave equation
		1.8.2 Wave equation in differential form
	1.9 Longitudinal and Transverse Waves
		1.9.1 Longitudinal waves
		1.9.2 Transverse waves
		1.9.3 Difference between longitudinal waves and transverse waves
		1.9.4 Characteristic of progressive waves
	1.10 Stationary Waves
		1.10.1 Formation of stationary waves
		1.10.2 Characteristics of stationary waves
		1.10.3 Differences between progressive and stationary waves
	1.11 Reflection of a Wave at the Boundary of Two Media
		1.11.1 Reflection of transverse waves
		1.11.2 Reflection of longitudinal waves
	1.12 Refraction of a Wave at the Boundary of Two Media
		1.12.1 Refraction of transverse waves
		1.12.2 Refraction of longitudinal waves
	1.13 Wave Packet
	1.14 Phase Velocity and Group Velocity
		1.14.1 Phase velocity
		1.14.2 Group velocity
		1.14.3 Relation between phase velocity and group velocity
	1.15 Uncertainty Principle
		1.15.1 Uncertainty principle for classical waves
		1.15.2 Heisenberg’s uncertainty principle
	1.16 Superposition of Waves
		1.16.1 Basis for the principle of superposition
		1.16.2 Principle of superposition
		1.16.3 Two beams superposition in one direction
		1.16.4 Multiple beam superpositions
		1.16.5 Coherent and incoherent superposition
	Questions
	Problems
	Multiple Choice Questions
	Answers
2. Interference
	2.1 Introduction
	2.2 Huygens’ Principle
		2.2.1 Explanation
		2.2.2 Construction of a new wavefront
		2.2.3 Absence of backward waves
		2.2.4 Applications
	2.3 Interference of Water Waves
	2.4 Young’s Double Slit Experiment
	2.5 Coherent Sources
		2.5.1 Methods of practical realization of coherent sources
	2.6 Classification of the Interference Phenomenon
	2.7 Theory of Interference
		2.7.1 Constructive interference (I = Imax)
		2.7.2 Destructive interference (I = Imin)
		2.7.3 Fringe spacing b
		2.7.4 Intensity distribution curve
	2.8 Conservation of Energy in Interference
	2.9 Conditions for Interference of Light
	2.10 Shape of Interference Fringes
		2.10.1 Shape of interference fringes on XY-plane (Hyperbolic)
	2.11 Interference Fringes in 3-D Space
		2.11.1 Shape of interference fringes on the ZX-plane (Circular)
		2.11.2 Shape of interference fringes on the XY-plane (Hyperbolic)
		2.11.3 Shape of interference fringes on the YZ-plane (Hyperbolic)
	2.12 Newton’s Rings
		2.12.1 Experimental setup
		2.12.2 Theory
		2.12.3 Calculations
		2.12.4 Diameter of the nth order Newton’s ring
		2.12.5 Diameter of the nth order bright Newton’s ring
		2.12.6 Diameter of the nth order dark Newton’s ring
		2.12.7 Central fringe as seen by the reflected light
	2.13 Newton’s Rings by Transmitted Light
		2.13.1 Diameter of the nth order Newton’s ring
		2.13.2 Diameter of the nth order bright Newton’s ring
		2.13.3 Diameter of the nth order dark Newton’s ring
		2.13.4 Central fringe as seen by the transmitted light
		2.13.5 Discussions
	2.14 Determination of Wavelength of Light using Newton’s Ring
		2.14.1 Theory for the experiment
	2.15 Determination of Refractive Index of Liquids using Newton’s Rings
		2.15.1 Theory for the experiment
	2.16 Fresnel’s Biprism
		2.16.1 Determination of wavelength of light using a biprism
	2.17 Interferometers
		2.17.1 Michelson interferometer
	Questions
	Problems
	Multiple Choice Questions
	Answers
3. Diffraction
	3.1 Introduction
	3.2 Classification of Diffraction
	3.3 Fresnel’s Explanation of Rectilinear Propagation of Light
		3.3.1 Fresnel’s assumptions
		3.3.2 Calculation of the resultant amplitude
		3.3.3 Average distance of the nth Fresnel’s half period zone from the pole
		3.3.4 Phase difference among half period zones
		3.3.5 Schuster’s method of summing the series
	3.4 Zone Plate
		3.4.1 Types of zone plates
		3.4.2 Action of the zone plate
		3.4.3 Principle behind zone plates
		3.4.4 Multiple foci of a zone plate
		3.4.5 Presence of odd numbered foci
		3.4.6 Intensity of fifth order focus
		3.4.7 Absence of even numbered foci
		3.4.8 Intensity of the fourth order focus
		3.4.9 Comparison of a zone plate with a convex lens
	3.5 Fraunhofer Diffraction
		3.5.1 Fraunhofer diffraction due to a single slit
		3.5.2 Intensity distribution
		3.5.3 Width of the principal maximum
	3.6 Plane Diffraction Grating
		3.6.1 Theory of plane diffraction grating under normal incidence
		3.6.2 Theory of plane diffraction grating under oblique incidence
		3.6.3 Angular width of the principal maxima
		3.6.4 Formation of spectra by diffraction grating
	3.7 Dispersion
	3.8 Determination of Wavelength of Light by Grating
		3.8.1 Theory
		3.8.2 Adjustments
		3.8.3 Measurement of q
		3.8.4 Calculation of l
		3.8.5 Alternative application
	Questions
	Problems
	Multiple Choice Questions
	Answers
4. Polarization
	4.1 Introduction
	4.2 Polarization of Waves
		4.2.1 Mechanical demonstration of polarization of waves
		4.2.2 Demonstration of optical polarization of waves
		4.2.3 Pictorial representation of light
		4.2.4 Few definitions
	4.3 Classification of Polarized Light
		4.3.1 Plane polarized light
		4.3.2 Circularly polarized light
		4.3.3 Elliptically polarized light
	4.4 Polarization by Reflection
		4.4.1 Explanation of polarization by reflection
		4.4.2 Brewster’s law
	4.5 Polarization by Refraction
		4.5.1 Malus’s law
	4.6 Polarization by Scattering
	4.7 Double Refraction
		4.7.1 Few terms connected with the double refraction phenomenon
		4.7.2 Difference between ordinary ray and extraordinary ray
		4.7.3 Polarization by double refraction
		4.7.4 Huygens’ experiment on polarization by double refraction
		4.7.5 Huygens’ theory of double refraction
		4.7.6 Phenomenon of double refraction at normal incidence
		4.7.7 Phenomenon of double refraction at oblique incidence
		4.7.8 Special cases
	4.8 Nicol Prism
		4.8.1 Principle
		4.8.2 Construction
		4.8.3 Action of a Nicol prism
		4.8.4 Limitations
		4.8.5 Parallel and crossed Nicol prisms
	4.9 Retardation Plates
		4.9.1 Half-wave plate
		4.9.2 Quarter-wave plate
	4.10 Production of Circularly Polarized Light
		4.10.1 Principle
		4.10.2 Production
		4.10.3 Analysis of circularly polarized light
	4.11 Production of Elliptically Polarized Light
		4.11.1 Principle
		4.11.2 Production
		4.11.3 Analysis of elliptically polarized light
	4.12 Analysis of Light
	4.13 Optical Rotation
		4.13.1 Laws of optical rotation
		4.13.2 Fresnel’s theory of optical rotation
		4.13.3 Mathematical analysis of Fresnel’s theory of optical rotation
		4.13.4 Calculation of the angle of optical rotation
		4.13.5 Specific rotation
	4.14 Polarimeter
		4.14.1 Laurent’s half-shade polarimeter
	Questions
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	Multiple Choice Questions
	Answers
5. Electromagnetism
	5.1 Introduction
	5.2 Vector Calculus
		5.2.1 Line integrals
		5.2.2 Surface integrals
		5.2.3 Volume integral
		5.2.4 Gradient of scalar function
		5.2.5 Divergence of a vector function
		5.2.6 Curl of a vector function
		5.2.7 Gauss’s divergence theorem
		5.2.8 Stokes’ theorem
	5.2.9 Green’s theorem
	5.2.10 Useful vector relations
	5.3 Gauss’s Law
		5.3.1 Gauss’s law of electrostatics in free space
		5.3.2 Gauss’s law of electrostatics in a dielectric medium
		5.3.3 Applications of Gauss’s law
	5.4 Magnetic Induction
		5.4.1 Units of magnetic induction
		5.4.2 Special cases of magnetic induction
	5.5 Magnetic Field Strength (Intensity)
	5.6 Ampere’s Circuital Law
		5.6.1 Ampere’s circuital law in differential form
		5.6.2 Applications of Ampere’s circuital law
	5.7 Faraday’s Law of Electromagnetic Induction
		5.7.1 Integral form of Faraday’s law
		5.7.2 Differential form of Faraday’s law
	5.8 Displacement Current
		5.8.1 Physical significance of displacement current
		5.8.2 Distinction between conduction current and displacement current
	5.9 Maxwell’s Electromagnetic Equations
		5.9.1 Maxwell’s electromagnetic equations in differential form
		5.9.2 Special cases
		5.9.3 Maxwell’s electromagnetic equations in integral form
	Questions
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	Multiple Choice Questions
	Answers
6. Electromagnetic Waves
	6.1 Introduction
	6.2 Electromagnetic Energy Density
		6.2.1 Interpretation of the left-hand side of Eq. (6.8)
		6.2.2 Interpretation of the right-hand side of Eq. (6.8)
	6.3 Poynting’s Vector
	6.4 Poynting’s Theorem
	6.5 Vector Potential and Scalar Potential
		6.5.1 Magnetic scalar potential
		6.5.2 Magnetic vector potential
	6.6 Electromagnetic Wave Equations for E and B
		6.6.1 Electromagnetic wave equations for E
		6.6.2 Electromagnetic wave equations for H
		6.6.3 Electromagnetic wave equations for B
	6.7 Wave Equation in Terms of Scalar and Vector Potentials
		6.7.1 Wave equation in terms of vector potential A
		6.7.2 Wave equation in terms of scalar potential ФЕ
	6.8 Plane Electromagnetic Waves
	6.9 Transverse Nature of Electromagnetic Waves
		6.9.1 Transverse nature of vector E
		6.9.2 Transverse nature of vector H
		6.9.3 Relative orientation of E and H
	6.10 Speed of Electromagnetic Waves
	6.11 Average Value of Poynting’s Vector
	6.12 Propagation of Electromagnetic Waves in Plasma Medium
		6.12.1 Conductivity of ionized medium
		6.12.2 Wave equation in ionized medium
		6.12.3 Propagation constant in an ionized medium
		6.13 Reflection and Refraction of Electromagnetic Waves at Non-conducting and Conducting Boundaries
		6.13.1 Reflection and refraction of electromagnetic waves at a non-conducting surface
		6.13.2 Reflection and refraction of electromagnetic waves at a conducting surface
	Questions
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	Multiple Choice Questions
	Answers
7. Elementary Concepts of Quantum Physics
	7.1 Introduction
	7.2 Need for Quantum Physics
	7.3 Particles and Waves
	7.4 Particle Aspect of Waves
		7.4.1 Blackbody radiation
		7.4.2 Photoelectric effect
		7.4.3 Compton effect
		7.4.4 Pair production
		7.4.5 Characteristics of photon
	7.5 Wave Aspect of Particles
		7.5.1 Matter waves
		7.5.2 Davisson–Germer experiment
		7.5.3 Properties of matter wave
	7.6 Atom Models
		7.6.1 Rutherford’s atom model
		7.6.2 Bohr’s atom model
	7.7 Heisenberg’s Uncertainty Principle
		7.7.1 Statement
		7.7.2 Explanation
		7.7.3 Experimental illustration of the uncertainty principle
		7.7.4 Applications of uncertainty principle
	7.8 Transition from Deterministic Classical Physics to Probabilistic Quantum Physics
	7.9 Wave Function y
		7.9.1 Characteristics of the wave function of a matter wave
		7.9.2 Probability density
		7.9.3 Dimensional analysis of a wave function
	7.10 Superposition Principle
	7.11 Normalization
		7.11.1 Procedures for calculation of the normalization constant
	7.12 Observables and Operators
	7.13 Eigenvalues
	7.14 Eigenfunctions
	7.15 Operators, Eigenfunctions and Eigenvalues
	7.16 Expectation Value
		7.16.1 Procedures for calculation of the expectation value
	7.17 Schrödinger’s Equation
		7.17.1 Schrödinger’s time-dependent equation
		7.17.2 Schrödinger’s time-independent equation
		7.17.3 Newton’s equation and Schrödinger’s equation
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	Multiple Choice Questions
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8. Applications of Quantum Mechanics
	8.1 Introduction
	8.2 One-Dimensional Problems
	8.3 Boundary Conditions on y
	8.4 Free Particle
	8.5 Potential Steps
		8.5.1 Reflection and transmission at the boundary at x = 0
		8.5.2 Potential energy barrier
	8.6 Infinity Deep Potential Well
		8.6.1 Quantization of de Broglie wavelengths
		8.6.2 Quantization of energy (energy eigenvalues)
		8.6.3 Quantization of speed (speed eigenvalues)
		8.6.4 Eigenfunctions
	Questions
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	Multiple Choice Questions
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9. Special Theory of Relativity
	9.1 Introduction
	9.2 Frame of Reference
		9.2.1 Inertial frame of reference
		9.2.2 Non-inertial frame of reference
	9.3 Galilean Transformation
	9.4 Michelson–Morley Experiment
	9.5 Einstein’s Principles of Relativity
	9.6 Lorentz Transformation
		9.6.1 Mathematics of the Lorentz transformation
		9.6.2 Consequences of the Lorentz transformation equations
	9.7 Relativity of Simultaneity
	9.8 Relativistic Addition of Velocity
	9.9 Relativistic Momentum
	9.10 Variation of Mass with Speed
	9.11 Mass–Energy Equivalence
	9.12 Massless Particles (m0 = 0)
	9.13 Generalization of Newton’s Second Law
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10. Architectural Acoustics
	10.1 Introduction
	10.2 Basic Requirements of an Acoustically Good Hall
	10.3 Reverberation and Reverberation Time
		10.3.1 Sabine’s formula for reverberation time
	10.4 Sound Absorption
		10.4.1 Room averaged sound absorption coefficient
	10.4.2 Measurement of absorption coefficient
	10.5 Factors Affecting the Acoustics of Buildings
		10.5.1 Requisites for good acoustics
	10.6 Decibel Scale
	10.7 Acoustic Quieting
		10.7.1 Aspects of acoustic quieting
		10.7.2 Methods of quieting
		10.7.3 Quieting for specific observers
		10.7 4 Mufflers
	10.8 Soundproofing
		10.8.1 Airborne soundproofing
		10.8.2 Structure-borne soundproofing
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11. Ultrasonics
	11.1 Introduction
	11.2 Production of Ultrasonic Waves
		11.2.1 Galton’s whistle
		11.2.2 Magnetostriction oscillator
		11.2.3 Piezoelectric oscillator
	11.3 Detection of Ultrasonic Waves
	11.4 Properties of Ultrasonic Waves
	11.5 Wavelength Determination of Ultrasonic Waves
	11.6 Ultrasound Cavitation
		11.6.1 Parameters affecting ultrasonic cavitation
		11.6.2 Consequences of ultrasonic cavitation
	11.7 Applications of Ultrasonic Waves
	11.8 Sonograms
	11.9 Sonar
		11.9.1 Applications of sonar
		11.10 Hazards of Ultrasound
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	Multiple Choice Questions
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12. Non-Destructive Testing
	12.1 Introduction
	12.2 Objectives of NDT
	12.3 Methods of NDT
		12.3.1 Visual and optical testing (VOT)
		12.3.2 Dye penetrant testing (DPT)
		12.3.3 Magnetic particle testing
		12.3.4 Electromagnetic or eddy current testing
		12.3.5 Radiographic testing
		12.3.6 Ultrasonic testing
		12.3.7 Pulse–echo system
	12.4 Relative Merits of Various NDT Methods
	12.5 Non-Destructive Testing Methods and Applications
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	Multiple Choice Questions
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13. Nuclear Accelerators
	13.1 Introduction
	13.2 Need of Nuclear Accelerators
	13.3 Basic Mechanism of a Nuclear Accelerator
	13.4 Main Components
		13.4.1 Ion sources
		13.4.2 Accelerating tube
	13.5 Performance Index
	13.6 Types of Accelerators
	13.7 D.C. Accelerators
		13.7.1 Cockcroft–Walton accelerator (D.C. accelerator)
		13.7.2 Van de Graaff accelerator (D.C. accelerator)
		13.7.3 Tandem accelerator (D.C. accelerator)
	13.8 R.F. Accelerators
		13.8.1 Linear accelerators
		13.8.2 Cyclotron
	13.9 Electron Accelerators
		13.9.1 Betatron
	13.10 Applications of Accelerators
		13.10.1 Radiation processing of materials
		13.10.2 Uses of isotopes
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	Multiple Choice Questions
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14 Holography
	14.1 Introduction
	14.2 Basic Principles of Holography
	14.3 Types of Holograms
		14.3.1 Reflection holograms
		14.3.2 Transmission holograms
		14.3.3 Comparison of transmission and reflection holograms
	14.4 White Light Holograms
	14.5 Necessity of Laser Source
	14.6 Basic Requirements of a Holographic Laboratory
	14.7 Viewing a Hologram
	14.8 Difference between Photography and Holography
	14.9 Applications of Holography
		14.9.1 Common applications of holography
		14.9.2 Application of holographic interferometry
		14.9.3 Application of holographic microscopy
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Bibliography
Index