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Waves and Optics

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CHAPTER 1 SUPERPOSITION OF HARMONIC OSCILLATIONS  
1.1  Introduction 1
1.2 Superposition Principle 2
1.2.1 Linearity and superposition principle’s applications 2
1.3 Superposition of simple Harmonic Oscillations 3
1.4 Superposition of two collinear harmonics oscillations of equal frequencies 4
1.5 Superposition of two collinear harmonics oscillations of different frequencies 7
1.6 Superposition of many harmonic oscillations of same frequency (method of vector addition) 9
1.7 Superposition of two Mutually Perpendicular Harmonic Oscillations of same Frequency 11
1.8 Lissajous figures with equal and unequal frequency 16
1.8.1 Composition of two rectangular vibrations of different amplitudes but same frequency 17
1.8.2 Composition of two rectangular vibrations of different amplitudes and of frequencies in the ratio 2:1 20
1.9 Uses of Lissajous Figures 22
1.10 Beats 24
Multiple choice Questions 28
Numericals 31
Conceptual Q/A 38
CHAPTER 2 WAVES MOTION & VELOCITY 40
2.1 Introduction 40
2.2 Classification of waves 41
2.3 Mechanical waves 42
2.4 Transverse Waves 42
2.4.1 Transverse waves on a string 45
2.4.2 Reflections of Transverse Waves 46
2.5 Standing waves or Stationary waves 46
2.5.1 Standing waves – Fixed and Free Ends 48
2.5.2 Standing waves in strings and normal modes of vibrations 52
2.6 Longitudinal Waves 57
2.7 Velocity of longitudinal waves in an elastic medium 59
2.8 Longitudinal Standing Waves and Normal Mode

 

59
2.9 Electromagnetic Waves & Surface Waves 61
2.10 Plane Progressive wave 62
2.10.1 Equation of a plane progressive waves 62
2.10.2 Properties of plane progressive wave 64
2.10.3 Characteristics of progressive waves 65
2.11 Plane waves 66
2.12 Spherical  waves 67
2.13 Wave equation 67
2.14 Wave intensity 68
2.15 Phase and group velocity 71
2.16 Particle and wave velocities 74
2.17 Velocity of a transverse wave along a stretched string 75
2.18 Energy Transport 76
2.19 Newton’s formula for the velocity of sound waves in air 78
2.20 Laplace Correction 78
2.21 Meld’s Experiment 79
2.22 The Principle of Superposition of waves 84
2.23 Standing waves in closed organ pipes: Analytical Treatment 85
2.24 Standing waves in open organ pipes: Analytical Treatment 88
2.25 Water waves: ripple and gravity waves 91
Multiple choice questions 99
Numericals 104
Conceptual Q/A 113
CHAPTER 3 WAVE OPTICS 117
3.1 Introduction of Light 117
3.2 Electromagnetic nature of light 118
3.3 Wave front 120
3.4 Huygens’s principle 121
3.4.1 Huygen’s Construction of a spherical waves front and plane wave front 122
3.5 Coherence 123
3.5.1 Spatial Coherence 124
3.5.2 Temporal Coherence 124
Multiple choice questions 125
Numericals 127
Conceptual Q/A 130
CHAPTER 4 SHM & SOUND 133
4.1 Simple Harmonic Motion 133
4.1.1 SHM graphs 134
4.2 Time Period of a mass – spring system 135
4.2.1 Time period of a Pendulum 135
4.3 Forced vibration 135
4.4 SHM and Energy 138
4.4.1 Characteristics of Musical sound 139
4.5 Threshold of Hearing 140
4.5.1 Intensity of Sound 140
4.6 Intensity Level 142
4.6.1 The Decibel scale 142
4.7 Basic Requirement for the Acoustically Good Halls 143
4.8 Reverberation and time of Reverberation 144
4.9 Sabine’s Formula for Reverberation time 144
4.9.1 Decay of energy density 148
4.9.2 Jaeger’s method for derivation of Sabine’s formula 149
4.10 Absorption Coefficient and its Measurement 151
4.10.1 Measurement of a absorption coefficient 152
4.11 Transmission of sound and Transmission loss 153
4.11.1 Transmission of sound 153
4.11.2 Transmission loss 153
4.12 Factors Affecting the Architectural Acoustics and their Remedy 153
4.13 Sound Absorbing Materials 157
Multiple Choice Questions 159
Numericals 162
Conceptual Q/A 166
CHAPTER 5 INTERFERENCE 170
5.1 Introduction to Interference 170
5.2 Young’s Double-slit Experiment 170
5.2  Lloyd’s Single Mirror 174
5.3 Fresnel’s Biprism 176
5.3.1 Determination of wavelength of light 177
5.3.2 White light fringes 179
5.3.3 Location of zero order fringes 179
5.4 Phase change on Reflection 180
5.5 Interference in Thin Films 181
5.5.1 Interference due to reflected light 181
5.5.2 Interference due to transmitted light 184
5.5.3 Colours of thin films 185
5.6 Wedge-Shaped Films 186
5.6.1 Nature of interference pattern 187
5.6.2 Spacing between two consecutive bright bands 188
5.7 Newton’s Rings 189
5.7.1 Experiment arrangement 189
5.7.2 Formation of Newton’s rings 190
5.7.3 Newton’s rings by reflected light 191
5.7.4 Newton’s rings by transmitted light 193
5.9 Determination of Wave Length of Sodium Light using Newton’s Rings 194
5.10 Michelson’s Interferometer 196
5.11 Formation of Circular Fringes 198
5.12 Localized Fringes 201
5.13 White Light Fringes 202
5.14 Application of Michelson’s Interferometer 202
5.15 Newton’s Rings Formed By Two Curved Surfaces 206
5.29 Fabry- Perot Interferometer 208
  Multiple Choice Questions 212
  Numericals 216
  Conceptual Q/A 241
CHAPTER 6 DIFFRACTION
6.1 Introduction 246
6.2 Diffraction Pattern Due to a Single slit – intensity distribution 246
6.2 Fraunhoffer Diffraction at a Circular Aperture 248
6.3 Fraunhoffer Diffraction at a Double Slit 250
6.4 Difference between Single Slit & Double Slit Diffraction Pattern 253
6.5 Fresnel integral 254
6.6 Kirchhoff integral theorem 255
6.7 Resolving Power of Telescope 256
6.8 Resolving Power of a Diffraction Grating 257
  Multiple Choice Questions 259
  Numericals 263
  Conceptual Q/A 279
CHAPTER 7 POLARIZATION
7.1 Introduction 282
7.2 Polarization of light Waves 282
7.3 Representation of Various Type of Light 285
7.4 Plane of Polarisation 286
7.5 Production of Plane Polarised Light 286
7.6 Reflection Method 286
7.7 Classification of Polarization 288
  Multiple Choice Questions 290
  Numericals 293
  Conceptual Q/A 299
CHAPTER 8 HOLOGRAPHY
8.1 Introduction 301
8.1.1 Basic principle of Holography 302
8.2 Conditions for Recording Holograms 305
8.3 Variants of Holographic Techniques 305
8.4 Recording of Hologram 306
8.5 Reconstruction of image from hologram 307
8.6 Applications of Holography 309
  Multiple Choice Questions 311
  Conceptual Q/A 314
 
Practice Exercise 316
Solutions to Practice Exercise 326
Weight .650 kg

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