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Second Edition
Fundamentals of
Optics
Devraj Singh
Fundamentals of Optics
SECOND EDITION
DEVRAJ SINGH
Assistant Professor and Head
Department of Applied Physics
Amity School of Engineering and Technology
Bijwasan, New Delhi
Delhi-110092
2015
FUNDAMENTALS OF OPTICS, Second Edition
Devraj Singh
© 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be
reproduced in any form, by mimeograph or any other means, without permission in writing from the
publisher.
ISBN-978-81-203-5146-2
The export rights of this book are vested solely with the publisher.
Second Printing (Second Edition) …
…
August, 2015
Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj
Industrial Estate, Delhi-110092 and Printed by Syndicate Binders, A-20, Hosiery Complex, Noida,
Phase-II Extension, Noida-201305 (N.C.R. Delhi).
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The source of light sparkling like a gem,
who is eternal and destroyer of poverty;
and replica of the Sun, we pray to Him to make us purified.
Contents
Preface....................................................................................................................................................xv
Acknowledgements..............................................................................................................................xvii
Part I GEOMETRICAL OPTICS
1. Fermat’s Principle...........................................................................3–15
1.1Introduction........................................................................................................................4
1.2 Optical Path........................................................................................................................4
1.3 Fermat’s Principle of Extreme Path.................................................................................5
1.4 Laws of Reflection by Fermat’s Principle.......................................................................6
1.4.1 First Law...................................................................................................................6
1.4.2 Second Law..............................................................................................................7
1.5 Laws of Refraction by Fermat’s Principle......................................................................8
1.5.1 First Law...................................................................................................................8
1.5.2 Second Law..............................................................................................................8
1.6 Case of Maximum Path or Extremum Time................................................................10
Formulae at a Glance...................................................................................................................11
Solved Numerical Problems.........................................................................................................11
Conceptual Questions..................................................................................................................13
Exercises.......................................................................................................................................13
Theoretical Questions.........................................................................................................13
Numerical Problems...........................................................................................................14
Multiple Choice Questions.................................................................................................15
v
vi Contents
2. Geometrical Optics.......................................................................16–42
2.1Introduction......................................................................................................................17
2.2 Lenses: Thin and Thick Lenses......................................................................................17
2.3 Lens Equation...................................................................................................................17
2.4 Lens Maker’s Formula.....................................................................................................19
2.4.1 Lens Maker’s Formula for a Double Convex Lens...........................................20
2.4.2 Lens Maker’s Formula for a Double Concave Lens.........................................22
2.5 Cardinal Points of a Coaxially Optical System............................................................23
2.5.1 Principal Points.....................................................................................................23
2.5.2 Focal Points............................................................................................................24
2.5.3 Nodal Points..........................................................................................................25
2.6 Combination of Two Thin Lenses (Equivalent Lenses): Coaxial Lens System.......26
2.7 Matrix Method in Paraxial Optical System..................................................................30
2.7.1 Translation Matrix................................................................................................30
2.7.2 The Refraction Matrix...........................................................................................31
2.7.3 The Reflection Matrix...........................................................................................32
Formulae at a Glance...................................................................................................................33
Solved Numerical Problems.........................................................................................................35
Conceptual Questions..................................................................................................................38
Exercises.......................................................................................................................................39
Theoretical Questions.........................................................................................................39
Numerical Problems...........................................................................................................40
Multiple Choice Questions.................................................................................................41
3. Dispersion of Light........................................................................43–67
3.1 Introduction.......................................................................................................................44
3.1.1 Newton’s Classic Experiment on Dispersion of White Light.........................44
3.1.2 Cause of Dispersion (Cauchy’s Relation)..........................................................45
3.2 Angular Dispersion and Dispersive Power.................................................................45
3.3 Combination of Prisms...................................................................................................47
3.3.1 Deviation without Dispersion............................................................................47
3.3.2 Dispersion without Deviation............................................................................49
3.4 Direct Vision Spectroscope.............................................................................................51
3.5 Rainbow............................................................................................................................51
3.5.1 Primary Rainbow..................................................................................................52
3.5.2 Secondary Rainbow..............................................................................................56
3.6 Sundogs and Halos..........................................................................................................57
Formulae at a Glance...................................................................................................................59
Solved Numerical Problems.........................................................................................................60
Conceptual Questions..................................................................................................................62
Contents vii
Exercises.......................................................................................................................................63
Theoretical Questions.........................................................................................................63
Numerical Problems...........................................................................................................64
Multiple Choice Questions.................................................................................................65
4. Lens Aberrations......................................................................... 68–103
4.1Introduction......................................................................................................................69
4.2 Types of Aberrations.......................................................................................................69
4.2.1 Chromatic Aberration..........................................................................................69
4.2.2 Monochromatic Aberration.................................................................................69
4.3 Types of Monochromatic Aberration and their Reduction.......................................70
4.3.1 Spherical Aberration.............................................................................................70
4.3.2Coma.......................................................................................................................75
4.3.3Astigmatism...........................................................................................................77
4.3.4 Curvature of Field.................................................................................................78
4.3.5Distortion...............................................................................................................80
4.4 Chromatic Aberration......................................................................................................81
4.4.1 Types of Chromatic Aberration.........................................................................82
4.4.2 Achromatism of Lenses.......................................................................................85
4.5 Aplanatism and Aplanatic Points..................................................................................90
4.5.1 Aplanatic Points for a Spherical Refracting Surface........................................91
4.5.2 Oil-immersion Objective of High Power Microscope......................................92
Formulae at a Glance...................................................................................................................93
Solved Numerical Problems.........................................................................................................95
Conceptual Questions..................................................................................................................99
Exercises.....................................................................................................................................100
Theoretical Questions.......................................................................................................100
Numerical Problems.........................................................................................................101
Multiple Choice Questions...............................................................................................102
5. Optical Instruments.................................................................. 104–142
5.1Introduction....................................................................................................................105
5.2Microscopes....................................................................................................................105
5.2.1 Simple Microscope..............................................................................................106
5.2.2 Compound Microscope......................................................................................108
5.3Telescopes.......................................................................................................................112
5.3.1 Astronomical Telescope.....................................................................................112
5.3.2 Terrestrial Telescope...........................................................................................115
5.3.3 Reflecting Telescopes..........................................................................................116
5.4 Eyepieces or Oculars.....................................................................................................117
5.4.1 Huygen’s Eyepiece.............................................................................................119
viii Contents
5.4.2 Ramsden’s Eyepiece...........................................................................................122
5.4.3 Relative Merits and Demerits of Huygen’s and Ramsden’s Eyepieces......125
5.4.4 Gauss Eyepiece....................................................................................................125
5.5Spectrometer...................................................................................................................126
5.5.1 Measurement of Refractive Index by a Spectrometer....................................128
5.6 Electron Microscope......................................................................................................129
Formulae at a Glance.................................................................................................................131
Solved Numerical Problems.......................................................................................................133
Conceptual Questions................................................................................................................137
Exercises.....................................................................................................................................138
Theoretical Questions.......................................................................................................138
Numerical Problems.........................................................................................................139
Multiple Choice Questions...............................................................................................140
Part II VIBRATIONS AND WAVES
6. Fundamentals of Vibrations..................................................... 145–196
6.1Introduction....................................................................................................................146
6.2 Simple Harmonic Motion and Harmonic Oscillator................................................147
6.3 Energy of Harmonic Oscillator....................................................................................150
6.4 Average Values of Kinetic and Potential Energy......................................................151
6.5 Example of Harmonic Oscillator: Simple Pendulum...............................................152
6.6 Damping Force /Damping Motion.............................................................................155
6.7 Damped Harmonic Oscillator......................................................................................157
6.8 Power Dissipation in Damped Harmonic Oscillator................................................162
6.9 Quality Factor (Q) of Damped Harmonic Oscillator................................................163
6.10 Forced Harmonic Oscillator.........................................................................................163
6.11Resonance.......................................................................................................................166
6.12 Amplitude Resonance...................................................................................................167
6.13 Sharpness of Resonance................................................................................................169
6.14 Half Width of Resonance Curve..................................................................................169
6.15 Velocity Resonance........................................................................................................170
6.16 Power Absorption of Forced Harmonic Oscillator...................................................171
6.17 Quality Factor (Q) of Forced Harmonic Oscillator...................................................173
Formulae at a Glance.................................................................................................................175
Solved Numerical Problems.......................................................................................................179
Conceptual Questions................................................................................................................184
Exercises.....................................................................................................................................186
Theoretical Questions.......................................................................................................186
Numerical Problems.........................................................................................................187
Multiple Choice Questions...............................................................................................191
Contents ix
7. Wave Motion.............................................................................197–236
7.1Introduction....................................................................................................................198
7.2 What Propagates in Wave Motion?.............................................................................198
7.3 Characteristics of Wave Motion...................................................................................198
7.4 Types of Wave Motion..................................................................................................199
7.4.1 Transverse Wave Motion...................................................................................199
7.4.2 Longitudinal Wave Motion...............................................................................200
7.5 Important Definitions....................................................................................................201
7.6 Differential Equation of Wave Motion.......................................................................202
7.7 Plane Progressive Wave in Fluid Media....................................................................207
7.7.1 Wave Equation of Propagation of Sound Waves in Fluid Media................208
7.8 Pressure Variation in Longitudinal Wave (Acoustic Pressure)..............................211
7.8.1 Relation between y and (P).............................................................................212
7.9 Energy of Plane Progressive Wave.............................................................................212
7.9.1 Intensity................................................................................................................214
7.10 Reflection and Transmission of Transverse Waves in a String...............................215
7.11 Reflection and Transmission of Longitudinal Waves at Discontinuity ................217
7.12 Superposition of Progressive Waves: Stationary Wave...........................................219
7.12.1 Analytical Treatment of Stationary Waves and their Properties..............219
7.12.2 Energy of Stationary Waves...........................................................................221
7.12.3 Characteristics of Stationary Wave...............................................................223
7.13 Comparison between Progressive Waves and Stationary Waves..........................224
Formulae at a Glance.................................................................................................................225
Solved Numerical Problems.......................................................................................................228
Conceptual Questions................................................................................................................231
Exercises.....................................................................................................................................232
Theoretical Problems........................................................................................................232
Numerical Problems.........................................................................................................233
Multiple Choice Questions...............................................................................................234
Part III PHYSICAL OPTICS
8. Interference of Light Waves..................................................... 239–354
8.1Introduction....................................................................................................................240
8.2 Wavefront and Rays......................................................................................................240
8.2.1 Wavefront.............................................................................................................240
8.2.2 Ray of Light..........................................................................................................242
8.3 Huygen’s Principle of Secondary Wavelets...............................................................243
8.4 Principle of Superposition of Light Waves................................................................244
Fundamentals Of Optics
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