OpticsOpticsFundamentals of

Second Edition

Devraj Singh

ok UV Title (Optics) only

Fundamentals of OpticsSECOND EDITION

DEVRAJ SINGHAssistant Professor and Head

Department of Applied PhysicsAmity School of Engineering and Technology

Bijwasan, New Delhi

Delhi-1100922015

FUNDAMENTALS OF OPTICS, Second EditionDevraj 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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&Jh vkfnR; ân; Lrks=e~ “yksd 142

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.

v

Contents

Preface ...................................................................................................................................................xv

Acknowledgements .............................................................................................................................xvii

Part I GEOMETRICAL OPTICS

1. Fermat’s Principle ..........................................................................3–151.1 Introduction .......................................................................................................................41.2 Optical Path .......................................................................................................................41.3 Fermat’s Principle of Extreme Path ................................................................................51.4 LawsofReflectionbyFermat’sPrinciple ......................................................................6

1.4.1 First Law ..................................................................................................................61.4.2 Second Law .............................................................................................................7

1.5 LawsofRefractionbyFermat’sPrinciple .....................................................................81.5.1 First Law ..................................................................................................................81.5.2 Second Law .............................................................................................................8

1.6 Case of Maximum Path or Extremum Time ...............................................................10Formulae at a Glance...................................................................................................................11Solved Numerical Problems ........................................................................................................11Conceptual Questions .................................................................................................................13Exercises ......................................................................................................................................13

Theoretical Questions ........................................................................................................13Numerical Problems ..........................................................................................................14Multiple Choice Questions ................................................................................................15

vi Contents

2. Geometrical Optics ......................................................................16–422.1 Introduction .....................................................................................................................172.2 Lenses: Thin and Thick Lenses .....................................................................................172.3 Lens Equation ..................................................................................................................172.4 Lens Maker’s Formula ....................................................................................................19

2.4.1 LensMaker’sFormulaforaDoubleConvexLens ..........................................202.4.2 LensMaker’sFormulaforaDoubleConcaveLens ........................................22

2.5 CardinalPointsofaCoaxiallyOpticalSystem ...........................................................232.5.1 Principal Points ....................................................................................................232.5.2 Focal Points ...........................................................................................................242.5.3 Nodal Points .........................................................................................................25

2.6 CombinationofTwoThinLenses(EquivalentLenses):CoaxialLensSystem ......262.7 MatrixMethodinParaxialOpticalSystem .................................................................30

2.7.1 Translation Matrix ...............................................................................................302.7.2 The Refraction Matrix ..........................................................................................312.7.3 TheReflectionMatrix ..........................................................................................32

Formulae at a Glance...................................................................................................................33Solved Numerical Problems ........................................................................................................35Conceptual Questions .................................................................................................................38Exercises ......................................................................................................................................39

Theoretical Questions ........................................................................................................39Numerical Problems ..........................................................................................................40Multiple Choice Questions ................................................................................................41

3. Dispersion of Light .......................................................................43–673.1 Introduction ......................................................................................................................44

3.1.1 Newton’s Classic Experiment on Dispersion of White Light ........................443.1.2 CauseofDispersion(Cauchy’sRelation) .........................................................45

3.2 AngularDispersionandDispersivePower ................................................................453.3 CombinationofPrisms...................................................................................................47

3.3.1 DeviationwithoutDispersion ...........................................................................473.3.2 DispersionwithoutDeviation ...........................................................................49

3.4 Direct Vision Spectroscope ............................................................................................513.5 Rainbow ...........................................................................................................................51

3.5.1 PrimaryRainbow .................................................................................................523.5.2 SecondaryRainbow .............................................................................................56

3.6 Sundogs and Halos .........................................................................................................57Formulae at a Glance...................................................................................................................59Solved Numerical Problems ........................................................................................................60Conceptual Questions .................................................................................................................62

Contents vii

Exercises ......................................................................................................................................63Theoretical Questions ........................................................................................................63Numerical Problems ..........................................................................................................64Multiple Choice Questions ................................................................................................65

4. Lens Aberrations ........................................................................ 68–1034.1 Introduction .....................................................................................................................694.2 TypesofAberrations ......................................................................................................69

4.2.1 ChromaticAberration .........................................................................................694.2.2 MonochromaticAberration ................................................................................69

4.3 TypesofMonochromaticAberrationandtheirReduction ......................................704.3.1 SphericalAberration ............................................................................................704.3.2 Coma ......................................................................................................................754.3.3 Astigmatism ..........................................................................................................774.3.4 CurvatureofField ................................................................................................784.3.5 Distortion...............................................................................................................80

4.4 ChromaticAberration .....................................................................................................814.4.1 TypesofChromaticAberration ........................................................................824.4.2 Achromatism of Lenses ......................................................................................85

4.5 Aplanatism and Aplanatic Points .................................................................................904.5.1 Aplanatic Points for a Spherical Refracting Surface .......................................914.5.2 Oil-immersionObjectiveofHighPowerMicroscope .....................................92

Formulae at a Glance...................................................................................................................93Solved Numerical Problems ........................................................................................................95Conceptual Questions .................................................................................................................99Exercises ....................................................................................................................................100

Theoretical Questions ......................................................................................................100Numerical Problems ........................................................................................................101Multiple Choice Questions ..............................................................................................102

5. Optical Instruments ................................................................. 104–1425.1 Introduction ...................................................................................................................1055.2 Microscopes ...................................................................................................................105

5.2.1 Simple Microscope .............................................................................................1065.2.2 Compound Microscope .....................................................................................108

5.3 Telescopes ......................................................................................................................1125.3.1 Astronomical Telescope ....................................................................................1125.3.2 Terrestrial Telescope ..........................................................................................1155.3.3 ReflectingTelescopes .........................................................................................116

5.4 EyepiecesorOculars ....................................................................................................1175.4.1 Huygen’sEyepiece.............................................................................................119

viii Contents

5.4.2 Ramsden’sEyepiece ..........................................................................................1225.4.3 RelativeMeritsandDemeritsofHuygen’sandRamsden’sEyepieces .....1255.4.4 GaussEyepiece ...................................................................................................125

5.5 Spectrometer ..................................................................................................................1265.5.1 MeasurementofRefractiveIndexbyaSpectrometer ...................................128

5.6 Electron Microscope .....................................................................................................129Formulae at a Glance.................................................................................................................131Solved Numerical Problems ......................................................................................................133Conceptual Questions ...............................................................................................................137Exercises ....................................................................................................................................138

Theoretical Questions ......................................................................................................138Numerical Problems ........................................................................................................139Multiple Choice Questions ..............................................................................................140

Part II VIBRATIONS AND WAVES

6. Fundamentals of Vibrations .................................................... 145–1966.1 Introduction ...................................................................................................................1466.2 Simple Harmonic Motion and Harmonic Oscillator ...............................................1476.3 EnergyofHarmonicOscillator ...................................................................................1506.4 AverageValuesofKineticandPotentialEnergy .....................................................1516.5 Example of Harmonic Oscillator: Simple Pendulum ..............................................1526.6 Damping Force /Damping Motion ............................................................................1556.7 Damped Harmonic Oscillator .....................................................................................1576.8 Power Dissipation in Damped Harmonic Oscillator ...............................................1626.9 QualityFactor(Q)ofDampedHarmonicOscillator ...............................................1636.10 Forced Harmonic Oscillator ........................................................................................1636.11 Resonance.......................................................................................................................1666.12 Amplitude Resonance ..................................................................................................1676.13 Sharpness of Resonance ...............................................................................................1696.14 HalfWidthofResonanceCurve .................................................................................1696.15 VelocityResonance .......................................................................................................1706.16 PowerAbsorptionofForcedHarmonicOscillator ..................................................1716.17 QualityFactor(Q)ofForcedHarmonicOscillator ..................................................173Formulae at a Glance.................................................................................................................175Solved Numerical Problems ......................................................................................................179Conceptual Questions ...............................................................................................................184Exercises ....................................................................................................................................186

Theoretical Questions ......................................................................................................186Numerical Problems ........................................................................................................187Multiple Choice Questions ..............................................................................................191

Contents ix

7. Wave Motion ............................................................................197–2367.1 Introduction ...................................................................................................................1987.2 WhatPropagatesinWaveMotion? ............................................................................1987.3 CharacteristicsofWaveMotion ..................................................................................1987.4 TypesofWaveMotion .................................................................................................199

7.4.1 TransverseWaveMotion ..................................................................................1997.4.2 LongitudinalWaveMotion ..............................................................................200

7.5 ImportantDefinitions ...................................................................................................2017.6 DifferentialEquationofWaveMotion ......................................................................2027.7 PlaneProgressiveWaveinFluidMedia....................................................................207

7.7.1 WaveEquationofPropagationofSoundWavesinFluidMedia ...............2087.8 PressureVariationinLongitudinalWave(AcousticPressure) .............................211

7.8.1 Relationbetweenyand(P) ............................................................................2127.9 EnergyofPlaneProgressiveWave ............................................................................212

7.9.1 Intensity ...............................................................................................................2147.10 ReflectionandTransmissionofTransverseWavesinaString ..............................2157.11 ReflectionandTransmissionofLongitudinalWavesatDiscontinuity ...............2177.12 SuperpositionofProgressiveWaves:StationaryWave ..........................................219

7.12.1 AnalyticalTreatmentofStationaryWavesandtheirProperties .............2197.12.2 EnergyofStationaryWaves ..........................................................................2217.12.3 CharacteristicsofStationaryWave ..............................................................223

7.13 ComparisonbetweenProgressiveWavesandStationaryWaves .........................224Formulae at a Glance.................................................................................................................225Solved Numerical Problems ......................................................................................................228Conceptual Questions ...............................................................................................................231Exercises ....................................................................................................................................232

Theoretical Problems........................................................................................................232Numerical Problems ........................................................................................................233Multiple Choice Questions ..............................................................................................234

Part III PHYSICAL OPTICS

8. Interference of Light Waves .................................................... 239–3548.1 Introduction ...................................................................................................................2408.2 WavefrontandRays .....................................................................................................240

8.2.1 Wavefront ............................................................................................................2408.2.2 RayofLight .........................................................................................................242

8.3 Huygen’sPrincipleofSecondaryWavelets ..............................................................2438.4 PrincipleofSuperpositionofLightWaves ...............................................................244

Fundamentals Of Optics

Publisher : PHI Learning ISBN : 9788120351462 Author : SINGH, DEVRAJ

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