Demonstrational Optics: Part 1: Wave and Geometrical Optics

297 Pages·2003·8.041 MB·English

by  Oleg Marchenko, Sergei Kazantsev, Laurentius Windholz (auth.)

Demonstrational Optics
Demonstrational Optics
Part 1: Wave and
Geometrical Optics
Oleg Marchenko
St. Petersburg State University
St. Petersburg, Russia
Sergei Kazantsev
Paris Observatory
Paris, France
and
Laurentius Windholz
Technical University of Graz
Graz. Austria
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
Marchenko, Oleg.
Demonstrational optics / Oleg Marchenko, Sergei Kazantsev, Laurentius Windholz.
p. cm.
Includes bibliographical references and index.
Contents: pt. 1. Wave and geometrical optics.
1. Optics. 1. Kazantsev, S. A. (Sergei Anatol'evich) II. Windholz, L. III. Title.
QC355.3.M372004
535--dc22
2003061896
ISBN 978-1-4613-4723-1 ISBN 978-1-4419-8925-3 (eBook)
DOI 10.1007/978-1-4419-8925-3
©2003 Springer Science+Business Media New York
OriginalIy published by Kluwer Academic / Plenum Publishers, New York in 2003
Softcover reprint of the hardcover 1s t edition 2003
http://www.wkap.nV
10987654321
A C.I.P. record for this book is available from the Library of Congress
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Contents
Preface ix
1. HISTORICAL INTRODUCTION 1
1 Wave nature of light 1
2 Electromagnetic theory 6
3 Optical Spectroscopy 7
4 Quantum Optics 8
5 Atom model and relativity 10
6 Coherence and precision optical instrumentation 13
7 Light correlation and statistics 15
2. PROPERTIES OF LIGHT WAVES 17
1 Laws of electromagnetism 17
1.1 Maxwell's equations 17
1.2 Electric dipole radiation 20
2 Properties ofelectromagnetic waves 23
2.1 Wave equation 23
2.2 Plane waves 27
2.3 Plane monochromatic wave 28
2.3.1 Frequency, wavelength, light velocity 28
2.3.2 Transversality ofelectromagnetic waves 30
2.4 Spherical waves 33
2.5 Polarization states 35
3 Quasi-monochromatic waves 37
3.1 Envelope and carrier frequency 37
3.2 Spectrum ofquasi-monochromatic oscillations 38
4 Energy and momentum oflight 42
v
vi
4.1 Intensity of light 42
4.2 The Doppler effect 47
4.3 Monochromaticity 50
4.4 Natural light 53
4.5 Light pressure 55
4.5.1 Radiation of a harmonic oscillator 55
4.5.2 LORENTZ force 57
4.5.3 Evidence of light pressure 60
4.6 Photon representation 61
3. LIGHT POLARIZATION 73
1 Basic types of light wavepolarization 74
1.1 Linearly and circularly polarized waves 76
1.2 Elliptically polarized waves 78
1.2.1 Polarizer and analyzer 80
2 Polarization ofquasi-monochromatic light 82
2.1 Polarization degree 82
2.2 The STOKES parameters and JONES vectors 84
2.2.1 Description of a monochromatic wave 84
2.2.2 Measurements of the STOKES parameters 86
3 Optical dipole radiation and polarizing effects 89
3.1 Polarization under scattering 89
3.2 Polarization due to reflection 90
3.3 Dipole radiation at 3 em wavelength 92
4. LIGHT WAVESIN MEDIA 103
1 MAXWELL's equations in isotropic media 104
1.1 Wave equations, the POYNTING vector 104
1.2 Boundary conditions 106
2 Reflection and refraction 109
2.1 Snell's law 109
2.1.1 Refraction by a prism 110
2.2 The total reflection 111
2.2.1 Surface wave (evanescent wave) 112
2.2.2 Total reflection ofradio waves 114
2.2.3 Optical fibers 115
2.2.4 Rainbow 118
3 The Fresnel formulae 119
3.1 Reflectivity and transparency 121
Contents vii
3.1.1 Normal incidence 123
3.2 The Brewster angle 125
3.2.1 Polarizing devices 125
4 Dispersion 128
4.1 Classical theory ofdispersion 128
4.2 Observation ofdispersion 134
4.2.1 Crosses prisms 134
4.2.2 The Wood experiment 137
4.3 A wavetrain in a medium 138
4.3.1 Group velocity 138
4.3.2 Energy transfer 141
4.3.3 The Rayleigh formula 141
4.3.4 A modeling computation experiment 144
5 Radiation under uniform charge motion 147
5.1 VAVILOV-CHERENKOV radiation 147
5.2 Transient radiation 152
5.3 SMITH-PARSELL effect 153
5. OPTICAL ANISOTROPY 165
1 Double refraction in calcite 165
2 The structure ofcalcite 169
3 A monochromatic wavein an anisotropic crystal 173
3.1 Propogation ofthe energy and the phase 173
3.2 Nicol and Wollaston prisms 177
3.3 A model of an uniaxial crystal 178
3.3.1 Vector E parallel to the facesof the plates 179
3.3.2 Propagation across optical axis 180
4 Natural optical anisotropy ofmaterials 181
4.1 Retardation plates 181
4.1.1 Experiment with radio waves 182
4.1.2 Quarter-wave plates in optics 183
4.2 Liquid crystals 186
4.2.1 Optical anisotropy of a thin filmof a liquid crystal 187
4.2.2 A liquid crystal prism 188
5 Artificial birefringence 189
5.1 Photo-elastic effect 189
5.2 The Kerr effect 191
5.3 An experiment to determine the light velocity 194
viii
6 Optical activity 198
6.1 Natural quartz 198
6.2 The Fresnel experiment 200
6.3 Radio - waverotation 202
6.4 The Faraday effect 204
6.5 Magnetic domains 205
6. GEOMETRICAL OPTICS 223
1 Homocentric and astigmatic beams 223
2 One refracting surface 227
2.1 Positive and negative optical force 230
2.2 Real and imaginary image 233
2.3 Magnification ofa spherical refracting surface 234
2.4 Aspherical reflectingsurface 235
3 Centered optical systems 237
4 Lenses 240
4.1 General relations 240
4.2 Thick lenses 243
4.3 Thin lenses 246
4.4 Images formed by parallel rays 247
4.5 Two thin lenses 248
5 Errors ofoptical systems 252
6 Formation ofoptical images 257
6.1 Human eye 257
6.2 Magnifier 259
6.3 Telescopicsystem 260
6.3.1 Refracting telescope 260
6.3.2 Reflecting telescope 262
6.4 Microscope 264
6.5 Limitation oflight beams in optical systems 265
7 Light propagation inside inhomogeneous media 269
7.1 Concept ofeikonal 269
7.2 Light beam bending 275
7.2.1 Mirages 275
7.3 FERMAT'S principle 277
Index
289
Preface
In recent years, Optics has reemerged to be oneofthe most promising
sciences. Optical applications are found in widely differing scientific
fields - from physics and chemistry to biology, medicine and technical
sciences. Technical applications likelaser printers,compact disk players
and data transfer in optical fibers are presently state ofthe art, but will
certainly undergo remarkable progress in future.
This book isthe first ofa two-volume textbook which emphasizes the
experimental demonstration ofoptical effects and properties and - more
importantly - the physical background ofoptical phenomena in order to
ensure a more didactical approach to the entire field of optics. Besides
its use as a textbook for students of natural or technical sciences, it
may become a valuable compendium of optical experiments for univer
sity lecturers and motivated teachers insecondaryschools. Allnecessary
parametersrequiredto conductthedescribedexperimentswithout prob
lems in a standardly equipped lecture hall are included. Moreover, the
methodologicalapproachto thefieldofoptics via experimentsmay make
the book well-suited for practicing engineers who wish to increase their
understanding.
Thefirst volume (Waveand Geometrical Optics) discusses waveprop
erties of light such as its character as an electromagnetic wave and po
larization and includes a chapter on geometrical optics. Phenomena due
to coherence properties ofthe waves, likeinterference and diffraction as
wellas thestatistical properties oflight seen as a fluxofphotons willbe
treated in the second volume (Coherent and Statistical Optics).
ix
Chapter 1
HISTORICAL INTRODUCTION
Optics, treated as a field of science, is concerned with the study of
the properties of electromagnetic waves with short wavelengths (within
the spectral range of 200- 1000 nm), its propagation through vacuum
and matter, and with the interaction between light and matter. Such
electromagnetic waves have special significance for general human de
velopment and for practical applications.' Human eyes are sensitive to
wavelengths between 400 and 700 nm.
Nearly all basic scientific ideas and general concepts of nature have
been developed using visible radiation and optical studies. The his
tory and evolution ofthe basic natural sciences, likeastronomy,physics,
chemistry and biology etc., has always been strongly connected to op
tics. Much progress in all these fields has been made by developing
increasingly sophisticated optical instruments. But the development of
important physical ideas,principles ofvarious measurements and exper
imental methods isalsostronglyconnected to optical concepts. It issafe
to claim that optical methods still remain basic among all the instru
mental techniques of contemporary experimental physics. Even today
many revolutionary changes and achievements are taking place in scien
tific instrumentation, the creation ofnew measurement approaches, and
basic research. These developments, based on a deeper understanding
oflight as a physical entity and its interaction with matter, continue to
expand our knowledge about nature considerably.
1. Wave nature of light
Long before the wave concept oflight had been introduced, the prin
cipleoflinear light propagation wasthe basic assumption in optics. The
everyday experience of the shadow cast by bodies illuminated.by the
1
O. Marchenko et al., Demonstrational Optics
© Kluwer Academic/Plenum Publishers, New York 2003
2 DEMONSTRATIONAL OPTICS
Sun, as well as Sun rays breaking through clouds, led to the idea that
light propagates from asource as a beam along a straight linetrajectory.
For a long time, light was thought to be a stream of particles, emitted
from all visible bodies, penetrating into the eye. This model held un
til the beginning of the 18th century, and even LNEWTON (1643-1727)
considered light to have corpuscular nature. This model of light is in
agreement with the laws ofgeometrical optics.
But observations showed, that light propagation is a more complex
process. Thorough examination of the boundary between shadow and
light showed, that light alsopenetratesinto the regionofthe geometrical
shadow, violating slightly the idea of linear light propagation. Obser
vation of the light and dark bands near the boundary of a geometrical
shadow, and thesimilar effectofalternatingsequences ofbright and dark
bands, when light passes through a narrowslit in an opaquescreen, lead
to ideas that light may be deflected slightly by geometrical objects.
In order to explain this diffraction phenomenon the Dutch scien
tist CH.HUYGENS (1629-1695)introduced the followingconcept oflight
propagation [1]. Light can be represented as a kind of oscillation, or
light wave,while propagating. Every point ofthe light waveoriginating
from a source may act as the origin of secondary waves propagating in
all directions. The resultant wavefront at a particular moment may be
regarded as a superposition of all the secondary waves. This principle,
known as the HUYGENS principle, allowsthe determination of the posi
tion ofthe current wavefront,ifthe position ofthe wavefront is known
for an earlier moment. Ageometrical scheme, illustrating this principle,
isshown in Fig.!.!. Based on HUYGENS' geometrical representation the
phenomenon of light diffraction is easy to understand when considerat
ing secondary sources located outside the obstacle. Light waves arising
from these sources and propagating in all directions are the reason for
the bright bands within the region ofthe geometrical shadow.
Within the framework of HUYGENS' principle the phenomena oflight
refraction and reflection have been explained as well. HUYGENS pro
vided an explanation for the birefringence phenomenon, discovered by
E.BARTOLINUS (1625-1698) in 1665. It was supposed, that within the
birefringent crystal there exists a second extraordinary waveapart from
the normal ordinary one. Its velocity is dependent on the propagation
direction within the crystal. The shape of the wave front of the extra
ordinary wave is an ellipse, and not a circle as for the ordinary wave.
Studying the birefringence inIceland Spar, HUYGENS discovered the po
larization ofthe ordinary and the extraordinary beams. An explanation
ofthis phenomenon was offered much later.