Near the horizon: an invitation to geometric optics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
<<The>> Mathematical Association of America
[2016]
|
| Series: | The Carus mathematical monographs
number 33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xiv, 163 Seiten Diagramme, Illustrationen |
| ISBN: | 9780883851425 |
Staff View
MARC
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| 245 | 1 | 0 | |a Near the horizon |b an invitation to geometric optics |c Henk Broer, University of Groningen |
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Record in the Search Index
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|---|---|
| adam_text | Contents
A
Preface xi
1 Introduction and Overview 1
1.1 Towards a mathematical description.................... 5
1.1.1 Theoretical assumptions........................ 7
1.1.2 Discrete versus continous atmosphere,
conservation laws.............................. 9
1.2 Overview of the contents............................. 11
1.2.1 On Part I: Geometry of light rays in the
atmosphere.................................... 11
1.2.2 On Part II: Light rays as geodesics . ........ 13
1.3 Scholium............................................. 14
1 Geometry of light rays in the atmosphere
2 Geometric optics 19
2.1 More precise setting of the problem.................. 20
2.2 Derivation of the reflection and refraction laws..... 21
2.2.1 A straight boundary........................... 22
2.2.2 A curved boundary............................. 24
2.2.3 The limit angle............................... 25
2.3 Conservation laws.................................... 27
2.3.1 Atmosphere of the flat earth.................. 28
2.3.2 Atmosphere of the round earth................. 32
2.4 Scholium............................................. 36
vii
Vlll
Contents
3 Atmospheric optics 41
3.1 Fundamental concepts and terminology.................. 42
3.2 Discrete description of the atmosphere.............. 45
3.2.1 The Wegener sector.............................. 46
3.2.2 Optical scenarios near the horizon........... 48
3.2.2.1 The setting sun......................... 48
3.2.2.2 Including lower reflection.............. 52
3.2.2.3 Fata morganas........................... 53
3.2.3 Variations...................................... 57
3.2.3.1 Takens—profiles......................... 57
3.2.3.2 The green flash......................... 60
3.3 Continuous description of the atmosphere............... 61
3.3.1 The conservation law revisited.................. 61
3.3.2 Wegener sight ray .............................. 62
3.4 Scholium............................................... 65
3.4.1 Deepening....................................... 66
3.4.2 Nova Zembla phenomenon.......................... 67
4 Light and the cycloid 69
4.1 The cycloid............................................ 69
4.2 The cycloid as isochrone and tautochrone curve......... 71
4.2.1 The harmonic oscillator......................... 72
4.2.2 Intermezzo: the arclength of a cycloid....... 77
4.2.3 Dynamics along the cycloid...................... 78
4.2.4 A historical digression......................... 80
4.2.5 Two cycloids.................................... 83
4.2.6 Scholium........................................ 88
4.3 The flat earth atmosphere revisited................... 89
4.3.1 Two conservation laws........................... 89
4.3.2 The cycloid as the brachistochrone curve..... 90
4.4 Scholium............................................... 93
Contents ix
II Light rays as geodesics
5 The principles of Fermat and Hamilton 99
5.1 From Fermat via Euler-Lagrange to Hamilton...........100
5.1.1 Light rays as geodesics........................102
5.1.2 Euler and Lagrange.............................103
5.1.3 Via Legendre to Hamilton.......................105
5.1.4 General remarks................................106
5.2 The Noether Principle: Conservation laws by
symmetry.............................................108
5.2.1 The flat earth atmosphere......................109
5.2.2 The round earth atmosphere.....................Ill
5.3 Reduction of the symmetry............................112
5.4 Scholium.............................................116
6 The brachistochrone revisited 119
6.1 Reduction of the translation symmetry................119
6.2 The cycloid recovered................................121
6.3 Scholium.............................................124
7 Light rays as geodesics on a surface of revolution 127
7.1 Summary of the chapter...............................127
7.2 Geodesics on a surface of revolution.................128
7.3 Dynamics of the geodesics............................130
7.3.1 According to Euler—Lagrange....................130
7.3.2 According to Hamilton..........................131
7.4 Conservation laws....................................131
7.4.1 Reducing the symmetry..........................132
7.4.2 Description of the geodesics...................133
7.4.2.1 Near a geodesic parallel...............134
7.4.2.2 Reconstruction to four dimensions . . . 137
7.4.3 More global behavior of geodesics..............137
7.5 Geodesics and light rays.............................139
7.6 Isometric embeddability..............................142
x Contents
7.7 Scholium.............................................144
7.7.1 Rotation symmetry with or without surface of
revolution.....................................144
7.7.2 Free particle on a surface of revolution.......144
8 Scholium generale 149
8.1 Approximate rotational symmetry......................149
8.2 A connection with wave optics........................152
8.3 Caustics.............................................152
Bibliography 155
Index 161
* Jt-· p %
k . NEAR THE HORIZON:
V- ֊ AM. INVITATION TQ GEOMETRIC OPTICS
1
HENK W. BROER
When you look at the setting sun, sometimes you see surprising things.
Occasionally it may seem as if the sun is already setting while it is
still above the horizon. There may be a blank strip in ¿the middle of
the solar disk, or a flash of green light. These phenomena can be
explained by studying the geometry of light rays as they move through
the atmosphere. Near the Horizon takes them as the starting point and
goes on to connect geometric optics with the calculus of variations
and with differential geometry.
ISBN: 978-0-88385-142-5
78
0883
851425
9
|
| any_adam_object | 1 |
| author | Broer, Hendrik W. 1950- |
| author_GND | (DE-588)124653782 |
| author_facet | Broer, Hendrik W. 1950- |
| author_role | aut |
| author_sort | Broer, Hendrik W. 1950- |
| author_variant | h w b hw hwb |
| building | Verbundindex |
| bvnumber | BV044440408 |
| classification_rvk | UH 5080 |
| classification_tum | GEO 610f PHY 351f |
| ctrlnum | (OCoLC)1021376225 (DE-599)BSZ48966640X |
| dewey-full | 551.565 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.565 |
| dewey-search | 551.565 |
| dewey-sort | 3551.565 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geowissenschaften Geologie / Paläontologie Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:53:01Z |
| institution | BVB |
| isbn | 9780883851425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029841585 |
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| physical | xiv, 163 Seiten Diagramme, Illustrationen |
| publishDate | 2016 |
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| publishDateSort | 2016 |
| publisher | <<The>> Mathematical Association of America |
| record_format | marc |
| series | The Carus mathematical monographs |
| series2 | The Carus mathematical monographs |
| spelling | Broer, Hendrik W. 1950- Verfasser (DE-588)124653782 aut Near the horizon an invitation to geometric optics Henk Broer, University of Groningen Washington, DC <<The>> Mathematical Association of America [2016] xiv, 163 Seiten Diagramme, Illustrationen txt rdacontent n rdamedia nc rdacarrier The Carus mathematical monographs number 33 Meteorologische Optik (DE-588)4169666-9 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 gnd rswk-swf Meteorological optics Meteorologische Optik (DE-588)4169666-9 s Geometrische Optik (DE-588)4020241-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-61444-030-7 The Carus mathematical monographs number 33 (DE-604)BV001887236 33 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029841585&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029841585&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Broer, Hendrik W. 1950- Near the horizon an invitation to geometric optics The Carus mathematical monographs Meteorologische Optik (DE-588)4169666-9 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| subject_GND | (DE-588)4169666-9 (DE-588)4020241-0 |
| title | Near the horizon an invitation to geometric optics |
| title_auth | Near the horizon an invitation to geometric optics |
| title_exact_search | Near the horizon an invitation to geometric optics |
| title_full | Near the horizon an invitation to geometric optics Henk Broer, University of Groningen |
| title_fullStr | Near the horizon an invitation to geometric optics Henk Broer, University of Groningen |
| title_full_unstemmed | Near the horizon an invitation to geometric optics Henk Broer, University of Groningen |
| title_short | Near the horizon |
| title_sort | near the horizon an invitation to geometric optics |
| title_sub | an invitation to geometric optics |
| topic | Meteorologische Optik (DE-588)4169666-9 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| topic_facet | Meteorologische Optik Geometrische Optik |
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