Lenses and waves. Christiaan Huygens and the mathematical ...

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Lenses and Waves

Transcript of Lenses and waves. Christiaan Huygens and the mathematical ...

Lenses and Waves

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Contents

1 INTRODUCTION 1

2 TRACTATUS: UNDERSTANDING THE TELESCOPE 9

2.1 The Tractatus of 1653 92.1.1 Ovals to lenses 102.1.2 A theory of the telescope 14

2.2 Dioptrics and the telescope 232.2.1 Kepler and the mathematics of lenses 252.2.2 The use of the sine law 342.2.3 The need for theory 41

3 DE ABERRATIONE: IMPROVING THE TELESCOPE 53

3.1 The use of theory 553.1.1 The art of telescope making 563.1.2 Huygens innovating 63

3.2 Dealing with aberrations 673.2.1 Properties of spherical aberration 683.2.2 Putting theory to practice 793.2.3 Newton’s other look and Huygens’ reaction 86

3.3 The scholar and the craftsman 963.3.1 The mathematics of things 973.3.2 Theory and practice 110

4 ‘PROJET’: THE NATURE OF CAUSES 119

4.1 The nature of light and the laws of optics 1234.1.1 Alhazen and Perspectiva 1244.1.2 Kepler 1274.1.3 Analogies and mechanisms 137

4.2 The mathematics of strange refraction 1484.2.1 Bartholinus and Huygens on Iceland Crystal 1504.2.2 Rays versus waves 160

5 TRAITÉ: EXPLAINING THE LAWS OF OPTICS 171

5.1 A new theory of waves 1725.1.1 A first EUPHKA 1745.1.2 Undulatory theory 1855.1.3 Traité de la lumiere and the ‘Projet’ 195

5.2 Comprehensible explanations 2005.2.1 Mechanisms of light 2025.2.2 ‘Raisons de mechanique’ 211

5.3 The second EUPHKA 2215.3.1 Danish objections 2235.3.2 Hypotheses and deductions 228

6 HUYGENS, HIS TRAITÉ, AND MATHEMATICAL SCIENCE IN THESEVENTEENTH CENTURY 231

6.1 Towards Traité de la lumiere 2326.1.1 Completing ‘Dioptrique’ 2336.1.2 Traité de la lumiere and the advent of physical optics 243

6.2 A mathematical scientist 2526.2.1 Huygens’ cartesianism 2536.2.2 The reception of Huygens 267

7 LENSES AND WAVES 273

LIST OF FIGURES 285

BIBLIOGRAPHY 289

SUMMARY IN DUTCH 313

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