*Robert W. Batterman*

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195146479
- eISBN:
- 9780199833078
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195146476.003.0006
- Subject:
- Philosophy, Philosophy of Science

This chapter discusses limiting correspondence relations between the wave theory of light and the ray theory of light. The limit is singular and there is no reductive relation between the theories. ...
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This chapter discusses limiting correspondence relations between the wave theory of light and the ray theory of light. The limit is singular and there is no reductive relation between the theories. The focus is on the particular problem of understanding certain universal features of rainbows. The fruitfulness of studying this singular limit is demonstrated. The main conclusion of this chapter is that the fundamental theory (the wave theory) turns out to be explanatorily deficient and a new (asymptotic) explanatory theory characterizes the asymptotic borderland between the two theories.Less

This chapter discusses limiting correspondence relations between the wave theory of light and the ray theory of light. The limit is singular and there is no reductive relation between the theories. The focus is on the particular problem of understanding certain universal features of rainbows. The fruitfulness of studying this singular limit is demonstrated. The main conclusion of this chapter is that the fundamental theory (the wave theory) turns out to be explanatorily deficient and a new (asymptotic) explanatory theory characterizes the asymptotic borderland between the two theories.

*John A. Adam*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691148373
- eISBN:
- 9781400885404
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148373.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter focuses on the ray optics of the rainbow. Some of the most powerful tools of mathematical physics were developed explicitly to address the problem of the rainbow and closely related ...
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This chapter focuses on the ray optics of the rainbow. Some of the most powerful tools of mathematical physics were developed explicitly to address the problem of the rainbow and closely related problems. Indeed, the rainbow has served as a benchmark for testing theories of optics. The more successful of those theories now make it possible to describe the rainbow in mathematical terms—that is, to predict the distribution of light in the sky. The chapter first provides an overview of the physical features and historical details relating to the rainbow before discussing the ray theory of the rainbow from an elementary mathematics standpoint. In particular, it considers some relevant numerical values, polarization of the rainbow, and the divergence problem. It also explores related topics in meteorological optics, including the glory, coronas (simplified), and Rayleigh scattering.Less

This chapter focuses on the ray optics of the rainbow. Some of the most powerful tools of mathematical physics were developed explicitly to address the problem of the rainbow and closely related problems. Indeed, the rainbow has served as a benchmark for testing theories of optics. The more successful of those theories now make it possible to describe the rainbow in mathematical terms—that is, to predict the distribution of light in the sky. The chapter first provides an overview of the physical features and historical details relating to the rainbow before discussing the ray theory of the rainbow from an elementary mathematics standpoint. In particular, it considers some relevant numerical values, polarization of the rainbow, and the divergence problem. It also explores related topics in meteorological optics, including the glory, coronas (simplified), and Rayleigh scattering.

*Heiner Igel*

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0001
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ...
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The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ‘computational seismology’ is defined and contrasted with other more classical approaches such as ray tracing approaches and quasi-analytical solutions such as normal mode techniques and the reflectivity method. The structure of the volume content is illustrated and guidelines are given how to use the content in combination with the supplementary electronic material.Less

The need for numerical approximations of the seismic wave-propaga-tion problem in the field of seismology is motivated by the fact that we have to deal with complex 3D structures. The term ‘computational seismology’ is defined and contrasted with other more classical approaches such as ray tracing approaches and quasi-analytical solutions such as normal mode techniques and the reflectivity method. The structure of the volume content is illustrated and guidelines are given how to use the content in combination with the supplementary electronic material.