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1 - Introduction

Published online by Cambridge University Press:  05 April 2014

E. R. Tracy ,
A. J. Brizard ,
A. S. Richardson  and
A. N. Kaufman
E. R. Tracy
Affiliation:
College of William and Mary, Virginia
A. J. Brizard
Affiliation:
Saint Michael's College, Vermont
A. S. Richardson
Affiliation:
US Naval Research Laboratory (NRL)
A. N. Kaufman
Affiliation:
University of California, Berkeley
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Summary

The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and must descend from laws to consequences, by the deductive and synthetic way. We must gather and groupe appearances, until the scientific imagination discerns their hidden law, and unity arises from variety: and then from unity must re-deduce variety, and force the discovered law to utter its revelations of the future.

William Rowan Hamilton (1805–1865)

It is a fact of immediate importance to our everyday experience that light nearly always travels in straight lines from the source to our eyes, perhaps scattering off some object along the way. Without the ability to assume this as a fact about the world around us, our extraordinary talent for instinctively comprehending spatial relationships in everyday life would be severely compromised. Consider how much computer power must be expended to disentangle the multiple images of distant galaxies to map the dark matter distribution in the visible universe [MRE+07]. Imagine what life would be like if we had to do similar mental computations just to navigate around the furniture in our living room.

How do we build upon this insight that light nearly always travels in straight lines in order to develop a theory with predictive power?

Type
Chapter
Information
Ray Tracing and Beyond
Phase Space Methods in Plasma Wave Theory
 , pp. 1 - 61
Publisher: Cambridge University Press
Print publication year: 2014

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