Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T12:28:28.965Z Has data issue: false hasContentIssue false
This chapter is part of a book that is no longer available to purchase from Cambridge Core

Chapter 3 - The Role of Mathematics in Optics

M. M. Schiffer
Affiliation:
Stanford University
Leon Bowden
Affiliation:
University of Victoria, B. C.
Get access

Summary

To illustrate the part played by mathematics in the construction of scientific theories, we consider the development of optics.

Euclid's Optics

We begin with Euclid (c. 300 BC). Not unnaturally for a geometer, he wished, as doubtless had many geometers before him, to apply geometry to optics. Unlike the others he was successful. Conceiving light as propagated in straight lines enabled him to apply geometry to optics. On second thought this statement cannot stand. Until Euclid had applied geometry to optics there was, to use the Irish idiom, no such subject as optics. Nowadays, when diagrams are used as an ingredient of educated common sense, of course it is obvious that light is propagated in straight lines. If light rays could not be represented by lines, optical phenomena could not be illustrated by diagrams. We, with the arrogance of hindsight, cannot begin to understand Euclid's foresight in making his basic assertion that light is rectilinearly propagated. When the needle in the haystack has been pointed out to us, we are prone to suppose that finding it was no problem at all.

Physical objects that more or less crudely approximate straight lines readily come to mind, for example, a taut wire. But surely a shaft of sunlight piercing the shutters of a darkened room is singularly apt. Isn't this the perfect example? Euclid must have been well pleased with his observation. Yet note that his basic assertion embraces metaphysical speculation as well as physical observation.

Type
Chapter
Information
Publisher: Mathematical Association of America
Print publication year: 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×