Optics education would benefit by explicitly defining key terms. However, this practice seems remarkably rare. An egregious example is image. Much of optics has to do with images, and many textbooks discuss aspects of images, but I have yet to find a book that actually defines the word.
There are at least two reasons why definitions are so rare. First, definitions are difficult. It is easier to compute interference patterns than to define interference. Second, we humans are hard wired to recognize similarities and differences, and to classify. Once we see a couple of examples of diffraction, we recognize others, even without an explicit definition of diffraction. The ability to classify--indeed, the necessity--is biological and preverbal, and we get along surprisingly well with minimal explicit awareness of what we do.
Nevertheless, definition adds value.
- Technical people appreciate the depth of comprehension required to accomplish the famous act of "explaining things to a six year old." The ability to explain in this fashion is akin to the ability to define. And it's not just six year olds; it's people at cocktail parties, job interviewers, subordinates, and superiors. When the big boss drops in unexpectedly and asks about your work, "Duh" is not the best response. If you can define the key terms involved in your activity, you are a long way toward being able to communicate what you do. (How do you define your profession? Can you answer the question, "What do you do?")
- The act of defining is in itself a stimulating activity that improves comprehension. It expands the mind for the very reason that it is not automatic. Paradoxically, it is often the case that the more we know about something, the more difficult it becomes to define it. We all once understood what a light ray is. Then, we learned about wave optics. Now, we don't quite know anymore what a ray is and we may be slightly embarrassed that something so indispensable is so unreal.
- Defining brings things back to basics. Layers of abstraction build as physical quantities are mathematically defined in terms of others. Finally, we are left with a symbol. While this is mathematically appropriate and necessary, it is not all there is. It is beneficial to stop and ask, "just what is this quantity?" The act of defining can force a return to first principles; a peeling of the layers.
- The talk and thought in science and engineering ultimately produce predictions that are tested by measurement, and definitions are often related to measurement. Some quantities can be defined in terms of the outcomes of procedures.
- The search for definitions sharpens distinctions by turning up shortcomings in the language. Examples abound: (a) Is physical optics anything other than wave optics? Is there unphysical optics? (b) What is diffraction? As generally used, the term refers to two distinct aspects of wave behavior. One involves certain types of wave interaction with matter, e.g., obstacles. The other involves the propagation of waves thereafter. (c) Interference is an archaic term. It's really just addition. (Of course, you have to know what to add; you always do.) (d) Aberrations are the norm; perfect imaging is abnormal. (e) Virtual is an unfortunate and confusing term, now even more so because of its use in computer mind space. Instead of virtual image, how about inaccessible image? Likewise, consider accessible image instead of real image.
- Exploring definitions leads to word origins, which are just plain fascinating. For example: Lens comes from bean, as in lentil. Focus comes from fireplace or hearth. For pupil, Webster! says: "....diminutive of pupa, girl, doll, hence, one's image reflected on the cornea of another's eye ..."
An article on education should leave the reader with homework. Here are some assignments.
- For readers: Can you define in plain Strunk-and-White English the key terms in your work?
- For teachers, I propose an experiment: On the next exam or homework assignment, ask your students to define some key terms. You may be enlightened by a couple of the responses. The rest
may convince you that definitions should be part of pedagogy.
- To textbook writers, I beseech: Begin a subject by defining the terms, not by just talking about them.
- To anyone, I ask: What is a wave? ("A solution to the wave equation" is not acceptable.) What is a mode? ("An eigenfunction of a differential equation" is not acceptable.) What is an image? ("I know one when I see it" won't work) Remember--you are speaking to a six year old.
Webster's International Dictionary, Second Edition, G&G Merriam Company, Springfield, MA 1936.
Doug Goodman works in the Optical Engineering Dept. of Polaroid Corp. (Cambridge, MA) and is a member of SPIE's Education Committee.