B r i d g i n g t h e G a p

B e t w e e n T e a c h i n g

a n d L e a r n i n g i n

G e o m e t r i c a l O p t i c s :

By Paula R.L. Heron and Lillian C. McDermott

T he view among many faculty that teaching is sole­ly an art and not at all a science has prevented the cumulative progress that characterizes knowledge in the sciences. More often than not, new instruc­

tors start from scratch, trusting that personal charisma, intuition, and ex­

perience gained through trial and error will make them ef­fective teach­ers. On an in­

dividual basis this approach sometimes works quite well, especially when the primary measure of success is based on student perceptions. When student learning is used as a criterion, however, the outcome is often quite disappointing.

Systematic investigations have demonstrated that the gap between what is taught in physics and what is learned is often greater than many instructors realize.1-3

This article presents evidence that research on the learn­ing and teaching of physics can help bridge this gap. Examples from geometrical optics are used to illustrate how the Physics Education Group at the Univ. of Wash­ington conducts research and uses the results as a guide for the improvement of instruction.4

The Physics Education Group, which consists of fac­ulty, postdoctoral research associates, and graduate stu­dents, is an integral part of the physics department. Graduate students earn a Ph.D. in physics for research on the learning and teaching of physics. The group con­ducts a coordinated program, in which research, cur-

The Role of Research Research on the learning and teaching of

physics is discipline-specific, focuses on the

state of the student, and can be generalized

beyond a particular instructor, course, or

institution. As an example, this article

describes how results from research have

contributed to the improvement of student

learning in geometrical optics.

30 Optics & Photonics News/September 1998

1047-6938/98/9/0030/07-$0015.00 © Optical Society of America

riculum development, and instruction are tightly linked in an iterative cycle (see Fig. 1). Specific difficulties that students encounter in physics are identified. These find­ings are used to design curriculum to address these dif­ficulties. The materials that are produced are tested and revised on the basis of classroom experience. The group's two major curriculum development projects are Physics by Inquiry 5 and Tutorials in Introductory Physics.6 The first is designed to prepare prospective and practicing (K-12) teachers to teach science as a process of inquiry, the second, to supplement traditional intro­ductory algebra- or calculus-based physics instruction. The development of both curricula has been strongly influenced by our experience in several interrelated pro­jects through which we interact daily with the rest of the department and with other parts of the university.

The introductory course Students typically take introductory physics because it is a requirement. For most, algebra- or calculus-based physics is a terminal course. Instruction takes place pri­marily in lectures in which a great deal of material is cov­ered quickly. The presentation tends to be theoretical and abstract, proceeding from the general to the specific. While instructors expect students to develop problem solving and scientific reasoning skills, problems posed seldom require higher order thinking, such as deductive or inductive reasoning. Research results indicate that most students do not develop the ability to reason quali­tatively, nor understand what is meant by a physical explanation. They tend to view physics as a collection of facts and to believe that the key to solving a physics prob­lem is finding the right formula. This perception becomes more firmly entrenched as the course progresses.7

Investigation of student understanding Our group is very pragmatic in its efforts to improve instruction. We recognize that the physics community is deeply embedded in a common culture and it is often difficult to convince physics faculty to accept change. We therefore work within the traditional curriculum by asking the following ques­tions: "Is the standard presentation of a basic topic in a textbook or lecture adequate to develop a functional understanding? If not, what gaps need to be filled?" By func­tional understanding, we mean the ability to apply what has been learned in one context to another. The difference may be small for first-year students, but should increase with progress through more advanced courses.

The group begins to develop curriculum on a topic by first trying to determine what students are actually learning. We use two basic research methods. One is the individ­ual demonstration interview, in which a simple demonstration provides the basis for a dialogue between an investigator and a student. We also conduct descriptive studies that involve large numbers of students. We engage students in informal discussions and

analyze their written work. In this paper, these methods are illustrated in the context of research on student under­standing of geometrical optics. 8 , 9 We have also inves­tigated student understand­ing of physical optics, as well as many other topics.10

In a study conducted sev­eral years ago, we examined how students interpret the real image formed by a con­verging lens or concave mirror. 1 1 During exploratory interviews, it was found that students who had studied image formation by lenses and mirrors generally had no difficulty in locating the image formed by a thin con­verging lens. The general procedure for solving this type of problem is to apply the thin lens formula that relates the object and image distances (s and s') to the focal length (f) of the lens (see Fig. 2). The students could also draw the correspond­ing ray diagram with the three principal rays that can be used to locate the image. They could relate the numbers in the prob­lem to measurements on a real optical bench.

Having determined what stu­dents could do, we then conduct­ed about 20 individual demon­stration interviews to determine what they might not be able to do. Participants were volunteers from the top half of their respec­tive classes. The questions posed were based on the demonstration shown in Figure 3 (see page 32), which consists of a clear, brightly lit bulb, a converging lens, and

Thin lens formula:

Ray diagram:

Figure 1. Iterative cycle of research, curriculum development, and instruction.

Figure 2. Two methods for locating the image formed by a thin converging lens. The diagram shows the three principal rays that can be used to locate the image.

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Optics & Photonics News/September 1998 31

the inverted real image of the filament of the bulb on the screen. The students were asked if anything would change on the screen if certain speci­fied changes were made in the appara­tus. The interviews lasted from 45-60 minutes. Results are shown in the first col­umn of Table 1. They support the following generalization:

Facility in solving standard quantitative prob­lems is not an adequate criterion for functional understanding. Questions that require qualitative reasoning and verbal explanations are essential.

The students were first asked what change would occur if the lens was removed. Only about half predict­ed that there would be no image. Many stated that it would be right side up, apparently not recognizing the necessity of the lens to form the image. Instead they seemed to think that the function of the lens was to invert the image.

On the second interview task, the students were asked what would happen if the top half of the lens was blocked. Fewer than half seemed to recognize that even a very small part of a lens is sufficient to produce an image. The most popular response was "half a lens, half an image." Investigators tried to guide students by sug­gesting that they draw ray diagrams. One student drew a correct ray diagram, similar to the one shown in Figure 4. For the top and bottom of the object, he drew two of the three principal rays used to locate the image and explained that blocking the top half of the lens would cut off the two rays that form the bottom of the inverted image. He did not understand that tracing the principal rays through a lens is an algorithm, or rule, for locating the image, and that these rays are sufficient, but not nec­essary. Like many others, this student confused the method for locating the image with the actual physical situation, which involves an infinite number of rays.

In a third task, students were asked if anything would change on the screen if it were moved toward the lens. They were expected to recognize that if the screen were moved very far in either direction, no image would appear on it. Fewer than half of the stu­

dents gave this response. All had spent con­siderable time applying the thin lens for­mula, which expresses the o n e - t o - o n e re la t ionship between every

object point and its corresponding image point. Their inability to make a correct prediction indicated a failure to relate the formula to the physical situation that it describes.

Connections among concepts, formal represen­tations, and the real world are often lacking after traditional instruction. Students need repeated practice in interpreting physics formal­ism and relating it to the real world.

The difficulties related to the inversion of the image and to the interpretation of ray diagrams did not origi­nate from experience in daily life, but during instruc­tion. The poor performance of the students could not be attributed to an unusual lack of competence on their part or on the part of their instructors. Similar results were obtained from written questions given subsequent­ly to about 200 students (see Table 1).

Students who were sufficiently facile with mathe­matical manipulation could solve simple problems for which rote application of the thin lens formula was sufficient. However, they generally did not reason in terms of a conceptual model for geometrical optics. This observation suggests the following generalization:

A coherent conceptual framework is not typi­cally an outcome of traditional instruction. Students need to participate in the process of con­structing qualitative models that can help them understand relationships and differences among concepts.

From the perspective of a physicist, perhaps the most disappointing outcome of the introductory course is that students do not think of physics as a way of making sense of the natural world. They do not understand what a scientific model is, how it is constructed, how it is applied, or what its limitations are.

There is evidence that on certain types of qualitative questions, student performance is often essentially the same: before and after standard instruction; in the cal­culus- and algebra-based course; with and without a standard laboratory; with and without demonstrations; in large and small classes; and regardless of the profi­ciency of the lecturer. These findings lead to the follow­ing generalization:

Teaching by telling is an ineffective mode of instruction for most students. Students must be intellectually active to develop a functional understanding.

There is a serious mismatch between how the intro­ductory physics course is traditionally taught and how most students learn best. Lecture instruction is not as effective as has been tacitly assumed, and although a lec­turer can motivate and inspire the students, he or she cannot do their thinking for them. Students who are strongly motivated to learn physics will do so. When they do not understand a lecture, they will work their way through the textbook and struggle with problems. Just below this layer of students, however, is a much larger group who are capable of learning much more than they usually do. The right kind of help can make a difference for them.

Figure 3. Arrangement of bulb, converging lens, and screen used in interview tasks.

Figure 4. Ray diagram similar to one drawn by a student who responded that blocking the top half of the lens would result in half an image.

32 Optics & Photonics News/September 1998

Table 1. Results from interviews and written questions on how the image in Figure 3 would change if specified changes were made.

Tutorials: An instructional approach for addressing student difficulties At any one time in our physics department, there are about 2,000 students enrolled in introductory courses, with almost 1,000 taking calculus-based physics. All three academic quarters of this course—mechanics, electricity and magnetism, and waves and optics—are taught concurrently, in eight lecture sections, each with a different instructor. Faculty rotate through the course on a one-academic-quarter to three-year cycle. There are about 45 laboratory and 45 tutorial sections.

We were faced with the task of securing the mental engagement of students in large classes. Although our faculty are very con­scientious instructors, the department is strongly research-oriented. A system was needed that would be practical, flexible, and sustainable. The result is a tutorial sys­tem; the core is provided by Tutorials in Introductory Physics.6

The word "tutorial" was chosen to dis­tinguish these small-group sessions from the recitation, discussion, or quiz sections that are traditionally associated with small-group science instruction. The usual way of conducting such sessions is for a faculty member or teaching assistant (TA) to work problems for the students, or ask them to solve problems, or respond to questions (often with a mini-lecture). The tutorials are very different in purpose and structure. The emphasis is not on transmitting infor­mation and solving standard problems, but on constructing concepts, developing reasoning skills, and relating the formalism of physics to the real world.

Nature of the tutorials The tutorials are designed to promote active learning. They target critical ideas and skills that are known through research and teaching experience to present dif­ficulty. To secure the level of intellectual commitment necessary to bring about a significant conceptual change,

the tutorials use a variety of instructional strategies. One that has proved particularly effective can be summarized as a sequence of steps: elicit, confront, and resolve. The first step is to elicit a known difficulty by contriving a sit­uation in which students are likely to make an error that exposes that particular difficulty. The students then need to recognize the source of the error. While physics majors are more likely to try to improve their own understanding, other students may be more willing to tolerate inconsistency. It is therefore the responsibility of the instructor to insist that students confront and resolve underlying difficulties. If these are sufficiently serious and not addressed, they may remain latent and arise in other contexts. Tutorial homework assignments provide additional practice to help reinforce ideas developed during the tutorial. The students are given the opportu­nity to apply the relevant concepts in related but differ­ent contexts to reflect and generalize.

Description of the tutorial system The tutorials provide the context in which much of our research and curriculum development takes place. Each tutorial sequence begins with a pre-test (although it pre­cedes the tutorial, the material may have already been covered in lecture). The pre-tests have several purposes: to alert students to what they need to know and be able to do, to set the stage for the associated tutorial, and to

inform the course lecturers and tutorial instructors about the intellectual state of their students. Some pre­tests have been designed to elicit known difficulties.

During the tutorial sessions, about 20-24 students work collaboratively in groups of 3 or 4. Structure is provided by tutorial worksheets designed to help stu­dents confront and resolve specific difficulties, using questions that try to break the reasoning process into steps of just the right size for students to become active-

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Optics & Photonics News/September 1998 33

Figure 5. Q u e s t i o n s and c o r r e c t r e s p o n s e s for the latest vers ion of the pre-test. (a) S t u d e n t s were a s k e d to s k e t c h what they would s e e on the s c r e e n . (b) C o r r e c t a n s w e r s .

Iy involved. If the steps are too small, little thinking may be necessary; if too large, the students may become lost. A t least o n e - f o u r t h o f every course e x a m i n a t i o n requires qualitative reasoning and verbal explanations. The students quickly learn that they must work through the tutorials and do the related homework.

Preparation of TAs and other tutorial instructors For the tutorial system to work, ongoing prepara­tion of tutorial instructors in both the subject mat­ter and the instructional method is required. Most of us teach as we were taught. It is unrealistic to expect peer instructors, graduate TAs, or faculty to be able, without preparation, to teach by question­ing in a way that promotes development of reason­ing skills. Tutorial instructor preparation takes place on a weekly basis in a required graduate teaching seminar led by our group. The seminar is conducted on the same material and in the same manner that the instructors are expected to teach. Since the TAs take the same pre-tests as the introductory students, we have a measure of their level of understanding. Although they can generally solve the end-of-chap­ter problems, we find that they often do not have a sufficiently strong command of the material for the

type o f teaching by quest ion ing that the tutorials require. Advanced study does not necessarily lead to a deeper understanding of introductory physics. 1 2

Example of a tutorial: Light and shadow It is not possible here to describe any of the tutorials in detail, 1 3 but a brief overview is given of a tutorial devel­oped as part of a study examining how students inter­pret some simple phenomena involving light and shad­ow. 9 We hoped that by eliminating complications due to reflection and refraction, we would be able to determine whether some of the difficulties identified with lenses and mirrors had roots at a more elementary level. In particular, the group was interested in probing whether students could use their knowledge of the rectilinear propagation of light to account for the geometric image, the bright region produced on a screen when light is incident on an aperture. 1 4 The emphasis was on the ability to apply two basic principles from geometrical optics: light travels in straight lines and light rays from every point on an object travel outward in all directions.

The pre-test The pre-test for this tutorial has gone through several iterations and has been given in several forms to almost 5,000 students. It is based on a simple optical system consisting of a light source, a mask with a small triangu­lar hole (~1 cm), and a screen (see Fig. 5). In the first question, the light source is a very small bulb. The stu­dents are asked to sketch the appearance of the image. The same task is then posed for two other light sources: two very small bulbs (one above the other) and a long-filament bulb that is essentially a line source.

To give a correct response, students must recognize that light travels in a straight line and that a line source can be treated as a series of point sources. For the single small bulb, the image on the screen is triangular. With a second bulb, a second triangular image appears. If the bulbs are sufficiently close to each other, the images overlap. The image due to the long-filament bulb can be found by treating it as a string of many closely spaced smal l b u l b s , each of wh ich produces a t r iangular image. 1 5 Since the bulbs are closely spaced, the images overlap substantially. The resulting image is a vertical

Table 2. Resu l ts from pre- and post- tests administered in introductory phys ics c o u r s e s and graduate teach ing seminars . The table conta ins only data from the part of e a c h test pertaining to an ex tended light source . T h e pre-test ques t ion is the one s h o w n in F igure 5 a involving a long-f i lament bulb; p o s t - t e s t s are s h o w n in F igure 7. E a c h populat ion took only one post - test . A l though the c l a s s e s for w h o m the pre- and post - test d a t a are repor ted are not all the s a m e , the resul ts c a n be c o m p a r e d b e c a u s e there is typical ly little var iat ion from c l a s s to c l a s s .

34 Optics & Photonics News/September 1998

rectangle termi­nating at the top in a triangle.

Although the amount of instruc­tion varied from class to class, the results did not. 1 6

Almost all of the students correctly predicted a single triangular image for the single small bulb. About 60% gave a correct

response for the two bulbs. The most common error was to show a triangular image. The results for the ques­tion on the long-filament bulb are shown in the first column of Table 2. Only about 20% of the students answered correctly, either before or after instruction. (The variation in intensity due to the differing degree of overlap among the individual triangular images was ignored in our analysis of student responses.) About 70% predicted that the image would be triangular. It was clear that after traditional lecture and laboratory instruction many students were unable to apply their knowledge of the rectilinear propagation of light.

Certain conceptual difficulties are not overcome by traditional instruction. Persistent conceptual difficulties must be explicitly addressed by multi­ple challenges in different contexts.

Development of the tutorial With results from the pre-tests as a guide, a tutorial was designed based on the apparatus in Figure 5. The tutori­al begins by having students predict the images formed by point and line sources with apertures of various sizes and shapes. After the students have made predictions and explained their reasoning to one another, they observe what actually happens and try to resolve any discrepancies with their predictions. They are then asked to predict and explain up-down and left-right inversions of images produced by asymmetric sources. These and other exercises help students recognize that the size and shape of the source, the size and shape of the aperture, and the distances involved all can have an effect on the image. The students note that whether a light source can be treated as a point, line, or extended source also depends on a variety of factors.

Systematic monitoring in the classroom helped improve the tutorial. One exercise was added that has had a pronounced effect. The students are asked to pre­dict what they would see on the screen when a frosted light bulb is placed in front of a mask with a triangular hole. Many initially believe that the frosted bulb acts like a "large point source" and produces a large triangular image. They are surprised to see the inverted image of the bulb and eventually realize that the entire bulb can be considered as a collection of point sources. Superpo­sition of the images from the continuum of point sources produces an image that closely resembles the

shape of the extended source, but is affected by the shape of the aperture at the edges, where fewer images of the aperture overlap with one another (see Fig. 6).

Assessment of the tutorial Throughout the entire development of the tutorial, assess­ment played a critical role. In Figures 7a-c are three post-test questions based on the light source and aperture com­binations shown. The correct answers appear in Figures 7d-f. The questions were administered on different examinations to about 360 students who had worked through the current version of the tutorial, which includes the frosted bulb. We counted as correct or nearly correct all responses indicating either that the extended source was composed of point sources or that the image was basically the same shape as the source. The percentage of correct or nearly correct responses was 80%, an increase from 20% on the pre-test.17 Only 10% drew images the same shape as the aperture, in sharp contrast to the 70% who made this error on the pre-test (see Table 2).

We consider the pre-test performance of physics graduate students to be a reasonable post-test goal for introductory students. The last column of Table 2 shows the pre-test results on the long-filament bulb for 110

Figure 6. Image of f ros ted bulb result­ing from superposi t ion of i m a g e s of a tr iangular hole.

Figure 7. T h r e e pos t - tes ts . (a -c ) S t u d e n t s were a s k e d to s k e t c h what they would s e e on the s c r e e n . (d-f) Cor­rect a n s w e r s .

Optics & Photonics News/September 1998 35

TAs and post-docs. About 65% have given a correct or

nearly correct response. Compar ison of these results

with the post-test performance of the introductory stu­

dents indicates that the undergraduates achieve a better

functional understanding of this material than the grad­

uate students initially had.

Dur ing faculty development workshops, about 200

college and university physics instructors have taken a

pre-test slightly more difficult than the one in Figure 5.

A b o u t 45% have given a correct or nearly correct

response for the long-f i lament bulb. After working

through the tutorial, several participants have suddenly

connected their observations to their experience during

a solar eclipse when they saw many images of the partial­

ly eclipsed sun on the ground beneath a canopy of leaves.

Conclusion Results from research indicate that most students in a

traditional introductory course cannot do the qualitative

reasoning necessary to apply concepts to situations not

expressly memorized. Our experience has shown that

this ability can be developed if students are given prac­

tice in solving qualitative problems and in explaining

their reasoning. In this way, they can significantly deepen

their understanding of even very difficult material. We

and others have found that time spent on developing a

sound qualitative understanding does not detract from,

and often improves the ability to solve quantitative prob­

lems. 1 8 The tutorials are one example of how, within a

relatively small time allotment, a research-based curricu­

lum can help students learn to do the type of qualitative

reasoning that can make physics meaningful to them.

Growth in reasoning ability does not usually

result from traditional instruction. Scientific

reasoning skills must be expressly cultivated.

There is a price to be paid for an increased emphasis

on the development of scientific concepts and reasoning

ability. It is necessary to proceed more slowly and cover

less. This inevitable consequence is often difficult for

many instructors to accept. They are concerned that stu­

dents will be inadequately prepared for subsequent

courses. We have investigated student understanding in

courses beyond the introductory level in physics and in

other disciplines (e.g., engineering) for which a knowl­

edge of basic physics is assumed, and found that student

difficulties in these courses are more often due to lack of

depth in the conceptual underpinnings than to lack of

breadth in prior knowledge.

Acknowledgments The work described here represents a collaborative

effort by many members of the Physics E d u c a t i o n

Group , past and present. Major contr ibut ions were

made by Fred M . Goldberg, Peter S. Shaffer, and Karen

Wosilait. We are also grateful to NSF for its support.

References 1. This statement and its implications are discussed in gener­

al terms in L.C. McDermott, "Millikan lecture 1990: What we teach and what is learned—closing the gap," Am. J. Phys. 59, 301-315 (1991), and L.C. McDermott, "Guest comment: How we teach and how students learn—a mis­match?," Am. J. Phys. 61, 295-298 (1993).

2. This statement is supported by evidence presented in many papers that report on research by the Physics Education Group at the Univ. of Washington. See, e.g., L.C. McDer­mott and P.S. Shaffer, "Research as a guide for curriculum development: An example from introductory electricity. Part I: Investigation of student understanding," Am. J . Phys. 60, 994 -1003 (1992), and erratum to Part I, ibid. 61, 81 (1993); P.S. Shaffer and L.C. McDermott, "Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of instructional strategies," ibid. 60, 1003-1013 (1992); L.C. McDermott et al., "Research as a guide for teaching intro­ductory mechanics: An illustration in the context of the Atwood's machine," ibid. 62, 46 -55 (1994); and T.E. O'Brien Pride, S. Vokos, and L.C. McDermott, "The chal­lenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems," ibid. 68, 147-157 (1998).

3. This statement is also consistent with the conclusion reached by experienced physics instructors who have probed student understanding in less formal ways in the classroom. See, e.g., A . B . Arons, A Guide to Introductory Physics Teaching (John Wiley & Sons Inc., New York, N.Y., 1990) and E. Mazur, "Qualitative vs. quantitative thinking: Are we teaching the right thing?," Opt. & Phot. News 3 (2), 38 (1992).

4. The work described in this article has been presented at many talks and faculty development workshops from 1995-1998.

5. L.C. McDermott and the Physics Education Group at the Univ. of Washington, Physics by Inquiry, Vols. I and II (John Wiley & Sons Inc., New York, N.Y., 1996).

6. L.C. McDermott, P.S. Shaffer, and the Physics Education Group at the Univ. of Washington, Tutorials in Introductory Physics, Preliminary Edition (Prentice Hall, Upper Saddle River, N.J., 1998).

7. E.F. Redish et al., "Student expectations in introductory physics," Am. J. Phys. 66, 212-224 (1998).

8. F.M. Goldberg and L.C. McDermott, "Student difficulties in understanding image formation by a plane mirror," Phys. Teach. 24, 472-480 (1986) and "An investigation of stu­dent understanding of the real image formed by a converg­ing lens or concave mirror," Am. J. Phys. 55, 108-119 (1987).

9. K. Wosilait, P.R.L. Heron, P.S. Shaffer, and L.C. McDermott, "Development and assessment of a research-based tutorial on light and shadow," Am. J. Phys. (1998), in press.

10. B.S. Ambrose, P.S. Shaffer, R.N. Steinberg, and L.C. McDermott, "An investigation of student understanding of single-slit diffraction and double-slit interference," Am. J. Phys., in press.

11. See the second article in Ref. 8. 12. See the last article in Ref. 2 and R.N. Steinberg, G.E.

Oberem, and L.C. McDermott, "Development of a computer-based tutorial on the photoelectric effect," Am. J. Phys. 64, 1370-1379 (1996).

13. See the last three articles in Ref. 2 and Ref. 9 for greater detail.

14. In the discussion of the tutorial, the term image refers to the geometric image, which differs from the real image formed by a converging lens.

15. Alternatively, one can think of the triangular hole as a col­lection of closely spaced pinholes. Each pinhole produces a sharp, inverted image of the line source. The resultant image is a superposition of the individual pinhole images.

16. Other examples in which student performance on certain questions is essentially the same before or after standard instruction can be found in the second paper in Ref. 1 and the papers in Ref. 2, as well as in other reports of research by our group.

17. In the case of the O-shaped bulb, both the F-shaped hole and the inverted-L-shaped hole result in an image that is not precisely circular. However, we considered as correct or nearly correct all student diagrams showing a circular ring for the image due to the O-shaped bulb.

18. In addition to the second article in Ref. 2, see, e.g., B. Thacker et al., "Comparing problem solving performance of physics students in inquiry-based and traditional intro­ductory physics courses." Am. J. Phys. 62, 627 -633 (1994) and E. Mazur, Peer Instruction, A User's Manual (Prentice Hall, Upper Saddle River, N.J., 1997).

Paula R.L. Heron is research assistant professor of physics, and Lillian C. McDermott is professor of physics in the dept. of physics, Univ. of Washington, Seattle, WA.

36 Optics & Photonics News/September 1998