March 2025
Volume 93, Issue No. 3
Kepler's Moon puzzle—A historical context for pinhole imaging
In 16th-century European astronomy, determining the sizes of the Sun and Moon using a pinhole camera was common. However, calculating the Moon's diameter from the concave segment of the partially obscured Sun yielded puzzling results due to a lack of a comprehensive theory of the influence of the aperture on the image. This inconsistency led Tycho Brahe to question prevailing assumptions in celestial mechanics. Recognizing this, Johannes Kepler conducted measurements during a solar eclipse in Graz on July 10, 1600 and soon developed a theory of the pinhole camera that remains valid today. In this article, we recount the historical episode leading to Kepler's theory through original works, complemented by a series of illustrative experiments for classroom use. This historical case study offers a rich context for reflecting on Nature of Science aspects within physics education.
EDITORIAL
In this issue: March 2025 John Essick; Jesse Kinder; Raina Olsen; Beth Parks; B. Cameron Reed; Donald Salisbury. DOI: 10.1119/5.0260074
AWARDS
2025 AAPT award citations at the winter meeting in St. Louis, Missouri. DOI: 10.1119/5.0260071
2025 Jackson Award for Excellence in Graduate Physics Education lecture: There is more to graduate education than is found in Jackson's book Laurie E. McNeil. DOI: 10.1119/5.0260495
Editor's note: This paper is the text of a plenary talk given by the author at the AAPT Winter 2025 meeting when she accepted the J. D. Jackson Award for Excellence in Graduate Physics Education.
PAPERS
Kepler's Moon puzzle—A historical context for pinhole imaging Thomas Quick; Johannes Grebe-Ellis. DOI: 10.1119/5.0228366
Editor's Note: At the time of Tycho Brahe and Johannes Kepler, observations of eclipses were important for studying the movements of the Sun and the Moon, hence for deciding between competing theories of celestial mechanics. However, an issue was that observations made with pinhole cameras were in conflict with naked eye observations in the sense that the angular size of the Sun was too large as determined by the pinhole method. The resolution of this conflict occurred to Kepler while he was observing a solar eclipse in July 1600: The finite size of the pinhole aperture affects the solar image created. Analyzing this effect led Kepler to develop a theory of the pinhole camera and rigorously establish principles of geometrical optics. This interesting historical case study should be accessible to both astronomy and optics students.
Eddy currents of a magnet falling through a copper pipe with slits Keith Zengel; Lauren Boehnert; Jared Medina; Jieping Fang; Juliet Coe; Abby Curtis; William Fredenberg. DOI: Am. J. Phys. 93, 223–233 (2025) https://doi.org/10.1119/5.0216717
Editor's Note: The falling magnet is a favorite demonstration. We often compare the magnet's speed in a regular pipe to a pipe with slits in order to show that the slow fall really is due to eddy currents. But of course, as this paper shows, there are still non-zero eddy currents in a slit pipe. The authors calculate the eddy currents and demonstrate agreement with experimental observations. Instructors in electrodynamics or mathematical methods will find inspiration for projects.
The surprising subtlety of electrostatic field lines Kevin Zhou; Tomáš Brauner. DOI: 10.1119/5.0207201
Editor's Note: Field lines are ubiquitous in introductory physics but mainly as sketches to aid intuition. In this article, the authors explore the surprising and subtle mathematics of field lines. They focus on two questions from electrostatics: (1) When does a set of field lines represent a conservative field? (2) What systems give rise to straight field lines? The canonical examples of Gauss' law—spherical, planar, and line charge distributions—are familiar to physicists, but are there others? To answer these questions, the authors turn to differential geometry. They provide a self-contained introduction to integrability and curvature, starting from vector calculus. The elegant mathematics provides new insights into electrostatics and minimal surfaces, and the material could be used to supplement a wide range of courses. The mathematics will be familiar to students who have taken a junior-level electrodynamics or math methods course, and the methods and results can be applied across the gamut of theoretical physics.
A simple Minkowskian time-travel spacetime John D. Norton. DOI: /10.1119/5.0224022
Editor's Note: Time travel is enormously interesting to physics students, but many instructors do not feel like we can say anything about it. This article could be used in a course on general relativity to introduce a clever alteration of a flat two-dimensional spacetime diagram. One omits the negative spatial left half and then joins the edges to form a flat spacetime cone. The result is that if such a relativistic spacetime could exist, then an aging student could encounter a second continually younger version of his or her self. The unphysical feature of this model, as illustrated by the author, is the presence of a spacetime singularity at the tip of the cone.
Toward a more coherent and profession-related physics teacher education: Linking subject-specific and physics education content in the study entry phase by Antonia Bauer; Jonas Gleichmann; Philipp Bitzenbauer. DOI: 10.1119/5.0223735
Editor's Note: Do you want to create more enthusiasm among your pre-service teachers for learning physics? This paper suggests that, rather than spending their whole first year as learners, students should be encouraged to think as teachers, studying modern pedagogical methods and considering how to overcome misconceptions at the same time that they are mastering the material themselves. The series of worksheets that were developed are shared via supplementary material and may be useful in any introductory course that wishes to provide a reflective experience for students.
NOTES AND DISCUSSIONS
Color-coding strategies for multiple representations by Brianna S. Dillon Thomas. DOI: 10.1119/5.0229029
Editor's Note: Learning physics is hard, and, as instructors, we try to use all possible tools to help students. Here's a tool you may not have considered: use color to help students connect ideas. The author suggests three ways that color can help introductory students. You'll want to give them a try!
Note on a classical case of self-organization: The Persian Immortals by Santos Bravo Yuste. DOI: 10.1119/5.0237521
Editor's Note: This paper presents an extension and a simplification of a previous paper, making its results more appropriate for an undergraduate class. Using the distribution of fighting ability in the army of Persian Immortals as an example, it provides a compelling way to teach students about the cumulative distribution functions and self-organization.
Graphical approach to Bell's inequalities by Krzysztof Rȩbilas. DOI: 10.1119/5.0250670
Editor's Note: I learned long ago how to derive one form of the Bell inequality. Since then, I have simply accepted the other versions on faith. Now, thanks to this very understandable paper, I actually understand them! You'll want to share this graphical approach with your students.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
Educational Shack–Hartmann wavefront sensor by Khosrow Hassani; Veyana Khajehhassanirabori. DOI:10.1119/5.0230503
Editor's Note: This paper presents a low-cost Shack–Hartmann wavefront sensor (SHWFS) for measuring the shape of an optical wavefront. The experimental setup is designed for educational use and implements the SHWFS technique using a large-size lenslet array and CCD camera, along with a data analysis method carried out via freely available software. Data are obtained on collimated, spherical, and cylindrical wavefronts as well as on the effects of lens aberration. These experimental results are shown to be in excellent agreement with theoretical calculations. This work will be of interest to those wishing to introduce a classical optics experiment in their advanced instructional laboratory program.
An undergraduate lab experiment on matched filtering as used in gravitational wave detection by Michael Daam; Antje Bergmann; Carsten Rockstuhl; Ronny Nawrodt. DOI: 10.1119/5.0219962
Editor's Note: This paper introduces a platform for undergraduate laboratory investigations of matched filtering, a data analysis technique used in gravitational wave detection. This work is an excellent complement to the recently published LIGO analogy experiment (AJP, 2019). Noisy waveform data containing low-amplitude signals of various shapes are produced using a Michelson interferometer with one end mirror mounted on a piezo actuator. Students then use software supplied by the authors to extract the signal from the noise using the matched filtering technique. In this technique, the measured data are compared to various templates and a correlation coefficient for each template is calculated. The software only lets the user control two of the many variables involved in template generation, which reduces flexibility but greatly simplifies the plotting and analysis of results. The theory of matched filtering is outlined, and three potential instructional laboratory activities are described.
Additional Resources
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