AJP December 2023 coverDecember 2023 Issue,

Volume 91, No. 12

Numerical simulation of mirages above water bodies

A mirage or fata morgana is typically an upside-down “mirror” image of a scenery in deserts, over sun-heated roads, or above bodies of water. When the temperature gradient of air is large, as can happen near a surface, it results in a large gradient of the density and the refractive index as a function of height. Mirages appear when light travels through a medium with a gradient in its refractive index and, therefore, get bent towards the higher values, generating reflected images. A computer program that simulates mirages above water using the method of ray tracing has been developed and is presented here in detail for educational purposes. Results on the effect are shown by simulated images for various water-air temperature-difference cases with values ranging from 5 to 0 °C. Comparison of the simulations to a real-life scenario at Lake Balaton, Hungary has also been provided.


In this issue: December 2023 by John Essick; Harvey Gould; Claire A. Marrache-Kikuchi; Beth Parks; Todd Springer; Jan Tobochnik; Keith Zengel. DOI: Am. J. Phys. 91, 953–954 (2023) https://doi.org/10.1119/5.0184717


ChatGPT-4 with Code Interpreter can be used to solve introductory college-level vector calculus and electromagnetism problems by Tanuj Kumar; Mikhail A. Kats. DOI: 10.1119/5.0182627

Comment on “Avoid propagation of typos with numerical methods” [Am. J. Phys. 89(1), 9 (2021)] by B. Cameron Reed. DOI: 10.1119/5.0167881


Does active participation in a daily quiz (TOPday) improve long-term retention in biomechanics? by Florieke Eggermont; Moniek A. M. Munneke; Vera Adriaens; Cornelia R. M. G. Fluit; Jan G. M. Kooloos; Esther Tanck. DOI: 10.1119/5.0101494
All of us have experienced disappointment upon realizing we forgot something we once knew well. On the other hand, instructors may be delighted when a former student remembers an essential truth from a course many years ago. Training students in any discipline requires long-term knowledge retention, so studies on such retention are fundamentally important. The authors of this article provide convincing evidence that students who actively participated in optional daily physics quizzes retained significantly more physics knowledge after the course ended. Both students and instructors will find this article to be a stimulating read. Developing teaching techniques (and promoting study habits) that increase knowledge retention could benefit the entire community.

Pendulum waves: A model of Thomae's function Video Abstracts by Xiangdong Feng; Changhong Lu; Jurgen Schulte; Zengxu Shan; Gentong Liu. DOI: 10.1119/5.0131936
Readers may have seen the pendulum wave apparatus, which is a mesmerizing demonstration. The author connects the mathematics of the alignment of these columns of pendulums to Thomae's function, aiding instructors who want to show students the deep connections between physics and mathematics. A video abstract accompanies the online version of this paper.

Teaching rotational physics with bivectors by Steuard Jensen; Jack Poling. DOI: 10.1119/5.0109883
The vector nature of rotation is notoriously difficult for introductory physics students. Cross products and right-hand rules are among the many challenges students face in the traditional instructional approach. Educators who desire a novel approach will find this article interesting, as it explores rotation using the language of bivectors. Instead of using abstract arrows (vectors), rotational quantities are represented with oriented tiles. This fresh perspective may help students overcome conceptual barriers, while also preparing them for more advanced discussions of rotation in relativity or in more than three spatial-dimensions.

Nonlinear oscillator acceleration and period variation with amplitude by Peter F. Hinrichsen. DOI: 10.1119/5.0139124
Although physics instructors tend to emphasize simple harmonic motion, most real-world oscillating systems are nonlinear. Here, a new, simple system is introduced that allows students and instructors to easily tune the nonlinearity of air track glider oscillations using only linear components. This setup could be used in a mechanics laboratory activity or in a lecture demonstration of the sensitivity of oscillator motion to initial conditions and would pair well with an introduction to Fourier analysis.

Thermal physics in the data age—Students judge the applicability of the equipartition theorem by J. D. D. Martin. DOI: 10.1119/5.0146298
The equipartition theorem is such an important theorem in thermal physics that students may be led to think that it is always valid. However, this is not the case. Instead of deriving the equipartition theorem and then examining experimental data that corroborate it, this paper proposes to start from online available experimental data to examine the range of applicability of the theorem. Exploring deviations to the theorem may actually help students get a deeper understanding of it. Appropriate for undergraduate thermal physics classes as well as for introductory statistical mechanics.

Metastable states in a 1D quantum system by John Eric Goff; Don C. Colladay. DOI: 10.1119/5.0124407
Metastable states, that is, excited states that have a particularly long lifetime compared to other excited states, can be found in a simple 1D piecewise-constant potential problem. From the numerical solution to this problem, metastable states are compared to bound states, and some of their characteristics derived. The problem is also discussed using the scattering matrix technique. Appropriate for advanced quantum mechanics classes.

Numerical simulation of mirages above water bodies by Anna Horváth; Balázs Bámer; Gergely Gábor Barnaföldiv Am. J. Phys. 91, 999–1007 (2023) https://doi.org/10.1119/5.0111635
Who hasn't been fascinated by a mirage? This paper guides you through an understanding of mirages and shares scripts that students can use to model mirages that they have photographed. Suitable for projects in an optics or computational physics course. A video abstract accompanies the online version of this paper.


Pandemic modeling with the game of life by David Faux; Thesha Thavaraja; Alana Croucher. DOI: 10.1119/5.0166146
Computational models have been useful for recommending policies in the recent COVID-19 pandemic and are likely to be even more important in the future. The authors discuss how a qubit version of the Game of Life cellular automata can be used to model pandemics.


Molecular spectroscopy as a laboratory experiment: Measurement of important parameters of sodium diatomic molecules by Md Shakil Bin Kashem; Morgan Davies; Lok Pant; S. Burcin Bayram. DOI: 10.1119/5.0123126
While atomic spectroscopy is commonly part of an upper-level physics or chemistry laboratory course, molecular spectroscopy is rarer. However, this does not mean it cannot be included! This paper shows how to perform and interpret experiments measuring the spectrum of diatomic sodium molecules, allowing students to gain valuable experience that will help them understand research using light to probe quantum systems.

Using lock-in detection to build a barcode scanner by Riley E. Alexander; Maya M. DiFrischia; Margaret J. Doubman; Stefany Fabian Dubon; Lily Goltz; Yuqian Li; Rebecca A. Long; Genevieve Love; Nina Martinez Diers; Matangi Melpakkam; Catie Robinson; Elizabeth M. Tompkins; Avalon L. B. Vanis; Xinrui Wang; Mallory Yu; Sarah E. Spielman; Michael W. Noel. DOI: 10.1119/5.0151621
This article presents an instructional laboratory project in which students design and build an optical barcode scanner. A phase-sensitive detection system composed of low-cost discrete electronic and optical components is constructed and then used to acquire and decode the optical signal produced by scanning a UPC-A barcode. Through this work, students develop their understanding of lock-in detection, electronics, computer interfacing, and Python coding for data acquisition and analysis. This project will be of interest to instructors teaching electronics courses, upper-division instructional laboratories, or classes that incorporate experimental design at the beyond-introductory level.


Comment on the article “A note on Newton's shell-point equivalency theorem” [Am. J. Phys. 90, 394 (2022)] by Christian Carimalo. DOI: 10.1119/5.0153897
This Comment shares an alternate proof of the shell-point equivalency theorem, showing that equivalency occurs if and only if the potential is proportional to r-2 or r and relating this equivalency to the transmutation law of central forces.


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