**June 2022 Issue,**

**Volume 90, No. 6**

Optical measurements on a budget: A 3D-printed ellipsometer

Ellipsometry is an optical technique that uses light polarization to measure the physical properties of dielectric thin films. Such films are critical for integrated circuitry and optical coatings. Commercial ellipsometers, however, are too expensive to be included in student laboratories. In this article, the author describes a homemade, 3D-printed instrument that can be constructed inexpensively and is capable of measuring film thickness and index of refraction with accuracy comparable to commercial instrumentation. An EXCEL analysis program to extract film thickness and index of refraction from optical measurements is included in the supplementary materials, as are extensive construction details and files for 3D-printing. If you are interested in exposing your students to this important technique, this article will give you the tools to get started.

#### EDITORIAL

In this issue: June 2022 by Joseph C. Amato, Harvey Gould, Claire A. Marrache-Kikuchi, Beth Parks, B. Cameron Reed and Jan Tobochnik. DOI: 10.1119/5.0096677

#### LETTERS TO THE EDITOR

Comment on “Bouncing on a slope” [Am. J. Phys. 89, 143–146 (2021)] by Rod Cross. DOI: 10.1119/5.0096138

Response to Rod Cross's letter. DOI: 10.1119/5.0096573

Breakdown of a misinterpretation of Noether's theorem by Kirk T. McDonald. DOI: 10.1119/5.0097101

Talking 'bout misinterpretation by Nivaldo A. Lemos. DOI: 10.1119/5.0097179

#### PAPERS

Gravitoelectromagnetism: Removing action-at-a-distance in teaching physics by Friedrich Herrmann and Michael Pohlig. DOI: 10.1119/10.0009888

Unless one invokes general relativity, gravitation is still taught mostly in its Newtonian action-at-a-distance formulation. Little attention is paid to how the energy exchanges within a system of moving particles such as a mass being lifted in Earth’s gravitational field actually take place. A theory that avoids such issues, gravito-electromagnetism, was developed by Oliver Heaviside in 1893. Heaviside’s theory was analogous to Maxwell’s equations and the Poynting flux theorem, but it was not widely adopted because many of the effects it describes are small and the later emergence of general relativity seemed to make such a theory of gravitation unnecessary. This paper describes Heaviside’s theory and explores its application to some simple examples. Particularly interesting is the emergence of a gravitational “Lorentz force” analogous to the attractive or repulsive forces between parallel electrical currents. Appropriate for teaching upper-level students who are familiar with Maxwell’s equations.

How energy is conserved in Newtonian gravity by Vytenis M. Vasyliūnas. DOI: 10.1119/10.0009889

This paper points out that even within the purely classical theory of gravitation, in which gravitational fields and potentials change instantaneously throughout space, there are still many interesting questions concerning how energy is stored locally in fields and configurations. Making analogies with electromagnetic fields, the author presents three different forms for this energy. Students who are familiar with intermediate-level electromagnetism can be shown how to apply the tools and modes of thinking that were developed in electromagnetism in order to gain new insights into the subtleties of gravitational energy that they may have overlooked in an initial presentation of mechanics.

On the linearity of the generalized Lorentz transformation by Frank Verheest. DOI: 10.1119/10.0010234

Deriving the Lorentz transformations without assuming an invariant speed of light normally requires a fairly involved step showing that the transformations are linear with respect to time and space. This paper presents a simple demonstration of linearity based on velocity transformations.

Measuring the Hannay geometric phase by H. Fanchiotti, C. A. García Canal, M. Mayosky, A. Veiga and V. Vento. DOI: 10.1119/5.0081149

The Hannay phase is the geometric phase that is familiar to physicists as the latitude-dependent rotation rate of the plane of oscillation of a Foucault pendulum. While not all universities have a Foucault pendulum available for students to observe, they can all give students the opportunity to learn about the Hannay phase by building a simple circuit, as described in this paper, that is governed by exactly the same differential equation.

Modelling the Earth's magnetic field Video Abstract Icon by Nuno Barros e Sá, Lourenço Faria, Bernardo Alves and Miguel Cymbron. DOI: 10.1119/5.0074846

Why restrict your labworks to the usual laboratories and benches, when you can use the International Space Station as an extension of your workshop? This paper proposes to do just that: ask an astronaut to record the magnetic field on board the ISS as it orbits a few times around the Earth, and, from these measurements, retrieve the multipolar expansion of the Earth’s magnetic field. This requires a few tricks, including a few frame transformations, but the results are surprisingly precise. The same experiment could be adapted to ground measurements. It is appropriate for undergraduate electromagnetism labs or for a student project, and it will also encourage students to develop their programming skills.

Optical measurements on a budget: A 3D-printed ellipsometer by Matthew Mantia and Teresa Bixby. DOI: 10.1119/10.0009665

Ellipsometry is an optical technique that uses light polarization to measure the physical properties of dielectric thin films. Such films are critical for integrated circuitry and optical coatings. Commercial ellipsometers, however, are too expensive to be included in student laboratories. In this article, the author describes a homemade, 3D-printed instrument that can be constructed inexpensively and is capable of measuring film thickness and index of refraction with accuracy comparable to commercial instrumentation. An EXCEL analysis program to extract film thickness and index of refraction from optical measurements is included in the supplementary materials, as are extensive construction details and files for 3D-printing. If you are interested in exposing your students to this important technique, this article will give you the tools to get started.

Bringing three-dimensional learning to undergraduate physics: Insight from an introductory physics laboratory course by Jason M. May, Claudia De Grandi, Jordan M. Gerton, Lauren Barth-Cohen, Adam Beehler and Brianna Montoya. DOI: 10.1119/10.0009715

The National Research Council defined three dimensions of science learning—scientific concepts, experimental practices, and reasoning tools—as goals for K-12 science instruction. This paper shows how these goals can be extended into the university teaching laboratory, giving an example of their implementation in a life sciences laboratory course.

#### COMPUTATIONAL PHYSICS

Introducing simple models of social systems by Pablo Jensen. DOI: 10.1119/5.0086028

The author discusses the agent-based Schelling model of housing segregation originally proposed in the 1960s. The model shows that, even if everyone individually favors a mixed neighborhood, segregation can occur, nevertheless. A statistical mechanics derivation of the results, and the pros and cons of using physics motivated models to learn about social systems, are also discussed.

Voronoi cell analysis: The shapes of particle systems by Emanuel A. Lazar, Jiayin Lu and Chris H. Rycroft. DOI: 10.1119/5.0087591

Given the positions of many particles in space, the Voronoi cell of each particle is the region of space closer to it than to any other particle. The authors describe how the Voronoi cells are constructed and the many physical applications of this construction.

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