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I describe the sequential development of an interactive Desmos visualization of Fermat&#39;s Principle of Least Time. Upon applying the principle by a manual search and by a Desmos calculation, we numerically verify Snell&#39;s Law of Refraction and the Law of Reflection. I feel this helps make this abstract physical concept more accessible to students. Along the way, I will share some Desmos tricks that I learned in the process of creating such visualizations.

AAPT WM 22

Using Desmos to Visualize Fermat&#39;s Principle of Least Time

desmos

optics

simulation

visualization

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The technical exchange is a two day event held online this year due to COVID-19. It will feature two days of oral presentations, demonstrations, and posters from leaders in AR/VR and other display technologies, including government briefings on active projects within the DOD. The technical exchange is unclassified and we welcome participation from the Navy, DoD as well as from industry and academia. 

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Heidi Buck,  Director @ BEMR Lab, Naval Information Warfare Center, Pacific

Lauren Burnette, BEMR Lab, Naval Information Warfare Center, Pacific


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Questions regarding sponsorship/registration contact:  ndiasd@sandiegositepros.com

Conference host POC is Tammy Sanchez (NDIA):  tamsanch@cisco.com

TEAR 3M 2021

I describe the sequential development of an interactive Desmos visualization of Fermat's Principle of Least Time. Upon applying the principle by a manual search and by a Desmos calculation, we numerically verify Snell's Law of Refraction and the Law of Reflection. I feel this helps make this abstract physical concept more accessible to students. Along the way, I will share some Desmos tricks that I learned in the process of creating such visualizations.

Using Desmos to Visualize Fermat's Principle of Least Time

poster

This meeting is a great opportunity to explore sessions and workshops designed with your professional development in mind. Present your research and exchange ideas on the latest in teaching and pedagogy. Participate in a wide range of events, activities, plenaries, and so much more, connecting you with peers and colleagues who share your commitment to excellence in physics education.

This talk describes a two-week module on astrodynamics developed for incoming STEM students. The goal of the module is for students to design and simulate a mission from Earth to Venus using the Hohmann transfer---a space maneuver used to travel between two planetary orbits. This application was selected because it utilizes a variety of introductory physics topics. The participants were all low-income, Pell-eligible college students; most were Black, Hispanic, and/or first-generation college students. This group is most at risk of leaving STEM, yet 80% of students who took this course were retained in STEM. In this talk we will present the course learning objectives, details of the Hohmann transfer simulation in VPython, and student outcomes including grades, retention rates, and survey results. This module could be replicated at the high school or college levels to help students achieve proficiency in programming while learning basic physics and astronomy content.

Summer Short Course on Astrodynamics for Incoming STEM Majors

Physics remains an area of STEM with lower amounts of diversity among the student population, therefore it becomes important to consider how classroom culture may contribute to a lack of belonging for students in underrepresented groups. This study aimed to determine how students in physics courses at Miami University perceived peer interactions in their courses during formal and informal group work. Virtual interviews were conducted with nine physics majors and responses were coded for positive and negative statements related to themes of respect, contribution, outcome of the task and overall class culture. It was found that on average male students had a higher percentage of positive statements about class culture, while female students had a higher percentage of positive statements about task outcomes and a higher percentage of negative statements about communication and class culture.

Perceived Effectiveness of Peer Interaction in Physics Courses

Most people likely think of learning the constellations of the night sky when they think of planetariums, but that’s not going to help you teach physics; It may not even really be astronomy, but more like sky geography; I think it’s important to teach astronomy and physics whenever possible, and planetariums can help with so much more than just constellations; Planetariums can do things that regular classrooms cannot do. This in-dome presentation will look at both specific and general ways that planetariums can help you teach physics and astronomy.

Planetarium Potentials

The STEP UP project (STEPUPphysics.org) was designed to reduce barriers for high school women in physics and encourage them to pursue an undergraduate physics degree, in which women have been underrepresented historically. STEP UP focuses on implementing high school interventions by recruiting high school physics teachers, called Advocates, who are trained to teach STEP UP’s research-driven materials in their classroom. To understand the effects of material implementation on Advocates, surveys are being administered to them before and after the school year. Using a “tempered radicals” framing, this talk will present an analysis of initial survey responses describing the characteristics of teachers who are willing to be disruptive in order to reduce barriers for women and change the physics classroom culture. Results will inform our understanding of teachers and the ways in which we can support their development as tempered radicals.

Identifying Tempered Radicals in the STEP UP Advocate Program

The 2021 Inclusive Curriculum in Physics Workshop Series is a three part series organized and led by the National Society of Black Physicists, the National Society of Hispanic Physicists, and the American Association of Physics Teachers. The series leverages the expertise of equity, diversity and inclusion (EDI) experts, as well as an organizing team of physics students, faculty and STEM professionals at different stages of their studies and careers.The purpose of the series is to: Explore the importance of EDI in the classroom and the existing instructional materials that focus on EDI, with members of the broad physics education community; Engage participants in discussion and action items around the current challenges to equity in STEM education with input from experts in the field; Provide support to working groups through a network of partners to engage in specific physics education projects using the lens of inclusion.

The 2021 Inclusive Curriculum in Physics Workshop Series

In Advanced Lab classes, students often perform labs on radioactivity and nuclear spectroscopy as well as labs measuring several fundamental constants. Advanced labs classes can pose a problem for smaller public institutions as these classes usually have low enrollments and having multiple traditional lab setups is costly. However, advances in digital electronics have enabled the development of low cost ($2000), easy to use nuclear spectroscopy systems that can provide multiple lab activities. In addition to the traditional radioactivity and shielding labs, these systems can also be used with exempt radioactive sources to provide other laboratory activities including measuring to around 5%: 1) the charge of an electron using x-ray fluorescence and 2) the mass of an electron using Compton scattering. This eliminates the need for additional laboratory equipment making such labs more accessible to both undergraduate institutions and high schools.

A Simple Nuclear Lab To Measure The Electron's Rest Mass

It is customary to introduce students to quantum mechanics with the Schrödinger equation because the single-component wave function is easy to handle mathematically. However, the Schrödinger equation is not consistent with special relativity, nor does it describe spin angular momentum. We propose that the Dirac equation provides a better introduction because (1) it is consistent with the laws of physics, (2) it describes spin angular momentum, and (3) it is easily derived from the classical physics model of an ideal elastic solid. The resultant description of classical wave mechanics shares many features of relativistic quantum mechanics. These include Lorentz invariance, bispinor wave functions, half-integer azimuthal quantum numbers, standing waves with circular wave propagation, particle classifications similar to fermions and bosons, operators for physical quantities including spin angular momentum, Pauli exclusion principle, and interaction via potentials. The Schrödinger equation approximates the evolution of a single wave function component.

Relativistic Wave Mechanics for Undergraduates

A free Gaussian can be thought of as the ground state of a simple harmonic oscillator with the frequency adjusted to give the initial variance of the Gaussian. The free Hamiltonian, when expressed in terms of the raising and lowering operators, can be thought of as a squeezing operator acting on the SHO ground state. We show how this mapping can be used to understand the increasing variance of the Gaussian as it evolves in time. In cases where time evolution is taught after the operator method solution of the SHO, then one can explain free expansion in this alternative framework. One can even perform the calculation using only operator manipulations, instead of solving the time-dependent Schroedinger equation. We sketch how this is done. It requires the Weyl form of the BCH formula, the Hadamard lemma, and the exponential disentangling identity. This work was an REU project.

Free expansion of a Gaussian via squeezed harmonic oscillator states

One advantage of using Open Education Resources is increased flexibility in pedagogical strategies. If learning materials are restricted to publisher-derived content, instructors are forced to model their teaching methodologies around those resources. Thus,instructors are unable to utilize alternative resources if they “compete” with publisher content or would overwhelm students. This is especially true with respect to institutions that standardize content across course sections, and any deviation is considered inappropriate. OER allows instructors at community colleges to tailor learning materials to the local demographics and state-wide observations. This project's OER laboratories will allow faculty to choose and customize their learning materials. Many of Chattanooga State's students are from traditionally underrepresented backgrounds (e.g. Pell-eligible, minority race, non-traditional/returning students, and academically underprepared), many introductory astronomy students will benefit from decreased course costs. This presentation is our flagship laboratory on Expansion of the Universe and utilizes coding, spectroscopy and mathematical methods.

Expansion of the Universe: an OER approach to Hubble's Constant

Geometric Optics labs are a staple of many undergraduate physics labs. A simple but effective optics bench was developed to distribute for at-home optics labs during Spring 2020 and Spring 2021. The materials for the lab included three 38mm lenses (one concave, two convex), a PVC coupling, play-doh, used holiday light bulbs, and a few other common household items. The total cost for each set-up was only $10 - $15, making this a great option when the cost of a full optics bench is not feasible. These at-home experiments were just as effective as in-person versions used in previous years. In this poster, a full description of the lab set-up is described.

Using Desmos to Visualize Fermat's Principle of Least Time

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Summer Short Course on Astrodynamics for Incoming STEM Majors

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