Pub Date : 2024-04-15DOI: 10.1088/1361-6404/ad3eef
T. Quick, Johannes Grebe-Ellis
Lens phenomena, such as caustics, image distortions, and the formation of multiple images, are commonly observed in various refracting geometries, including raindrops, drinking glasses, and transparent vases. In this study, we investigate the ball lens as a representative example to showcase the capabilities of Berry’s eye caustic as an optical tool. Unlike the conventional paraxial approximation, the eye caustic enables a comprehensive understanding of image transformations throughout the entire optical space. Through experimental exploration, we establish the relationship between the eye caustic and traditional light caustics. Furthermore, we provide mathematical expressions to describe both the caustic and the image transformations that occur when viewing objects through the ball lens. This approach could be of interest for optics education, as it addresses two fundamental challenges in image formation: overcoming the limitations of the paraxial approximation and recognizing the essential role of the observer in comprehending lens phenomena.
{"title":"The Eye Caustic of a Ball Lens","authors":"T. Quick, Johannes Grebe-Ellis","doi":"10.1088/1361-6404/ad3eef","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3eef","url":null,"abstract":"\u0000 Lens phenomena, such as caustics, image distortions, and the formation of multiple images, are commonly observed in various refracting geometries, including raindrops, drinking glasses, and transparent vases. In this study, we investigate the ball lens as a representative example to showcase the capabilities of Berry’s eye caustic as an optical tool. Unlike the conventional paraxial approximation, the eye caustic enables a comprehensive understanding of image transformations throughout the entire optical space. Through experimental exploration, we establish the relationship between the eye caustic and traditional light caustics. Furthermore, we provide mathematical expressions to describe both the caustic and the image transformations that occur when viewing objects through the ball lens. This approach could be of interest for optics education, as it addresses two fundamental challenges in image formation: overcoming the limitations of the paraxial approximation and recognizing the essential role of the observer in comprehending lens phenomena.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"4 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140700707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-15DOI: 10.1088/1361-6404/ad3eed
Christian Baumgarten
We report about some obvious and severe flaws in Shawn Carlson's paper titled ``Why not energy conservation'', published in the Eur. J. Phys. 37 (2016), 015801.
{"title":"Comments on “Why not energy conservation?” (Eur. J.Phys. 37, 2016, 015801)","authors":"Christian Baumgarten","doi":"10.1088/1361-6404/ad3eed","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3eed","url":null,"abstract":"\u0000 We report about some obvious and severe flaws in Shawn Carlson's paper titled ``Why not energy conservation'', published in the Eur. J. Phys. 37 (2016), 015801.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"43 34","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140701583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-15DOI: 10.1088/1361-6404/ad3ef0
Mark Denny
Two classical mechanical systems—block-and-tackle machines and nonlinear oscillators—exhibit renormalization of numerical parameters. A simple one-dimensional integral illustrates several other facets of renormalization (regularization, renormalization group, resummation). These examples provide insight for students and non-specialists into the workings of a subtle, complicated and historically misunderstood subject.
{"title":"Elementary examples of renormalization from mechanics and integral calculus","authors":"Mark Denny","doi":"10.1088/1361-6404/ad3ef0","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3ef0","url":null,"abstract":"\u0000 Two classical mechanical systems—block-and-tackle machines and nonlinear oscillators—exhibit renormalization of numerical parameters. A simple one-dimensional integral illustrates several other facets of renormalization (regularization, renormalization group, resummation). These examples provide insight for students and non-specialists into the workings of a subtle, complicated and historically misunderstood subject.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"17 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140700654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, with the aim of bridging the gap between cutting-edge research and the classroom, we present a situated learning proposal to integrate astronomical data and tools in the teaching of mathematics and physics. Our approach focuses on the construction of magnitude-color diagrams for two well-known star clusters, the Pleiades and 47 Tucanae, which are visible from the southern hemisphere, using virtual observatory-based applications Aladin and Topcat, using Simbad data specifically to separate data differences due to proper motion and/or reddening due to absorption by interstellar dust. To assess the feasibility of implementing these tools at school, we organized a workshop for science teachers that received a positive response. In addition, we also discuss the limitations and challenges that could hinder the effective application of these tools for educational purposes.
{"title":"Construction of color-magnitude diagrams using real astronomical data for teaching at school","authors":"Irma Fuentes Morales, Carla Hernández, Fernanda Alarcon, Ignacia Benito, Rubén Montecinos","doi":"10.1088/1361-6404/ad3d44","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3d44","url":null,"abstract":"\u0000 In this paper, with the aim of bridging the gap between cutting-edge research and the classroom, we present a situated learning proposal to integrate astronomical data and tools in the teaching of mathematics and physics. Our approach focuses on the construction of magnitude-color diagrams for two well-known star clusters, the Pleiades and 47 Tucanae, which are visible from the southern hemisphere, using virtual observatory-based applications Aladin and Topcat, using Simbad data specifically to separate data differences due to proper motion and/or reddening due to absorption by interstellar dust. To assess the feasibility of implementing these tools at school, we organized a workshop for science teachers that received a positive response. In addition, we also discuss the limitations and challenges that could hinder the effective application of these tools for educational purposes.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140717925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1088/1361-6404/ad3d42
X. Prado, Angel Paredes Galan, Iván Area, Jose Manuel Domínguez Castiñeiras, Jorge Mira
Throughout history, scales have served as instrumental tools for quantifying the weight of objects, relying on a comparative assessment against a specified reference weight. Scales featuring uneven arms, such as the bismar scale, have proven particularly adept at gauging masses within a specific range relative to a predetermined reference mass. On the other hand, the kinematics of elastic collisions hinge on the inertial masses of the colliding entities. By observing the aftermath of a collision between a known reference mass and an object of unknown mass, one can deduce the latter’s mass. In this contribution, we highlight a fascinating and clear analogy between these two methodologies. We do so by adapting a geometric approach, initially applicable to the bismar scale, to both non-relativistic and relativistic elastic collisions, encompassing phenomena such as Compton scattering.
{"title":"The bismar scale and elastic collisions: a geometrical analogy","authors":"X. Prado, Angel Paredes Galan, Iván Area, Jose Manuel Domínguez Castiñeiras, Jorge Mira","doi":"10.1088/1361-6404/ad3d42","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3d42","url":null,"abstract":"\u0000 Throughout history, scales have served as instrumental tools for quantifying the weight of objects, relying on a comparative assessment against a specified reference weight. Scales featuring uneven arms, such as the bismar scale, have proven particularly adept at gauging masses within a specific range relative to a predetermined reference mass. On the other hand, the kinematics of elastic collisions hinge on the inertial masses of the colliding entities. By observing the aftermath of a collision between a known reference mass and an object of unknown mass, one can deduce the latter’s mass. In this contribution, we highlight a fascinating and clear analogy between these two methodologies. We do so by adapting a geometric approach, initially applicable to the bismar scale, to both non-relativistic and relativistic elastic collisions, encompassing phenomena such as Compton scattering.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"661 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140719240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1088/1361-6404/ad3d43
Jagoba Barata, M. Illarramendi, J. Grandes, J. Zubía, E. Arrospide
In this work we develop an experiment wherein the variation of the fringe visibilities with wavelength provides insights into the geometry of various stellar sources or components. The experiment is based on the Michelson stellar interferometer in which a filter wheel has been inserted between a detecting camera and a telescope obscured by a double aperture lid. The spatial and temporal incoherent light emitting from stellar sources has been simulated using polymer optical fibres and a broadband LED. By measuring the visibilities of the central fringe at different wavelengths we are able to determine the morphology of the analysed light sources, provided that the baseline used is sufficiently long. The experiment is suitable for postgraduate students seeking to delve deeper into light coherence theory and to gain practical experience in optical stellar interferometry.
{"title":"Stellar interferometer experiment by measuring visibilities at different wavelengths","authors":"Jagoba Barata, M. Illarramendi, J. Grandes, J. Zubía, E. Arrospide","doi":"10.1088/1361-6404/ad3d43","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3d43","url":null,"abstract":"\u0000 In this work we develop an experiment wherein the variation of the fringe visibilities with wavelength provides insights into the geometry of various stellar sources or components. The experiment is based on the Michelson stellar interferometer in which a filter wheel has been inserted between a detecting camera and a telescope obscured by a double aperture lid. The spatial and temporal incoherent light emitting from stellar sources has been simulated using polymer optical fibres and a broadband LED. By measuring the visibilities of the central fringe at different wavelengths we are able to determine the morphology of the analysed light sources, provided that the baseline used is sufficiently long. The experiment is suitable for postgraduate students seeking to delve deeper into light coherence theory and to gain practical experience in optical stellar interferometry.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140717793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-09DOI: 10.1088/1361-6404/ad3c80
P. D. S. de Lima, Joao M de Araujo, Mauro S Ferreira
Inverse problems in science normally involve the challenge of obtaining from a set of observations the causal factors that generated them in the first place. However, physics students are seldom exposed to such problems as part of their training. Here we revisit the mechanics problem of finding the shape of a hanging cable, but this time in reverse, {it i.e.}, by asking what mass density a cable must have to follow a specific shape. This concept is then generalised into the possibility of identifying a cable whose hanging shape follows any form we wish to design. This inverted design strategy is experimentally verified with an inexpensive setup that is suitable for classroom activities.
{"title":"Inverse Design from the Catenary Problem","authors":"P. D. S. de Lima, Joao M de Araujo, Mauro S Ferreira","doi":"10.1088/1361-6404/ad3c80","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3c80","url":null,"abstract":"\u0000 Inverse problems in science normally involve the challenge of obtaining from a set of observations the causal factors that generated them in the first place. However, physics students are seldom exposed to such problems as part of their training. Here we revisit the mechanics problem of finding the shape of a hanging cable, but this time in reverse, {it i.e.}, by asking what mass density a cable must have to follow a specific shape. This concept is then generalised into the possibility of identifying a cable whose hanging shape follows any form we wish to design. This inverted design strategy is experimentally verified with an inexpensive setup that is suitable for classroom activities.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"31 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140723601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-09DOI: 10.1088/1361-6404/ad3ca3
J. Pantaleone
When a book closes, the air between the approaching surfaces is accelerated and ejected through the open sides at large speeds. The air resists this motion, and so a reaction forces acts on the closing book. To study this force, an idealized book is placed on rollers so it is free to move horizontally. The speed gained by the book is measured for different initial opening angles and for different book lengths. The dependence on these parameters is found to be surprisingly simple, and the extrapolation to plates of infinite length agrees well with a simple model. This system is interesting because it is relatively easy to build, measure, and model, and also because colliding surfaces in a fluid are an everyday occurrence. This system can be used as either a classroom demonstration or a laboratory experiment.
{"title":"Jet propulsion from a closing book","authors":"J. Pantaleone","doi":"10.1088/1361-6404/ad3ca3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3ca3","url":null,"abstract":"\u0000 When a book closes, the air between the approaching surfaces is accelerated and ejected through the open sides at large speeds. The air resists this motion, and so a reaction forces acts on the closing book. To study this force, an idealized book is placed on rollers so it is free to move horizontally. The speed gained by the book is measured for different initial opening angles and for different book lengths. The dependence on these parameters is found to be surprisingly simple, and the extrapolation to plates of infinite length agrees well with a simple model. This system is interesting because it is relatively easy to build, measure, and model, and also because colliding surfaces in a fluid are an everyday occurrence. This system can be used as either a classroom demonstration or a laboratory experiment.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"109 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140723992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-02DOI: 10.1088/1361-6404/ad3999
Yue Yin, Jiabin Liu, Xi Ye, Wei Pan
Traditional physics laboratory adopted photogate and polarized light to measure the rotation motion in a fixed system, but they are not applicable to the rolling objects. Computer vision has played increasing important role in image analysis. The popularization of mobile-phones, cameras, and computers makes it possible to measure the rotation of an object in a simple but nonintrusive way in physics lab. "Tracker" has been used to analyze the rotation motion of large object, such as vehicle wheels, through recognizing the position of marker. However, it is still challenging to precise recognize the marker in small object via simple algorithms in physics lab. In this paper, we introduced a facile image processing technique to visualize the rotation and spin motion of spheres through marking it with two red- and green- semi-spheres. The basic formula of projection was derived to analyze the expression of spin angles with projection area of semisphere. The precision and suitability of the image processing technique was proved to be effective through comparison with the photogate-measure technique. The image processing technique has also been used to analyze the rotation and spin motion of two spheres bonded with rubber band. It provides not only the trajectory of sphere centers, but the evolution of spin angle, orbit diameter and orbit angle of spheres. By analyzing the relationship between spin angles and orbit diameter, it is clear that the rubber band experienced typical transformations between three different phases, twist, helix and superhelix, until the energy was exhausted. The method offers valuable insights into rotational dynamics, showcasing its potential for practical applications in physics lab and educational contexts.
{"title":"Visualizing the rolling motion of spheres connected with rubber band by imaging processing technique","authors":"Yue Yin, Jiabin Liu, Xi Ye, Wei Pan","doi":"10.1088/1361-6404/ad3999","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3999","url":null,"abstract":"\u0000 Traditional physics laboratory adopted photogate and polarized light to measure the rotation motion in a fixed system, but they are not applicable to the rolling objects. Computer vision has played increasing important role in image analysis. The popularization of mobile-phones, cameras, and computers makes it possible to measure the rotation of an object in a simple but nonintrusive way in physics lab. \"Tracker\" has been used to analyze the rotation motion of large object, such as vehicle wheels, through recognizing the position of marker. However, it is still challenging to precise recognize the marker in small object via simple algorithms in physics lab. In this paper, we introduced a facile image processing technique to visualize the rotation and spin motion of spheres through marking it with two red- and green- semi-spheres. The basic formula of projection was derived to analyze the expression of spin angles with projection area of semisphere. The precision and suitability of the image processing technique was proved to be effective through comparison with the photogate-measure technique. The image processing technique has also been used to analyze the rotation and spin motion of two spheres bonded with rubber band. It provides not only the trajectory of sphere centers, but the evolution of spin angle, orbit diameter and orbit angle of spheres. By analyzing the relationship between spin angles and orbit diameter, it is clear that the rubber band experienced typical transformations between three different phases, twist, helix and superhelix, until the energy was exhausted. The method offers valuable insights into rotational dynamics, showcasing its potential for practical applications in physics lab and educational contexts.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"23 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140753661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-02DOI: 10.1088/1361-6404/ad39bb
Jaroslav Franek, M. Šoka
The work is devoted to the calculation of the self-inductance of the Möbius strip (MS), assuming that a self-contained surface current flows on its surface. Subsequently, the vector potential corresponding to this situation is expressed in cases where: a) the surface current is constant b) the surface current is inversely proportional to the length of the line along which it flows. The self-inductance of the MS is determined by the integration of the vector potential. From the derived relations, the inductance of the MS is determined by computer simulation at different values of the ratio of width and radius of the MS. The reference value to the results for MS is the calculated and shown inductance of the cylindrical surface with a surface current flowing around the circumference of its shell. In conclusion, simple relations are derived that enable quick calculation of the inductances of both the MS and the cylindrical surface from their geometrical parameters. The article is intended for students of mathematical-physical and technical faculties as well as for graduates of these faculties dealing with the issue of (meta)materials.
这项研究致力于计算莫比乌斯带（Möbius strip，MS）的自感应强度，假定在其表面有自带的表面电流流动。随后，在以下情况下表达了与这种情况相对应的矢量电势：a) 表面电流恒定 b) 表面电流与沿其流动的线的长度成反比。MS 的自电感由矢量电势的积分决定。根据推导出的关系，在 MS 宽度和半径比值不同的情况下，通过计算机模拟确定 MS 的电感。MS 结果的参考值是圆柱表面的计算和显示电感值，表面电流围绕其外壳圆周流动。总之，本文推导出了简单的关系，可以根据 MS 和圆柱表面的几何参数快速计算出它们的电感值。这篇文章面向数学物理和技术专业的学生，以及这些专业中研究（元）材料问题的毕业生。
{"title":"On the inductance of a Möbius strip","authors":"Jaroslav Franek, M. Šoka","doi":"10.1088/1361-6404/ad39bb","DOIUrl":"https://doi.org/10.1088/1361-6404/ad39bb","url":null,"abstract":"\u0000 The work is devoted to the calculation of the self-inductance of the Möbius strip (MS), assuming that a self-contained surface current flows on its surface. Subsequently, the vector potential corresponding to this situation is expressed in cases where: a) the surface current is constant b) the surface current is inversely proportional to the length of the line along which it flows. The self-inductance of the MS is determined by the integration of the vector potential. From the derived relations, the inductance of the MS is determined by computer simulation at different values of the ratio of width and radius of the MS. The reference value to the results for MS is the calculated and shown inductance of the cylindrical surface with a surface current flowing around the circumference of its shell. In conclusion, simple relations are derived that enable quick calculation of the inductances of both the MS and the cylindrical surface from their geometrical parameters. The article is intended for students of mathematical-physical and technical faculties as well as for graduates of these faculties dealing with the issue of (meta)materials.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"100 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140754413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：