Sameen Ahmed Khan

Sameen Ahmed Khan
Dhofar University · Department of Mathematics and Sciences

PhD

About

227
Publications
599,475
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
833
Citations
Introduction
I have over sixteen years of College/University teaching experience in Oman, both Physics and Mathematics. Physics courses taught:: Physics-1 for Engineering, Physics-2 for Engineering, Physics, Engineering Mechanics and Engineering Physics. Besides, I have been involved in establishing the physics laboratories. Mathematics courses taught: Foundation Mathematics, Statistics, College Mathematics, Calculus with Numerical Methods, Advanced Calculus and Engineering Mathematics
Additional affiliations
September 2015 - present
Dhofar University
Position
  • Professor (Associate)
Description
  • https://orcid.org/0000-0003-1264-2302
May 2006 - March 2015
Salalah College of Technology
Position
  • Professor (Assistant)
Description
  • Courses Taught: Physics-1 for Engineering and Physics-2 for Engineering. Setting up the two Physics Laboratories. Academic Advising of Students. Served on thirteen College Committees.
May 2006 - January 2015
Salalah College of Technology
Position
  • Professor (Assistant)
Description
  • Courses Taught: Physics-1 for Engineering and Physics-2 for Engineering. Setting up the two Physics Laboratories. Academic Advising of Students.
Education
September 1991 - September 1997
Institute of Mathematical Sciences
Field of study
  • Mathematical Physics
July 1988 - December 1990

Publications

Publications (227)
Article
A unified formalism of light beam optics and light polarization is presented. The starting point of our formalism is an exact eight-dimensional matrix-representation of Maxwell's equations in an inhomogeneous medium, which is presented in detail. The beam-optical Hamiltonians are derived without any specifications on the varying refractive index. T...
Article
It is well-known that the Helmholtz equation describing scalar optics has a striking mathematical similarity with the Klein-Gordon equation of relativistic quantum mechanics. Exploiting this similarity, quantum methodologies are applied to the Helmholtz equation leading to a new formalism of scalar optics. Paraxial and aberrating Hamiltonians are d...
Article
Summary of one of the thirty papers selected under the theme, Optics in 2016, highlighting the most exciting peer-reviewed optics research to have emerged over the past 12 months. http://www.osa-opn.org/home/articles/volume_27/december_2016/features/optics_in_2016/
Article
Hamilton's optical-mechanical analogy between the trajectory of material particles in potential fields and the path of light rays in media with continuously variable refractive index played an important role in the development of Schrödinger's wave mechanics. We shall examine how the Hamilton's analogy between charged-particle beam optics and light...
Article
The way to generalize scalar to wave optics, thus including polarization in the treatment consistent with the Maxwell equations was shown by Mukunda, Simon and Sudarshan for paraxial systems, based on a group theoretical analysis. Here, the Mukunda–Simon–Sudarshan (MSS) theory for the passage from scalar to vector optics is derived by casting the b...
Article
The Norwegian Academy of Science and Letters in Oslo, Norway has awarded the Abel Prize for 2022 to Dennis Parnell Sullivan, USA. He holds the Albert Einstein Chair at the City University of New York Graduate Center, New York, USA and is a distinguished professor at Stony Brook University, Stony Brook, Long Island, New York, USA. The prize has a ca...
Article
The integrals $\int x^n e^{-x}\,dx$, $\int x^n e^x\,dx$, $\int x^n \sinh{x}\,dx$, and $\int x^n \sin{x}\,dx$ are seen to give rise to sets of Appell polynomials with the exponential generating functions $e^{xt}/(1 - t)$, $e^{xt}/(1 + t)$, $e^{xt}/\left( 1 - t^2 \right)$, and $e^{xt}/\left( 1 + t^2 \right)$, respectively, and these are special cases...
Article
We shall discuss the technique of the tabular integration by parts in detail with solved examples. The technique is used to derive the integral representation of the remainder in the Taylor expansion and the Laplace transform of the n-th derivative of a function. https://www.ias.ac.in/article/fulltext/reso/027/06/1049-1060 The Movie Clip from...
Data
The Movie Clip from the 1988 Movie, Stand and Deliver for the Article: https://www.researchgate.net/publication/361253523_Tabular_Integration_by_Parts
Preprint
Full-text available
An eight-dimensional matrix representation of the Maxwell equations for a linear inhomogeneous medium has been obtained earlier based on the Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A new eight-dimensional matrix representation, related to the earlier one by a similarity transformation, is derived starting ab in...
Article
Full-text available
Oman is located within Arid and Semi-Arid regions, where water resources are very scarce. The national average rainfall is just 80-100 mm per year. With high temperatures (30 ºC to above 40 ºC) the evaporation is also high. Therefore, it is absolutely necessary to conserve and recycle water in Oman. The study aims to identify ablution water (the ri...
Article
Full-text available
Publishing and presenting research findings are an integral part of the research. With a rapid growth in the number of journals and conferences, the task of finding the right choice has become difficult. In this article, we shall elaborate on the considerations for choosing the suitable journal publishers and conferences.
Article
The 2022 King Faisal International Prize for Medicine (Topic: Gene Editing Technologies) is awarded to David Ruchien Liu. The Science prize in the field of mathematics is awarded to Nader Masmoudi (for mathematical theory of fluid dynamics) and Martin Hairer for the theory of stochastic partial differential equations. https://www.currentscience.a...
Article
The 2021 UNESCO Sultan Qaboos Prize for Environmental Conservation has been jointly awarded to the Forest Research Institute Malaysia (FRIM), Malaysia and to the University for International Cooperation (UCI), Costa Rica. The Prize is awarded in alternate years. https://www.currentscience.ac.in/Volumes/122/04/0372.pdf
Article
The Division of Plasma Physics (DPP) under Association of Asia Pacific Physical Societies (AAPPS) has selected Taik Soo Hahm (Seoul National University, Seoul, Korea) as the 2021 Laureate of Subrahmanyan Chandrasekhar Prize of Plasma Physics. Plasma Innovation Prize is awarded to Anthony (Tony) Bruce Murphy. Both the prizes are awarded annually. Th...
Technical Report
As a result of countless efforts invested by the Dhofar University in encouraging researchers to indulge in impactful research to serve the community and to achieve the research vision and mission, two faculty members from the university have been selected among the top 2 per cent of scientists in the world by Stanford for the year 2021. They are...
Article
Full-text available
The world-wide energy demand is continuously increasing compounded with global warming. There is an ever-increasing demand in energy accompanied with depletion of fuel stocks, particularly the fossil fuels. The current energy consumption rates are unsustainable and thus have prompted for an active exploration and use of renewable energy sources. In...
Article
Full-text available
The main aim of this article is to start with an expository introduction to the trigonometric ratios and then proceed to the latest results in the field. Historically, the exact ratios were obtained using geometric constructions. The geometric methods have their own limitations arising from certain theorems. In view of the certain limitations o...
Conference Paper
A formalism of light beam optics including polarization is presented based on an exact matrix-representation of Maxwell’s equations, using quantum methodologies. The paraxial limit of the formalism explains the experimentally observed cross-polarization in laser beams.
Article
Mathematician László Lovász and the World Science Forum https://www.ams.org/journals/notices/202109/rnoti-p1453.pdf
Article
The Norwegian Academy of Science and Letters in Oslo, Norway has awarded the Abel Prize for 2021 to László Lovász, Hungary and Avi Wigderson, USA. The prize has a cash award of 7.5 million Norwegian kroner (USD 870,000). In the 1970s, when Wigderson and Lovász commenced their careers, theoretical computer science and pure mathematics were almost en...
Article
An introduction to the irrational numbers is done through the use of basic trigonometry, generally taught in the pre-university courses. The irrational sets of trigonometric ratios of rational angles are discussed in detail along with two major theorems and their proofs. Algebraic numbers along with the transcendental numbers are also covered....
Article
The 2021 King Faisal International Prize for Medicine (Topic: Regenerative Medicine in Neurological Conditions) is awarded to Stephen Mark Strittmatter and Robin James Milroy Franklin. The Science prize in the field of physics is awarded to Stuart Stephen Papworth Parkin for spintronic materials.
Article
Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy-Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law models for the axial magnetic field B(z) are studied. Paraxial quantum propagator for the Glaser model lens is obt...
Article
The Division of Plasma Physics (DPP) under Association of Asia Pacific Physical Societies (AAPPS) has selected Hyeon Keo Park (Korea) as the 2020 Laureate of Subrahmanyan Chandrasekhar Prize of Plasma Physics. Plasma Innovation Prize is awarded to Masaru Hori. Both the prizes are awarded annually. https://www.currentscience.ac.in/Volumes/119/09/14...
Article
Obtaining exact expressions for the trigonometric ratios is as old as the subject of trigonometry itself. In this article, we shall state the results from geometric methods. Tables of exact trigonometric ratios are presented and the patterns in them are illustrated. The power and limitations of the geometric methods for deriving the exact values...
Conference Paper
It is possible to apply quantum methodologies to the matrix-representation of Maxwell’s equations. This results in a unified formalism of light beam optics and light polarization, accompanied with wavelength-dependent contributions. https://doi.org/10.1364/FIO.2020.JTu1B.39
Chapter
Singapore has made rapid progress in industrial and sustainable development. This would not have been possible without government patronage for science and research. The government agencies responsible for science funding and research policy have played a crucial role in the scientific growth of the nation. Singapore has several premier institu...
Article
Ferenc Krausz and Paul Bruce Corkum and the Origins of Attosecond Physics https://science.sciencemag.org/content/369/6506/974/tab-e-letters
Article
Science in Latin America, https://science.sciencemag.org/content/369/6505/753/tab-e-letters
Article
Full-text available
The Tsallis q-exponential function \(e_{q}(x) = (1+(1-q)x)^{\frac {1}{1-q}}\) is found to be associated with the deformed oscillator defined by the relations \(\left [N,a^{\dagger }\right ] = a^{\dagger }\), [N,a] = −a, and \(\left [a,a^{\dagger }\right ] = \phi _{T}(N+1)-\phi _{T}(N)\), with ϕT(N) = N/(1 + (q − 1)(N − 1)). In a Bargmann-like repre...
Article
ATREE: Ashoka Trust for Research in Ecology and the Environment, https://science.sciencemag.org/content/369/6503/515.1/tab-e-letters
Article
Thymus Gland from a Vestigial Organ to the Focus of Immunotherapy, https://science.sciencemag.org/content/369/6503/eaba2429/tab-e-letters
Article
UNSCEAR and the Prohibition of Nuclear Weapon Testing in the Atmosphere, https://science.sciencemag.org/content/369/6502/350/tab-e-letters
Article
United Nations Scientific Committee on the Effects of Atomic Radiation, https://science.sciencemag.org/content/369/6502/361/tab-e-letters
Article
Need to replicate the European Synchrotron Research Facility in the African Continent https://science.sciencemag.org/content/369/6501/234/tab-e-letters
Article
UAE Mars Mission https://science.sciencemag.org/content/369/6500/127/tab-e-letters
Article
The 2019 UNESCO Sultan Qaboos Prize for Environmental Preservation has been awarded to the Bengaluru-based Ashoka Trust for Research in Ecology and the Environment (ATREE). This is in recognition of its socially just environmental conservation and sustainable development activities. The prize is awarded every two years, and consists of a diploma, a...
Article
Impact of COVID-19 on Cancer Patients, https://science.sciencemag.org/content/368/6497/1290/tab-e-letters
Article
COVID-19 Vaccine Trials in the African Continent https://science.sciencemag.org/content/368/6494/919/tab-e-letters
Article
T-Cells and Immunotherapy in the Context of COVID-19 https://science.sciencemag.org/content/368/6493/809/tab-e-letters
Article
Noninvasive Prenatal Testing and the Contributions of Yuk Ming Dennis Lo https://science.sciencemag.org/content/368/6491/598/tab-e-letter
Article
Tree Planting Exercise of Singapore https://science.sciencemag.org/content/368/6491/580/tab-e-letters
Article
We address the question of expressing the sums of the powers of polygonal numbers in closed forms using some basic functions. We obtain explicit expressions for the closed form expressions for the sums of the squares of reciprocals of polygonal numbers, the sums of the cubes of reciprocals of polygonal numbers the sums of the fourth-powers of recip...
Article
Jordan and the Arab Women in Science https://www.science.org/do/10.1126/comment.742709/full/ https://science.sciencemag.org/content/368/6487/113/tab-e-letters
Article
The last two decades were marked with repeated occurrences of the epidemic worldwide and Oman was affected by the same in more than one way [1]. The same two decades were also marked with phenomenal growth in Information Technologies (IT) and the Internet [2]. Information Technologies have been extensively utilized during the epidemics. For instanc...
Article
The 2020 King Faisal International Prize for Medicine (Topic: Haemoglobinopathies) is awarded to Stuart Holland Orkin (Harvard, Boston, USA) for his contributions to the understanding of the function of the blood system, the control of stem cells and the molecular basis of inherited blood disorders. The Science prize in the field of biology is awar...
Article
Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between two transverse planes at different points on the curved optic axis of the system is derived starting with the n...
Chapter
Many problems in calculus cannot be solved analytically and numerical methods play a significant role in such situations. Numerical calculus provides accurate solutions to a desired degree of accuracy. Numerical calculus using ordinary scientific calculators is cumbersome and prone to errors. The commonly available Microsoft Excel spreadsheets of...
Article
The Division of Plasma Physics (DPP) under Association of Asia Pacific Physical Societies (AAPPS) has selected Liu Chen and Kazunari Shibata as the 2019 Laureates of Subrahmanyan Chandrasekhar Prize of Plasma Physics. Plasma Innovation Prize is awarded to Roderick William Boswell. Both the prizes are awarded annually. https://www.currentscience.a...
Article
Triple Helix Structure of Collagen, https://science.sciencemag.org/content/366/6461/43/tab-e-letters
Article
Fifty million persons speak Urdu accounting for over four percent of the Indian population. In 1994, Mohammad Aslam Parvaiz a botanist by training started the Urdu Science Mahnamah’ (Urdu Science Monthly, http://urduscience.org/), which has a record of uninterrupted publication. The other Urdu science magazine with such a feat is the ‘Science-ki-Du...
Article
In 2001, the team of Krausz was the first to generate and measure the attosecond light pulse and make use of it for capturing electrons’ motion inside atoms, marking the birth of attophysics [1-2]. This enabled them to trace the movements of electrons on a subatomic scale in real time. Using this window, Krausz and collaborators became the first ob...
Article
Physics in Mexico https://science.sciencemag.org/content/365/6451/301/tab-e-letters https://science.sciencemag.org/content/365/6451/305/tab-e-letters
Book
Quantum Mechanics of Charged Particle Beam Optics in Devices from Electron Microscopes to Particle Accelerators Classical Charged Particle Beam Optics used in the design and operation of all present-day charged particle beam devices, from low energy electron microscopes to high energy particle accelerators, is entirely based on classical mechanic...
Chapter
This chapter reviews quantum mechanics required to pursue the quantum charged particle beam optics, the central theme of this book. All physical phenomena are quantum mechanical at the fundamental level. Classical mechanics observed in the macroscopic world is an approximation. That is why it raises a curiosity when classical mechanics is found to...
Chapter
This chapter provides a basic introduction to classical charged particle beam optics before proceeding to the development of quantum charged particle beam optics in later chapters. Charged particle beam optics is the study of transport of charged particle beams through electromagnetic optical systems. Such systems, like different types of electroma...
Chapter
This Chapter develops the scalar quantum charged particle beam optics, applicable to spin-$0$ and spinless particles ({\em i.e.}, particles for which the spin is ignored), based on the relativistic Klein-Gordon equation and the nonrelativistic Schr\"{o}dinger equation. Normal magnetic quadrupole which focuses and defocuses the charged particle beam...
Chapter
This chapter points to the synergy between optics and mechanics citing the relevant example of the early days of electron optics when the analogy with light optics provided much guidance. The inspiration for the spinor theory of charged particle beam optics also came from the studies on the optics of polarized light! It is recalled that the formali...
Chapter
This chapter provides the essential concepts of classical mechanics required for understanding the classical charged particle beam optics. All charged particle beam devices, from low energy electron microscopes to high energy particle accelerators, are designed and operated very successfully on the basis of classical mechanics though the beams prop...
Chapter
This chapter considers the quantum charged particle beam optics for spin-$\frac{1}{2}$ particles. For electrons, or for any spin-$\frac{1}{2}$ particle, the proper equation to be the basis for the theory of quantum beam optics is the Dirac equation. This chapter presents a general formalism of spinor quantum charged particle beam optics based on t...
Chapter
The main aim of this chapter is to provide the motivation for studying the quantum mechanics of charged particle beam optics. It summarizes briefly the contents of the later chapters on classical mechanics, quantum mechanics, classical charged particle beam optics, and the scalar and spinor theories of quantum charged particle beam optics. http:/...
Article
16 May has been proclaimed as the International Day of Light (IDL) by UNESCO. The purpose of an International Day of Light is to provide an annual focal point for the continued appreciation of the central role that light plays in the lives of the citizens in the world in areas of science, culture and art, education, sustainable development, and in...
Article
On Tuesday the 26 February 2019, a ceremony was held to mark the official inauguration of the solar power plant of SESAME: Synchrotron-light for Experimental Science and Applications in the Middle East. This make SESAME the very first large accelerator complex to be fully powered by solar energy. The SESAME synchrotron located in Jordan also has th...
Research Proposal
Full-text available
Applications of renewable energy in Oman nowadays, however, in a very minimal state, despite several research and field studies have been conducted to promote the alternative energy sources and also open the way to use, and application of renewable energy as a clean and future alternative national of energy source. It is also anticipated that the f...
Article
The 2019 King Faisal International Prize for Medicine (Topic: Bone Biology and Osteoporosis) is awarded to Steven L. Teitelbaum (for developing new treatments for the prevention and cure of diseases such as osteoporosis) and to Bjørn Reino Olsen (for genetic discoveries which have enhanced the understanding of bone development, and the basis of inh...
Article
Out of 113 King Faisal International Prize science/medicine laureates, 20 are Nobel laureates. 3.53% of them are women. This is marginally higher than for Nobels: just 20 women (3.29%) are named among the 607 Nobel prizewinners in the fields of science and medicine since 1901. http://dx.doi.org/10.1038/d41586-018-07805-z https://www.nature.com/...
Article
In addition to his own discoveries, polymath Hermann von Helmholtz influenced the development of a whole group of illustrious physicists. https://rdcu.be/bcEDs http://dx.doi.org/10.1038/d41586-018-07613-5 https://www.nature.com/articles/d41586-018-07613-5 https://www.nature.com/magazine-assets/d41586-018-07613-5/d41586-018-07613-5.pdf
Article
The King Faisal Foundation in Riyadh, Saudi Arabia has awarded the 2018 King Faisal International Prize (KFIP) for Science to Sir John Macleod Ball of UK for his fundamental contributions to nonlinear partial differential equations, the calculus of variations, and applications to materials science and liquid crystals. The prize consists of a certif...
Article
E. C. G. Sudarshan had a multifaceted personality with immense contributions to diverse areas of physics. One of his contributions not widely known is to do with the emerging field of ‘quantum mechanics of charged-particle beam optics’. The present note elaborates on the origins and the development of this emerging field. http://www.currentscienc...
Article
Caucher Birkar presented a new Medal: Other Prizes at the International Congress of Mathematicians eLetter http://science.sciencemag.org/content/361/6402/534/tab-e-letters
Chapter
In this chapter, we describe the measures taken by Oman towards environment, through its dedicated ministries, since the 1970s. We also discuss the origins of the UNESCO Sultan Qaboos Prize for Environmental Preservation and its establishment in 1989. The prizes are awarded very regularly in alternate years through UNESCO. It is the first Arab...
Chapter
From the onset, the government of His Majesty Sultan Qaboos Bin Said was committed to protecting and sustaining this environment at a time when the Sultanate was proceeding with rapid industrial, agricultural and large-scale constructional developments. His Majesty Sultan Qaboos Bin Said, Sultan of Oman – May Allah Bless Him – made a historic impac...
Conference Paper
In the traditional prescriptions, the Fermat’s principle of least time or/and the Helmholtz equation are used to derive the beam-optical Hamiltonian. Now, we know that the Maxwell’s electromagnetism gives rise to the correct theory of light. So, we developed a formalism of beam optics starting with an exact matrix-representation of Maxwell’s equati...
Article
The 2018 King Faisal International Prize for Medicine (Topic: Immunotherapy for Cancer) is awarded to James Patrick Allison of USA, for his outstanding contribution to the development of the field of immunotherapy of cancer. The Science prize in the field of mathematics is awarded to Sir John Macleod Ball of UK for his fundamental contributions to...
Article
Curtail climate-change effects using Singapore Index of Cities’ Biodiversity. http://dx.doi.org/10.1038/d41586-018-04168-3 https://www.nature.com/articles/d41586-018-04168-3 https://www.nature.com/magazine-assets/d41586-018-04168-3/d41586-018-04168-3.pdf See also Sameen Ahmed Khan, 2017 UNESCO Sultan Qaboos Prize for Environmental Preservat...
Article
I read your Japan special report with a keen interest. My first visit to Japan was in March 1994 to attend the JSPS-KEK International Spring School: High Energy Ion Beams – Novel Beam Techniques and their Applications. http://dx.doi.org/10.1088/2058-7058/31/4/30 http://live.iop-pp01.agh.sleek.net/physicsworld/reader/#!edition/editions_apr_2018/a...
Article
The 2017 UNESCO Sultan Qaboos Prize for Environmental Preservation has been awarded to the National Parks Board of Singapore. The Prize is awarded in alternate years. http://www.currentscience.ac.in/cs/Volumes/114/02/0252.pdf
Article
The scalar optics is based on a Hamiltonian derived using the Fermat's principle of least time. The same Hamiltonian can now be derived from the Maxwell equations. The Helmholtz equations has a striking mathematical similarity to the Klein-Gordon equation for the relativistic spin-0 particle. It is possible to make use of this strong similarity thr...
Article
Maryam Mirzakhani the first and to-date only female winner of the Fields Medal died on Friday the 14 July 2017. http://www.asiapacific-mathnews.com/07/preserved-docs/0701/0036_0039.pdf
Chapter
A summary of the results on synchrotron radiation is presented along with notes on its properties and applications. Quantum aspects of synchrotron radiation are mentioned briefly. Synchrotron radiation facilities are described, with a focus on the upcoming synchrotrons. An outline of the {\em quantum theory of charged-particle beam optics} is...
Article
The 24th Congress of the International Commission for Optics (ICO-24) was held in Tokyo, Japan during 21-25 August 2017. The ICO Congress has established itself as one of the most prestigious international conferences in the field of optics and photonics. This article has a report on this landmark event.
Article
Maryam Mirzakhani the first and to-date only female winner of the Fields Medal died on Friday the 14 July 2017. http://www.currentscience.ac.in/Volumes/113/05/0982.pdf
Chapter
The UN designated International Year of Light and Light-based Technologies (IYL2015), provided a world-wide stimulus to optical sciences and associated technologies. The yearlong celebrations of light were a good occasion to revisit the history of optics. Year 2015 had the millennium anniversary of the encyclopedic seven volumes on optics by the le...
Chapter
We address the theme of international science collaborations, in the light of examples of the institutions from Europe, which were built after the Second World War. These international institutions devoted to science played a pivotal role in the rebuilding of Europe devastated by the wars. CERN, the European Laboratory for Particle Physics in Genev...
Chapter
A unified formalism of light beam optics and light polarization is presented. The starting point of our formalism is an exact matrix-representation of Maxwell's equations in an inhomogeneous medium, which is presented in detail. The beam-optical Hamiltonians are derived without any specifications on the form of the varying refractive index. The new...
Article
Tadamitsu Kishimoto of Japan has been awarded the KFIP in recognition of his prominent role in developing a novel biologic therapy for autoimmune diseases. The prize for Science in the field of physics is awarded to Daniel Loss of Switzerland and Laurens W. Molenkamp of Netherlands. Daniel Loss is a pioneer in the theory of spin dynamics and sp...
Article
We explore the ways to linearize the wave equations. Special emphasis is paid to the Klein-Gordon equation for a spin-0 relativistic particle and the Helmholtz equation governing scalar optics. Owing to the mathematical similarity, both of these equations are linearized using the Feshbach-Villars procedure. Maxwell's equations are linear but couple...
Article
The spherometers are the instruments widely used for measuring the radii of curvature of spherical surfaces. The principle of this device is on some geometric properties of circles and spheres known from Euclidean geometry. We present the formula for the spherometer obtained from coordinate geometry. Importantly, the coordinate geometric approach e...