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Blackbody radiation in classical physics: A historical perspective
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| Pengarang | : | Weinburgh, Molly |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 495-509 |
| Abstrak | : | We point out that current textbooks of modern physics are a century out-of-date in their treatment of blackbody radiation within classical physics. Relativistic classical electrodynamics including classical electromagnetic zero-point radiation gives the Planck spectrum with zero-point radiation as the blackbody radiation spectrum. In contrast, nonrelativistic mechanics cannot support the idea of zero-point energy; therefore, if nonrelativistic classical statistical mechanics or nonrelativistic mechanical scatterers are invoked for radiation equilibrium, one arrives at only the low-frequency Rayleigh-Jeans part of the spectrum, which involves no zero-point energy, and does not include the high-frequency part of the spectrum involving relativistically invariant classical zero-point radiation. Here, we first discuss the correct understanding of blackbody radiation within relativistic classical physics, and then we review the historical treatment. Finally, we point out how the presence of Lorentz-invariant classical zero-point radiation and the use of relativistic particle interactions transform the previous historical arguments, so as now to give the Planck spectrum including classical zero-point radiation. Within relativistic classical electromagnetic theory, Planck's constant appears as the scale of source-free zero-point radiation. |
Spherical aberration, coma, and the Abbe sine condition for physicists who don't design lenses
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 487-494 |
| Abstrak | : | Treatments of lens aberrations tend to be either short and descriptive surveys or detailed theoretical treatments. In this article, we take an intermediate approach, showing that the mechanism of spherical aberration can be easily understood on a qualitative level by comparing a sphere with the ideal lens shape prescribed by the Principle of Least Time, and by using a similar argument to understand coma aberration. We also use a simple argument from radiant flux conservation to explain why aberration-free imaging of finite-sized flat objects (as opposed to discrete points or curves) is impossible with just a single thin lens, and we provide a simple explanation of the Abbe Sine Condition as a figure of merit in aberration correction. |
A classical analogy for quantum band formation
| Pengarang | : | Parker Roberts |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 609-615 |
| Abstrak | : | Electrons in an atom are confined to distinct, quantized energy levels. When atoms form solids, the interaction of the electrons causes their energy levels to split into multiple closely spaced levels, or bands, separated by forbidden regions called band gaps. Each band contains a number of energy levels equal to the number of atoms in the solid. This model of the origin of band structure can be reproduced by using a classical array of harmonic oscillators (masses connected by springs). In this system, each oscillator plays the role of an atom and its resonant frequencies play the roles of electronic energy levels. When coupled, a system of oscillators yields a spectrum of resonant frequencies and when the number of oscillators becomes sufficiently large, the system exhibits the formation of “resonant frequency bands,” similar in structure to the energy bands of an atomic solid. We experimentally demonstrate band formation using coupled harmonic oscillators and highlight the effects of both number of oscillators and coupling strength on the band structure. Additionally, we show that experimental results of this band formation follow a theoretical analysis of the system. |
A simple method of coil design
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 602-608 |
| Abstrak | : | In this article, we present a method to design a coil producing an arbitrarily shaped magnetic field by restricting the path of the coil's wires to a regular grid. The solution is then found by a simple least squares minimum. We discuss practical applications, in particular, in the active magnetic field stabilization system of the neutron electric dipole moment experiment at the Paul Scherrer Institute in Villigen, Switzerland. We also publish the software implementation of the method. |
Using a shoebox spectrograph to investigate the differences between reflection and emission
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 594-601 |
| Abstrak | : | For various reasons, optics laboratories often become activities of following instructions and being told to look at one thing or another. This approach can prevent students from exploring optics on their own and diminishes opportunities for “play” and discovery, which are critical to learning. On the other hand, letting students simply explore with equipment that they are just learning to use can be risky and expensive. This is particularly true for spectroscopy with monochromators and spectrographs. To help students gain a better understanding of spectroscopy through inquiry-based discovery learning, we have designed a low-budget and durable spectrograph, which we call a “shoebox spectrograph” that students assemble themselves. Our spectrograph (less than $30 per unit, which includes a webcam to collect spectral images) can then be used in discovery-themed experiments enabling students to explore spectroscopic properties of light as it extends to vision without much fear of student destruction. In this report, we discuss how our spectrograph works, its construction, and explore a student experiment that explores reflected light versus fluorescence. |
The apparent (gravitational) horizon in cosmology
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 585-593 |
| Abstrak | : | In general relativity, a gravitational horizon (more commonly known as the “apparent horizon”) is an imaginary surface beyond which all null geodesics recede from the observer. The Universe has an apparent (gravitational) horizon, but unlike its counterpart in the Schwarzschild and Kerr metrics, it is not static. It may eventually turn into an event horizon—an asymptotically defined membrane that forever separates causally connected events from those that are not—depending on the equation of state of the cosmic fluid. In this paper, we examine how and why an apparent (gravitational) horizon is manifested in the Friedmann–Robertson–Walker metric, and why it is becoming so pivotal to our correct interpretation of the cosmological data. We discuss its observational signature and demonstrate how it alone defines the proper size of our visible Universe. In so doing, we affirm its physical reality and its impact on cosmological models. |
Combined viscous and dry friction damping of oscillatory motion
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 577-584 |
| Abstrak | : | The acceleration, velocity, and displacement of a glider on an air track undergoing oscillatory motion subject to viscous and dry frictional damping are investigated using an accelerometer, which allowed a detailed investigation of the dynamics, experimental observation of the predicted acceleration discontinuities due to the reversal of the friction force, and the variation of the drag with time, velocity, and displacement. The investigation included systematic variation of the air track air pressure to explicitly control the relative contribution of viscous and dry frictional damping. Although frictional damping of oscillatory motion has been treated by a number of authors, most investigations have been restricted to measurements of displacement only, with the primary interest being in the decay of the amplitude. In this paper, an exact theory of the acceleration of oscillatory motion, assuming viscous damping proportional to the velocity plus a Coulomb friction force independent of velocity or position, is presented and compared with experiment. |
Resource Letter GECC-1: The Greenhouse Effect and Climate Change: Earth's Natural Greenhouse Effect
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 8) |
| Halaman | : | 565-576 |
| Abstrak | : | Earth's greenhouse effect is manifested as the difference between thermal infrared radiation emitted at the Earth surface and that emitted to space at the top of the atmosphere. This difference, which is due mainly to absorption and downward emission of radiant energy by atmospheric trace gases, results in global mean surface temperature about 32 K greater than what it would otherwise be for the same planetary absorption of solar radiation, and is thus of enormous importance to Earth's climate. This Resource Letter introduces the physics of the greenhouse effect and more broadly of Earth's climate system and provides resources for further study. A companion Resource Letter (GECC-2), planned for the following issue, examines the increase in the greenhouse effect due to human activities over the past 200 years and its consequences for Earth's climate system. |
A simulated annealing approach to the student-project allocation problem
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 9) |
| Halaman | : | 701-708 |
| Abstrak | : | We describe a solution to the student-project allocation problem using simulated annealing. The problem involves assigning students to projects, where each student has ranked a fixed number of projects in order of preference. Each project is offered by a specific supervisor (or supervisors), and the goal is to find an optimal matching of students to projects taking into account the students' preferences, the constraint that only one student can be assigned to a given project, and the constraint that supervisors have a maximum workload. We show that when applied to a real dataset from a university physics department, simulated annealing allows the rapid determination of high quality solutions to this allocation problem. The quality of the solution is quantified by a satisfaction metric derived from empirical student survey data. Our approach provides high quality allocations in a matter of minutes that are as good as those found previously by the course organizer using a laborious trial-and-error approach. We investigate how the quality of the allocation is affected by the ratio of the number of projects offered to the number of students and the number of projects ranked by each student. We briefly discuss how our approach can be generalized to include other types of constraints and discuss its potential applicability to wider allocation problems. |
Reflected diffraction from linearly patterned surfaces
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 9) |
| Halaman | : | 690-700 |
| Abstrak | : | We discuss the optical analogy of reflected electron diffraction from a grating with non-uniform spacing at the nanoscale, and its relationship to another grating with uniform spacing. Two analytical approaches that offer a quantitative solution for the reflected diffraction from a grating are presented. A compact and low-cost experimental kit for demonstrating the physics behind the reflected diffraction from one-dimensional surface structures is described. As an example, the convolution theorem is used to explain the reflected diffraction from a sample consisting of two individual one-dimensional surface structures overlapping orthogonally. This study will broaden students' understanding of the physics behind diffraction. |