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We recorded diffraction patterns using a commercially available slit and sensor over a wide range of experimental circumstances, including near- and far-field regimes and oblique incidence at large angles. We then compared the measured patterns with theoretical intensity curves calculated via the numerical integration of formulas derived within the framework of scalar diffraction theory. Experiment and theory show particularly good agreement when the first Rayleigh–Sommerfeld (R-S) formula is used. The Kirchhoff formula, though problematic in the context of mathematical consistency, agrees with the first R-S formula, even for large incidence angles, whereas the second R-S formula differs visibly. To obtain such a good agreement, we replaced the assumption of an incident plane wave with that of a Gaussian beam and implemented geometric corrections to account for slit imperfections. These results reveal how the scope of scalar diffraction theory can be extended with a small set of auxiliary assumptions.

Earlier research has shown that students have tremendous difficulties with understanding certain aspects of rolling without slipping, such as the zero-velocity at the contact point and plausibility of application of the law of conservation of mechanical energy despite action of the friction force. The aim of this research was to explore whether using analogies and reasoning about extreme cases can facilitate conceptualization of the above-mentioned phenomena. A pre-test – post-test quasi-experiment has been conducted, with 93 students in the control group (CG) and 91 students in the experimental group (EG). Whereas control group students received conventional teaching, in the experimental group rolling of a cylinder has been considered as a special case of a tumbling prism for which the number of prism surfaces tended to infinity. The results of analysis of covariance showed that students from the experimental group significantly outperformed their peers from the control group on the Rolling Motion Concept Test (RMCT). Between-group differences were greater on test items that required higher level of cognitive transfer. This research suggests that using analogies and extreme case reasoning can facilitate comprehension of certain seemingly counterintuitive aspects of rolling motion. Keywords: analogy-based teaching, energy conservation, extreme case reasoning, misconceptions, rolling motion.

With the increasing availability of single- board computers equipped with fast analog-to- digital converters based on field-programmable gate arrays (FPGA), researchers and educators gain access to relatively inexpensive hardware that can be programmed for advanced coincidence counting. We demonstrate this capability by developing software for a dual-channel open- source data acquisition platform, enabling it to perform energy- and time-resolved coincidence counting and testing our system using an 241Am source. Measuring the coincidence between alpha and gamma radiation allowed us to determine the half-life of the 237Np excited state. The obtained value of 67.7 ± 0.1 ns is compatible with the value cited in the literature. Furthermore, the use of digital signal processing enabled us to sort time- resolved counts by alpha and gamma energy, which resulted in additional information on the decay scheme. Correlation heatmaps between the two spectra were plotted and used to verify the decay scheme. The half-lives of the other features visible in the gamma spectrum were determined as well.

In this paper, we are going to show how learning about some counterintuitive aspects of rolling motion can be facilitated by combining the use of analogies with extreme case reasoning. Specifically, the intuitively comprehensible examples of "rolling" polygonal prisms are used as an analogical anchor that is supposed to help the students to develop conceptual understanding about counter intuitive aspects of rolling motion.

In this work we analyze the wave–particle aspects of radiation in (incoherent) Compton scattering in the radiation energy range from 2–100 keV. From the calculated cross sections of the scattering from the electron (positron), hydrogen and positronium we construct the interpretation functions (IFs), where our assertion is that the Compton scattering from the free electron (positron) is an established example of the particle behavior of radiation. These IFs estimate the possibility of the interpretation of radiation in terms of waves or particles in an analogy with the analysis carried out in the coherent scattering of light. Based on these IFs we propose a new criterion for the estimation of the validity of the impulse approximation (IA).