@article{Vollmer2020, author = {Vollmer, Michael}, title = {Below the horizon-the physics of extreme visual ranges}, series = {Applied Optics}, volume = {59}, journal = {Applied Optics}, number = {21}, publisher = {Optica Publishing Group}, doi = {10.1364/AO.390654}, pages = {F11 -- F19}, year = {2020}, language = {en} } @article{VollmerMoellmann2020, author = {Vollmer, Michael and M{\"o}llmann, Klaus-Peter}, title = {Unsichtbares sichtbar gemacht: Infrarotkameras f{\"u}r Smartphones}, series = {Physik in unserer Zeit}, volume = {51}, journal = {Physik in unserer Zeit}, number = {1}, publisher = {Wiley-VCH}, doi = {https://doi.org/10.1002/piuz.201901551}, pages = {29 -- 35}, year = {2020}, language = {de} } @article{VollmerMoellmann2020, author = {Vollmer, Michael and M{\"o}llmann, Klaus-Peter}, title = {Wenn Licht die Biege macht}, series = {Physik in unserer Zeit}, volume = {51}, journal = {Physik in unserer Zeit}, number = {1}, publisher = {Wiley-VCH}, doi = {https://doi.org/10.1002/piuz.202001569}, pages = {46 -- 47}, year = {2020}, language = {de} } @article{Vollmer2021, author = {Vollmer, Michael}, title = {Gefrierende Gew{\"a}sser}, series = {Physik in unserer Zeit}, volume = {52}, journal = {Physik in unserer Zeit}, number = {1}, publisher = {Wiley-Blackwell}, doi = {10.1002/piuz.202001589}, pages = {19 -- 25}, year = {2021}, language = {de} } @article{VollmerEberhardt2024, author = {Vollmer, Michael and Eberhardt, Wolfgang}, title = {Ein einfaches Modell f{\"u}r die Vorhersage von CO2 Konzentrationen in der Atmosph{\"a}re in Abh{\"a}ngigkeit von globalen CO2 Emissionen}, series = {PhyDid B, Didaktik der Physik, Beitr{\"a}ge zur DPG-Fr{\"u}hjahrstagung}, volume = {1}, journal = {PhyDid B, Didaktik der Physik, Beitr{\"a}ge zur DPG-Fr{\"u}hjahrstagung}, number = {1}, publisher = {FU Berlin}, organization = {Fachverband Didaktik der Physik}, issn = {2191-379X}, pages = {379 -- 388}, year = {2024}, abstract = {Es wird das vielleicht einfachst m{\"o}gliche Modell vorgestellt, mit dem zeitabh{\"a}ngige CO2 Konzent-rationen c(t) in der Atmosph{\"a}re ausgehend von verschiedenen globalen Emissionsszenarien f{\"u}r CO2berechnet werden. Dazu wird eine einzelne inhomogene lineare Differenzialgleichung 1. Ordnung hergeleitet, deren Parameter sich aus den quantitativen Daten des global carbon project sowie Mauna Loa Daten f{\"u}r CO2 Konzentrationen errechnen. Das Modell wird erstens getestet am Zeitraum 1960 bis 2020 mit vergleichsweise guter quantitativer {\"U}bereinstimmung zu Messdaten. Zweitens wird f{\"u}r zwei typische IPCC Emissions-Szenarien ein Vergleich der Modellvorhersagen mit denen der kom-plexen IPCC Earth-System-Klimamodelle diskutiert mit qualitativer {\"U}bereinstimmung des zeitli-chen Verlaufs. Drittens werden Ergebnisse einiger ausgew{\"a}hlter neuer Emissionsszenarien pr{\"a}sen-tiert. Ungeachtet einiger Abweichungen zu komplexeren Klimamodellen zeichnet sich unser Mo-dell durch zwei wichtige Vorteile f{\"u}r die Lehre aus. Zum einen ist es sehr einfach f{\"u}r Studierende und begabte Sch{\"u}ler nutzbar, da die erforderliche L{\"o}sung der Differentialgleichung bereits mit han-dels{\"u}blicher Tabellenkalkulationssoftware wie z.B. Excel programmiert werden kann. Dadurch ge-stattet es zum anderen auch sehr einfach, den zeitlichen Verlauf von Emissionsszenarien zu ver{\"a}n-dern und innerhalb weniger Sekunden Ver{\"a}nderungen aufgrund ge{\"a}nderter Eingaben zu berechnen. Insofern eignet sich das Modell sehr gut als Einstieg in das Thema Klimamodellierung in einf{\"u}hren-den Hochschulvorlesungen zum Themenbereich Kohlenstoffkreislauf und Klimawandel. In der Schule kann es gegen Ende der Sekundarstufe 2 beispielsweise im Projektunterricht zum Themen-komplex Nachhaltigkeit in Physik und/oder Mathematik eingesetzt werden}, language = {de} } @article{Vollmer2024, author = {Vollmer, Michael}, title = {Limitations of the eye and how to overcome them}, series = {Journal of Physics: Conference Series}, volume = {2750}, journal = {Journal of Physics: Conference Series}, number = {1}, doi = {10.1088/1742-6596/2750/1/012001}, pages = {1 -- 10}, year = {2024}, abstract = {Human eyes have spatial, temporal, and spectral limitations which impose constraints on our perception. With appropriate optical devices and cameras, the limitations can be easily overcome. As a consequence, a huge variety of physical phenomena can be made accessible for teaching.}, language = {en} } @article{Vollmer2025, author = {Vollmer, Michael}, title = {Nachtsicht ins All mit dem bloßen Auge: Sag mir, wie weit die Sterne steh'n}, series = {Physik in unserer Zeit}, volume = {2025}, journal = {Physik in unserer Zeit}, publisher = {Wiley}, doi = {10.1002/piuz.202501751}, pages = {2 -- 10}, year = {2025}, language = {de} } @article{Vollmer2025, author = {Vollmer, Michael}, title = {Naked eye celestial objects and phenomena: how far can we see at night?}, series = {European Journal of Physics}, volume = {46}, journal = {European Journal of Physics}, number = {3}, publisher = {IOP Science}, doi = {10.1088/1361-6404/adbf74}, pages = {18}, year = {2025}, abstract = {How far can we see with the naked eye at night? Many celestial objects like stars and galaxies as well as transient phenomena such as comets and supernovae can be observed in the night sky. We discuss the furthest distances of such objects and phenomena observable with the naked eye during the night-time for Earth-bound observers. The physics of night-time visual ranges differs from that of daytime observations because human vision shifts from cones to rods. In addition, mostly point sources are observed due to the large distances involved. Whether celestial objects and phenomena can be detected depends on the contrast of their radiation and the background sky luminance. We present a concise overview of how far we can see at night by first discussing the effects of the Earth's atmosphere. This includes attenuation of transmitted radiation as well as its role as a source of background radiation. Disregarding the attenuation of light due to interstellar and intergalactic dust, simple maximum night-time visual range estimates are based on the inverse square law, which can be easily verified by laboratory and demonstration experiments. From the respective calculations, we find that individual stars within the Milky Way galaxy of up to 15 000 light years are observable. Even further away are observable galaxies with several billion stars. The Andromeda galaxy can be observed with the naked eye at a distance of around 2.5 million light years. Similarly, the observability of supernovae also allows a visual range beyond the Milky Way galaxy. Finally, gamma ray bursts as the most energetic events in the universe are discussed concerning naked eye observations.}, language = {en} } @article{Vollmer2025, author = {Vollmer, Michael}, title = {How far can we see at day?}, series = {European Journal of Physics}, volume = {46}, journal = {European Journal of Physics}, number = {3}, publisher = {IOP Science}, doi = {10.1088/1361-6404/adc4a0}, pages = {17}, year = {2025}, abstract = {We discuss the farthest objects on Earth observable for the unaided, healthy naked eye during the daytime, i.e., the maximum visual range for observers on Earth. Visual range depends first on the properties of the material between observer and object and its interaction processes with radiation, but second also on our visual perception system. After a rough comparison of ranges in water, glass, and the atmosphere, we focus on the physical basis of visual range for the latter. As a contrast phenomenon, visual range refers to allowed light paths within the atmosphere. It results from the interplay of geometry, refraction, and light scattering. We present a concise overview of this field by qualitative descriptions and quantitative estimates as well as classroom demonstration experiments. The starting point is the common geometrical visual ranges, followed by extensions due to refraction and limitations due to contrast, which depend on scattering and absorption processes within the atmosphere. The quantitative discussion of scattering is very helpful to easily understand the huge ranges in nature from meters in dense fog to hundreds of kilometers in clear atmospheres. Extreme visual ranges from about 300 km to above 500 km require optimal atmospheric conditions, cleverly chosen locations and times, and a sophisticated topography analysis. Even longer visual ranges are possible when looking through the vertical atmosphere. From the ISS, daytime ranges well above 1000 km are possible.}, language = {en} } @article{Vollmer2026, author = {Vollmer, Michael}, title = {How many stars appear colored to the naked eye?}, series = {Applied Optics}, volume = {65}, journal = {Applied Optics}, number = {9}, publisher = {Optica Publishing Group}, doi = {10.1364/AO.580635}, pages = {C27 -- C37}, year = {2026}, abstract = {Naked eye studies of the clear night sky reveal that a certain percentage of all observable stars can be perceived as having color. Subjective estimates differ widely, ranging from just a few to a maximum of above two hundred. Explanations are based on the emission spectra of the stars, which are modified by interstellar dust clouds, the Earth atmosphere, and mostly the inverse square law. Color changes occur not only for variation of the star's angular elevation above the horizon, but as well for decreasing nighttime sky brightness due to the transition from photopic via mesopic to scotopic vision. The maximum number of stars showing color to the naked eye depends on star illuminances on Earth and the background sky luminance. The limit of observing color is found to correspond to apparent visual magnitudes around , defining the number of colored stars. This also means that naked eye perception of stars with color is only possible for a certain star distance range, which is well below the maximum naked eye visual range of stars.}, language = {en} }