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Institute
Koronen sind farbige Ringsysteme um Sonne oder Mond. Sie entstehen in der Atmosphäre durch Beugung des Lichts an Wassertropfen in Wolken oder anderen kleinen Teilchen. Wichtig ist dabei, dass die Wolken optisch dünn sind. Dann streut das Licht auf seinem Weg von der Lichtquelle ins Auge des Beobachters nur an einem einzigen Tropfen. Außerdem sollten die streuenden Teilchen eine möglichst enge Größenverteilung haben. Erst dann wird die Korona in voller Ausprägung mit zentraler Aureole und mehreren farbigen Ringen sichtbar. Ihre grundlegenden physikalischen Eigenschaften lassen sich durch Beugung an einer einfachen Kreisblende verstehen. Genaue Resultate liefert die Mie-Theorie. Koronen können mit Computersimulationen und einfachen Experimenten gut im Unterricht behandelt werden. Aus den Abmessungen einer Korona lässt sich die Tröpfchengröße ermitteln.
A cone of light appears in a tank of water when a laser pointer shines through the water onto a white piece of paper upon which the tank is sitting. We describe how students can understand the origins of this cone by constructing multiple explanations, then proposing and designing experiments to test their explanations. This process is the foundation of the Investigative Science Learning Environment (ISLE) framework, designed to engage students in the reasoning activities similar to those that physicists use to construct and apply new knowledge. We describe typical student ideas and provide a list of equipment and suggestions for facilitating student exploration relating to optics. We also explain the formal physics behind the phenomena that are involved in the experiment. Finally, we suggest how the ISLE framework can be used to help instructors find problems and experiments that engage students in devising and testing multiple explanations.
Twice in a blue moon
(2009)
Irradiance and color during the total lunar eclipses of 2007 and 2008 are simulated using a ray tracing model that includes refraction, scattering by molecules, and observed or climatological distributions of aerosols, ozone, clouds, and topography around the terminator. Central portions of the umbra appear deep red for almost all eclipses due to preferential removal of short wavelengths in the spectrum of sunlight by scattering in the lower troposphere. The fringe of the umbra appears turquoise or blue due to selective removal of wavelengths around 600 nm by the Chappuis absorption bands of ozone in the stratosphere. Asymmetric distributions of clouds and aerosols, particularly for the 2008 eclipse, produce minimum calculated irradiance up to 17 arc min from the umbra center, while high ozone content over the arctic makes the northern edge of the umbra deepest blue.
© 2008 Optical Society of America
We present simple radiative transfer models for the radiance and color of atmospheric optical phenomena. Skylight, halos, and rainbows are treated as singly scattered sunlight that is depleted by scattering as it passes through a plane-parallel atmosphere and a vertical rain shaft or a geometrically thin cloud layer. Skylight in a molecular atmosphere grades from deep blue at the zenith to pale blue near the horizon whenever the solar zenith angle sun ≤ 80°. Skylight near the horizon is orange resulting from wavelength-dependent scattering by air molecules and aerosol particles through a long oblique path through the atmosphere when the sun is low in the sky (sun ≥ 85°). Halos (and coronas) seen through clouds facing the sun are brightest for cloud optical depth τcld ≈ cos(sun), and fade to obscurity for τcld ≥ 5. Rainbows (and glories), seen by light that is backscattered from clouds, also appear most dramatic when 0.2 ≤ τcld ≤ 1, but remain visible even in the thickest clouds.
Model simulations of laboratory-generated and natural crepuscular rays are presented. Rays are created in the laboratory with parallel light beams that pass through artificial fogs and milk–water solutions. Light scattered by 90° in a dilute mixture of whole milk first increases in intensity with distance from the source to a maximum as a result of multiple scattering by mainly small angles before decreasing exponentially due to extinction as distance continues to increase. Crepuscular rays are simulated for three cloud configurations. In case 1, the Sun at the zenith is blocked by a cloud with an overhanging anvil. The rays appear white against blue sky and are brightest when atmospheric turbidity, β≈11 . Shading by the anvil separates maximum brightness from apparent cloud edge. In case 2, a ray passes through a rectangular gap in a cloud layer. The ray is faint blue in a molecular atmosphere but turns pale yellow as β and solar zenith angle, ϕsun , increase. At ϕsun=60° it appears most striking when the cloud is optically thick, β≈5 , and the beam width Δx≈1000 m . In these cases, increasing aerosol radius, raer , to about 1000 nm brightens, narrows, and shortens rays. In case 3, the twilight Sun is shaded by a towering cloud or mountain. The shaded rays are deeper blue than the sunlit sky because the light originates higher in the atmosphere, where short waves have suffered less depletion from scattering. The long optical path taken by sunlight at twilight makes color and lighting contrasts of the rays greatest when the air is quite clean, i.e., for β−1≪1 . In all cases, the brightest rays occur when sunlight passes through an optical thickness of atmosphere, τ≈O(1) .
© 2011 Optical Society of America
Abstract
So far experiments with artificial halos from single transparent crystals have suffered from the lack of apparatus that allows simultaneous rotation around two and three axes. A new setup is presented which overcomes these restrictions by combining electrical as well as pneumatic concepts. This enables reproducible experiments of the most common halos observed in nature and for the first time artificial ring halos from single hexagons rotating around three axes simultaneously. In addition, an old qualitative halo demonstration based on perceived colors of rotating colored areas whose contours represent scattering plots has been reinvestigated and the usually nonsaturated color of artificial parhelia was visualized using a crossed prism method. These new experiments are discussed in the context of all known artificial halo experiments.
© 2014 Optical Society of America
Small sodium and silver particles were generated on dielectric substrates like LiF, quartz and sapphire under ultrahigh vacuum conditions. The optical transmission spectra of the clusters were measured as a function of cluster size and shape, for low and high substrate temperatures as well as for s- and p- polarization of the incident light. Excitation of dipolar surface plasmon oscillations in the directions normal and parallel to the substrate surface could be identified. Furthermore, optical spectra for Na and Ag clusters were calculated with the classical Mie theory. The measured spectra vary strongly if the experimental conditions are changed and can be exploited, for example, to characterize the particles with regard to their size and shape. In particular, the axial ratio of the spheroidal clusters could be determined. Its value is considerably different for the two investigated metals and depends on the substrate material. Furthermore, the temperature of the substrate has a pronounced influence on the shape of the particles. At low temperature of T=100 K two-dimensional island growth is predominant. The particles extend only little in the direction perpendicular to the surface and coalesce readily at small coverage of metal atoms. In contrast, the clusters are truly three-dimensional at T=300 K. At this stage, sodium particles still exhibit a rather small axial ratio whereas silver clusters appear almost spherical. Thus, measurements of the optical spectra permit direct in situ monitoring of cluster growth during the nucleation of adsorbed atoms and of temperature induced shape variations. In addition to investigations of the shape of the particles, the quadrupolar surface plasmon mode was observed for Ag clusters.
Laser-induced desorption of metal atoms from the surface of small metal particles has been investigated as a function of the shape of the particles and the polarization of the incident laser light. The particles were supported on LiF, quartz or sapphire substrates. In a first set of experiments, the shape of the particles was determined by recording optical transmission spectra with s- and p-polarized light incident under an angle of typically 40° with respect to the surface normal. The metal particles turn out to be oblate, the ratio of the axes perpendicular and parallel to the substrate surface being on the order of 0.5. This ratio decreases with increasing particle size. Also, the particles change shape if the temperature is raised. In further experiments, s- and p-polarized light has been used to stimulate desorption of atoms via surface plasmon excitation. It is found that the desorption rate markedly depends on the polarization of the light. This is explained by excitation of the collective electron oscillation along different axes of the non-spherical particles.
The Moon’s time-dependent luminance was determined during the 9 February 1990 and 3 March 2007 total lunar eclipses by using calibrated, industry standard photometers. After the results were corrected to unit air mass and to standard distances for both Moon and Sun, an absolute calibration was accomplished by using the Sun’s known luminance and a pre-eclipse lunar albedo of approximately 13.5%. The measured minimum level of brightness in the total phase of both eclipses was relatively high, namely −3.32 mvis and −1.7 mvis , which hints at the absence of pronounced stratospheric aerosol. The light curves were modeled in such a way as to let the Moon move through an artificial Earth shadow composed of a multitude of disk and ring zones, containing a relative luminance data set from an atmospheric radiative transfer calculation.
© 2008 Optical Society of America
Results on laser-induced desorption of metal atoms from small metal particles are presented. Experiments have been performed on sodium, potassium, and silver particles supported on a LiF(100) single-crystal surface under ultrahigh vacuum conditions. Measurements include the determination of the desorption rate as a function of laser wavelength, laser intensity, average particle size, and substrate temperature, the determination of the kinetic energy of the desorbed atoms, the investigation of the optical spectra of the supported metal particles, and the study of the influence of adsorbate molecules on the desorption rate. Furthermore, theoretical extinction and absorption spectra of the metal particles have been calculated with the classical electrodynamical Mie theory as a function of average particle size and excitation wavelength. Also, the radial electric field at the particle surface was computed. The results of the experiments and theoretical calculations are combined to give a consistent picture of the mechanism of metal-atom desorption by electronic excitation with laser light. A realistic surface potential from which the atoms escape and nonlocal optical effects are taken into account. The latter introduce additional absorption channels by the formation of electron-hole pairs in the surface layer of the particle which relax into antibonding states before desorption occurs. Finally, the mechanism is discussed in the light of similar phenomena observed for thin metal films. Possibilities for future work are outlined.
© 1993 The American Physical Society
Beleuchtet man die Oberfläche eines Festkörpers mit Laserlicht, können darauf adsorbierte Atome oder Moleküle abgelöst werden. Solche Desorptionsprozesse sind in jüngster Zeit in zahlreichen Experimenten untersucht worden, wobei sich das Interesse sowohl auf die Erforschung der zugrundeliegenden Mechanismen als auch auf mögliche Anwendungen dieser Reaktionen, zum Beispiel zur gezielten Modifizierung von Oberflächen, konzentriert. Besonders interessant ist das laserinduzierte Aufbrechen von Bindungen zur Oberfläche dann, wenn es nicht einfach als thermischer Prozeß durch eine Temperaturerhöhung hervorgerufen wird, sondern direkt auf einer elektronischen Anregung beruht. Solche nichtthermischen Prozesse werden selbst für Metalle beobachtet, obwohl die Kopplung der elektronischen Anregung an das Substrat hier besonders schnell abläuft. Der zugrundeliegende Mechanismus beruht auf dem Zusammenspiel einer kollektiven Elektronenoszillation und einer lokalisierten Einzelelektronenanregung, wobei auch nichtlokale optische Effekte in der Metalloberfläche eine wichtige Rolle spielen.
Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping
(1993)
The damping of collective electron resonances in clusters which develop into plasmon polaritons at larger sizes is investigated for free, supported, and embedded neutral metal clusters. Embedding of free 2 nm Ag clusters of 2-nm diameter into a SiO2 matrix leads to an increase of the width of the resonances by more than a factor of 3. The optical spectra are compared with the Mie theory using size-effect-modified dielectric functions of the solid state. The results corroborate the assumption that the widths of the resonances strongly depend on chemical interface effects. The results are briefly discussed with regard to limited-mean-free-path and quantum-size-effect theories and a recent approach by Persson. It is demonstrated that the widths of the spectra of supported and embedded clusters have to be interpreted with care since true intrinsic size effects of the clusters appear to be less effective than previously believed and can be obscured by the chemical interface damping.
© 1993 The American Physical Society
Coole Experimente
(2001)
Experimente mit flüssigem Stickstoff kommen in der Lehre - vor allem an Hochschulen - bislang zu kurz. Dabei gibt es schöne Versuche aus nahezu allen Bereichen der Physik, die in Lehrveranstaltungen relativ einfach vorgeführt werden können. Wir stellen hier einige Experimente vor, die eindrucksvoll demonstrieren,wie sich physikalische Eigenschaften bei tiefen Temperaturen ändern.
Haushaltsmikrowellen bieten ein interessantes Feld für einfache, teilweise spektakuläre Vorführexperimente. Mit Thermofaxpapier und Infrarotkamera lassen sich zum Beispiel die Modenverteilungen des Zentimeterwellenfeldes im Garraum sichtbar machen. Eine Reihe von Versuchen kann die Absorption durch Metalle zeigen, besonders interessant sind dabei dünne Drähte und Drahtspitzen: Lampenbirnen glühen und Wunderkerzen zünden von selbst. Mikrowellen können auch Entladungslampen starten, Wasser im Eisblock erhitzen und Eier explodieren lassen.
The physics behind the sometimes strange effects and 'unnatural' appearance of near-infrared (NIR) photographs is discussed in terms of reflection, absorption and transmission of NIR radiation with the respective objects. Besides discussing how NIR cameras work, several visible and NIR photograph pairs are presented, which include vegetation, natural water, clouds, the sky, and humans. In addition, some physics-oriented experimental NIR images are presented which clearly demonstrate some of the basic physics behind some of these awesome sights.
Rotwein zu Wasser
(2015)
Abstract
Die Sensoren von Digitalkameras sind fähig, Licht im Nahinfraroten (NIR) bis hin zu Wellenlängen von 1100 nm aufzunehmen. Infrarotfilter blockieren diesen für den Menschen nicht sichtbaren Spektralbereich, um irritierende Falschfarbeneffekte in den Aufnahmen zu verhindern. Diese Filter sind aber entfernbar, und derart umgerüstete Kameras erschließen eine verblüffende Welt. Beim Übergang zum NIR ändern sich die optischen Eigenschaften vieler Objekte. In Landschaftsaufnahmen werden Blätter zu den hellsten Objekten. Rotwein, Cola oder Kaffee werden scheinbar zu Wasser. Man kann zudem unter die Oberfläche von Farben, Stoffen, Lacken und sogar der Haut schauen.
Thermography of Microsystems
(2004)
Bei Interferometrie denkt man an teure optische Aufbauten. Doch für Schulversuche geht es viel einfacher. Auf einem Küchentisch lassen sich mit Laserpointern oder Laserdioden, Glasplättchen, Spiegeln, Linse und Knetgummi in wenigen Minuten komplette Interferometer aufbauen. Wir konnten das mit funktionsfähigen Jamin-, Michelson- und Mach-Zehnder-Interferometern demonstrieren. Sie erlauben sogar Versuche mit Proben, zum Beispiel die Bestimmung der Brechzahl von erhitzter Luft.
Die Physik der Haushaltsmikrowelle ist erstaunlich reichhaltig: Sie umfasst die Erzeugung von Mikrowellen in Magnetrons, Wellenleiter und Resonatoren für elektromagnetische Felder, die dielektrische Relaxation bei der Orientierungspolarisation von Wasser, und die Eindringtiefe elektromagnetischer Wellen in Materie. Eine Abschätzung der Bedingungen für Multiphotonenionisation und Dissoziation zeigt, dass Haushaltsmikrowellen Speisen chemisch nicht verändern können.
Max Planck legte 1900 mit dem nach ihm benannten Strahlungsgesetz das quantitative Fundament zu so genannten Wärmebildsystemen. 100 Jahre später gibt es — mit bedingt durch Fortschritte in der Halbleitertechnologie und Mikrosystemtechnik — Infrarotkameras, mit denen sowohl die von Planck untersuchten Strahlungsgesetze zur Hohlraumstrahlung als auch allgemein wissenschaftliche und technische Anwendungen der Temperaturstrahlung von Körpern untersucht werden können. Darüber hinaus bieten sich solche Systeme auch für didaktische Zwecke an, da physikalische Gesetzmäßigkeiten mit Energieaustauschprozesssen aus sehr vielen Gebieten der Physik durch eine etwas andere, physikalische Sehweise visualisiert und damit für Lehrzwecke eingesetzt werden können.
Measurements of illuminance during a solar eclipse are presented. The data are compared to theoretical predictions, based on a geometrical model for obscuration. The model assumes a straight and uniform motion of the sun and moon as well as a spherical shape of both, i.e. it neglects any effects of limb darkening. Furthermore, the sun's disk is assumed to have homogeneous luminosity, i.e. any luminosity variations due to sun spots are neglected. Input parameters are the duration of the eclipse, the duration of totality, the impact parameter, i.e. the distance between the two trajectories of sun and moon, and the sizes of sun and moon. The model applies to all types of eclipses, partial, annular and total.
nfrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes.
Experimente mit IR- Kameras
(2014)
Die moderne optische Spektroskopie kann geringste Substanzmengen nachweisen. Für schnelle Routinemessungen reichen konventionelle Zweistrahl-Spektralphotometer. Eine wesentlich höhere Nachweisempfindlichkeit im ppm- oder sogar ppb-Bereich ermöglichen das Atomabsorptions-Spektrometer (AAS) und das Fourier-Transformations-Infrarot-Spektrometer (FTIR). Ein AAS atomisiert die Probe vollständig und weist dann einzelne Elemente nach. Deshalb ist es zum Beispiel für die Schwermetall-Analyse geeignet. Bei der Analyse von Molekülen dominieren heute FTIR-Geräte. Ihr Herzstück ist meist ein Michelson-Interferometer. Zusammen mit schnellen Fourier-Algorithmen erlaubt es, sehr schnell breite Spektren aufzunehmen. Stationäre und mobile FTIR-Geräte können vielfältig eingesetzt werden.
Abstract
The brilliant visible colors of various hot springs and pools in Yellowstone National Park are explained with a combination of scattering from the water and from microbial mats that coat the bottoms of these thermal features. A simple 1D radiative transfer model was used to simulate the colors recorded in visible photographs and the spectrum of light making up these colors. The model includes attenuation in water by absorption and molecular scattering as well as reflection characteristics of the microbial mats and surface reflection of the water. Pool geometries are simulated as simple rough cones scaled to have depths and widths that match published data. Thermal images are also used to record the spatial distribution of water skin temperature. The measurements and simulations confirm that colors observed from shallow-water features arise primarily from the spectral properties of the microbial mat, which is related to the water temperature, while colors observed from deeper water arise primarily from the wavelength-dependent absorption and scattering in the water.
This article forms the second of two papers on the subject of microwave cookers. In the first paper Michael Vollmer describes the physics behind the production of microwaves in the magnetron of the oven, the waveguide and the interaction between the microwaves and the food. This article looks at the physics of cooking, and how the appliance and the food industries have developed products which are now part of many of our students' lifestyles. We include many interesting demonstrations that illustrate this history and which could be used to teach many principles of physics.
Solar load and reflection effects and respective time constants in outdoor building inspections
(2009)
The surface to volume ratio in thermal physics: from cheese cube physics to animal metabolism
(2008)
A procedure to experimentally simulate pollen coronas is discussed. Observed coronas are due to pine and birch pollen having different geometries. Using computer simulations, two-dimensional projections of a large number of pollenlike objects with adjustable shapes, with or without preferential orientation and statistical or regular spatial distribution, are generated. The photograph of the printout allows samples with typical sizes between 20 and 200 µm. Their diffraction patterns can closely resemble the ones observed in nature and predicted by theory.
© 2005 Optical Society of America
In den letzten Jahren gab es einen wahren Boom von Neugründungen so genannter Science Center. Sie sollen die Naturwissenschaften insbesondere die Physik für einen breiten Personenkreis erfahr- und lernbar machen. In loser Folge werden wir einige dieser Center im deutschsprachigen Raum vorstellen. Der vorliegende einführende Beitrag gibt eine kurze Übersicht über Konzepte, Anliegen und Trends dieser Einrichtungen.
abstract
Nature provides many beautiful optical phenomena that can be used to teach optical principles. Here we describe an interdisciplinary education project based on a simple computer model of the colors observed in the famous thermal pools of Yellowstone National Park in the northwestern United States. The primary wavelength-dependent parameters that determine the widely varying pool colors are the reflectance of the rocks or the microbial mats growing on the rocks beneath the water (the microbial mat color depends on water temperature) and optical absorption and scattering in the water. This paper introduces a teaching module based on a one-dimensional computer model that starts with measured reflectance spectra of the microbial mats and modifies the spectra with depth-dependent absorption and scattering in the water. This module is designed to be incorporated into a graduate course on remote sensing systems, in a section covering the propagation of light through air and water, although it could be adapted to a general university optics course. The module presents the basic 1-D radiative transfer equation relevant to this problem, and allows them to build their own simple model. Students can then simulate the colors that would be observed for different variations of the microbial mat reflectance spectrum, skylight spectrum, and water depth. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Infrared Yellowstone
(2017)
Abstract
Simultaneous visible and long-wave infrared (IR) images of the Moon were used with a simple energy-balance model to study the spatial pattern of lunar surface temperatures. The thermal images were obtained with a radiometrically calibrated, compact, low-cost, commercial IR camera mounted on a small telescope. Differences between the predicted and measured maximum Moon temperatures were used to determine the infrared optical depth (OD), which represents the path-integrated extinction of an elevated layer of wildfire smoke in the atmosphere. The OD values retrieved from the IR Moon images were combined with simultaneous OD measurements from a ground-based, zenith-pointing lidar operating at a wavelength of 532 nm to determine an IR-to-visible OD ratio of 0.50±0.18 for moderately aged wildfire smoke aerosol.
© 2014 Optical Society of America
Physikdidaktik in Deutschland: Ergebnisse einer Umfrage der Europäischen Physikalischen Gesellschaft
(2003)
Aufgrund einer Initiative der Division of Education der europäischen physikalischen Gesellschaft (EPS) wurde eine europaweite Umfrage zur Physiklehrerausbildung und Forschung in Bereich Fachdidaktik der Physik durchgeführt. Insgesamt wurden Fachleute in 30 Ländern befragt. Da in der Bundesrepublik bezüglich der Lehrerausbildung mit den 16 verschiedenen Regularien der Bundesländer quasi ein kleines Europa existiert, wurde zusätzlich jeweils mindestens ein Fachdidaktiker in jedem Bundesland befragt, um für Deutschland eine detaillierte Analyse vornehmen zu können. Insgesamt ergab sich in Deutschland ein Rücklauf von 22 Fragebögen aus den 16 Bundesländern. Die wesentlichen Ergebnisse der deutschen Umfrage werden im Zusammenhang mit früheren Studien und Empfehlungen zur Fachdidaktik vorgestellt.
Es werden eine Reihe einfacher Freihandexperimente zum Thema Unterdruck vorgestellt. Viele der Beispiele sind vom grundlegenden Aufbau her bekannt, gestatten jedoch neue Varianten, Erweiterungen bzw. die Korrektur von Fehlvorstellungen. Neben der Druckmessung in Einmachgläsern und der Funktionsweise von Ausgussreinigern und Saughaken werden Druck- sowie Tragfähigkeitsmessungen an Staubsaugern diskutiert. Des weiteren wird untersucht, welche Saughöhe per Strohhalm realisiert werden kann. Es wird eine physikalisch einleuchtende, aber dennoch verblüffende Erweiterung des Versuchs mit dem umgedrehten Wasserglas präsentiert.
Wahlverhalten von Schülern der Sekundarstufe II im Fach Physik seit 1990 im bundesweiten Vergleich
(2000)
Die visuelle menschliche Wahrnehmung in andere Spektralbereiche zu erweitern – dafür gibt es viele, technisch sogar recht einfache Möglichkeiten. Insbesondere die Infrarotkameras haben sich für Wellenlängen unter 15 µm zu hervorragenden quantitativen Messinstrumenten entwickelt. Zum Einsatz kommen sie in der Grundlagen- und angewandten Forschung sowie zunehmend auch in der Lehre der Physik auf Hochschul- und Schulniveau.
Diffraction revisited : position of diffraction spots upon rotation of a transmission grating
(2005)
The question of how the line spectrum of atoms is transformed into the continuous spectrum of thermal radiation of a gas by repeated absorption and emission of photons is addressed. We consider a simple model of a hydrogen-like gas in thermal equilibrium where only the Lyman-α transition is allowed and calculate the spectra for increasing thickness of the gas. The transition from line spectra for optically thin samples to the spectra of thermal radiation for optically thick samples is demonstrated. We estimate the emissivities for hot gases and study the line width of spectral lines due to self-absorption processes.