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# Basic Physics III Lecture 12

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Erkannte Entitäten

Sprachtranskript

00:05

so soviet talked about a amorous last time and images and

00:10

you might remember that I gave this equations and help you to find the location and size image given that you not these location and size of the object just as a reminder creation relates distance Of the object to the core of me 0 lead distance of the image with America Adams Media focal length of the focal length Air Force won all import From now and that it is given by with a radius of curvature divided by vendor magnification of the image that the height of the image H I'm divided by hired of the object 0 0 is given by minus V a distance of the image divided by the distance of the object of with these radiation you can always find an position as well as the size of the image this equation is valid both for concave and convex and their prevention that for concave because assume a radius of curvature is bigger than your therefore focal length because and floor for Convex Melrose this year it is the other way around foreplay Melrose won over the radius and 1 over the focal length equal zeros a costly most focus 1 special case of the equation parallel life gets always reflected in the Beemer equation is also valid for us both real and virtual images show up writing images and images for objects and the images in front of the world behind and if they're multiple lows and the problems that you can apply a Murray creation sequentially and image of the 1st becomes the object of the 2nd and M is called lateral magnification and for the equation to right to be very careful with the signing of various Kwan when news sold by a Member of problems you should always draws a rate diagrams as a cross-check even if you're going to calculate analytically ever image is going to be in what size it's going to have 1st already diagrams so that you know the approximate and then apply the equation and magnification equation be careful with the signs left of the rarest positive underwriters negative operators positive and is negative and then checked the analytical solution with diagram make sure that the did make a mistake

03:27

an example of a let's assume we have 0 1 centimeter high object that is 10 centimeters in front of a concave and the radius of curvature is given a 30 centimeters so the 1st ponders draw array diagram to locate approximately the position of the image then add we we calculate the position of the image and magnification and the soulful pot a broad array diagram fully heavy object given by points TO and the only draw the race for the top of the object of the 1st Ray redraw is via a parallel array of its rating on 1 of goes parallel to the optical axis here and parallel rays get a reflective tho the focal point so therefore for this race continues like rips the next jurists focal race that is a that uh that goes through the focal point of connects focal points the top of the object than those raise always get reflected apparel Powell raised a bit reflected from the focus and vocal raised the apparel so this way therefore it goes to respond here and that is reflected in the apparel race to them and mostly is Leon sentry gray so that that connects the standoff the sphere of the object for this end of this year and almost always given by the way itself incident angle 0 and a reflected and would also 0 on subject raise Our reflected on top of each other so it goes like this and that's reflected back onto itself and the along the century that hits the center of the world In that case there is no difference between a plane of crude we actually the incident angle and we can draw the reflected Angolan gets reflect the of course to relocate image tool of those forays are sufficient but if you draw more venue increased accuracy finding the image so in this case as we reflected raised they at virtually that means that the images virtual and behind the rural drawn in by dashed lines here so we could just continue those reflected raised with dashed lines Tilda needed some point and that this be the location of the image . 4 top object so now that they have done that we go to the beat hard and calculated analytically used America creation for the image so 1 over the image distances 1 focal length minus 1 over the object of a focal length half of the radius of 15 cm soared this becomes 1 of 15 cents then add the object's distance distances 10 sending me for 2nd term marijuana with tents and if we had had this entire calculator then that we gets that the image distance must be minus 30 sending and so the analytical solution also tells us that the image is behind in the world because this distances wall or tells us that the images given the object just like it looks like drawing him and so that seems to be consistent from our we applied magnification creation of the ratification is given as a ratio of minus the image distance of the object minus the image distances must be sent and public distances still 10 said so we get our magnification factor for because the magnification has a positive sign it means that the orientation of image it's the same as the orientation of the object ever up right virtually emerged this bad

08:04

happens to be the case for concave most of the object is placed closer than the focal length so if you had an object closer than the focal length and bit of virtual image that is bigger than the object and abused behind object that uh make use of the shaving most of our cosmetic it about half it's always half the Raiders call stroke spherical and know it there rule over the images a version will over age Rio but larger there are lots of rules that you can find out radio from the occasional by by dawn raid so 1 of those rules is that if the object of concave mirror the object is closer than the focal length then the image will turn out to be a virtual and it will be up for a while if it's further away than the focal length than the image will be inverted and they will be real effects placed at twice the focal length which is at the center point is located magnification will be equal to 1 so image and object will be the same size and image will still be Real and do so that all such rules but Bell whole bunch of them they are not completely general because area have different rules for concave and convex mirrors and so I don't mention all but dead yes there are such rules and another Wooldridge ritual later that if you have a convex no problem concave and the image is always a good show that must be it the plaque how to get ready for a great number 4 is like reflection on on the plenary so this wrangle with respectively are horizontal from incoming rate must be the same as that angle with the deflected were and that is because this horizontal line as the normal edema or whether it has positive or negative curvature of playing so at SSA you don't necessarily need all 4 race was just the mall raise you draw as more accuracy you get Over the images coming back to this example as so this is made use of 4 for cosmetic nozzle shaving and the reason by whites use of this because you want some magnification see yourself better demand for you so associating a concave knows or cosmetic are complete with a relatively long focal length so that when you stand in front of them your close 1 focal length therefore you give up right image that there's virtually meaning that it's on the other side of the room and the image will be magnified compared to the original and you can try that out by standing far away from low-cost medical shaving and you will discover that too get them an inverted image of you look up but if there's an amateur there is still wanna see the image and the way our eyes of filters became focus on our list of Poland and focus on close objects and distant objects don't Eminem said they emit almost peril erased because the following months and Close objects on the other hand where will put beverage in Rio not accustomed To the situation where we have converging it seemed to come together so if he stepped in front of the image of books spherical than we just see a bureau because the I cannot cannot focus is sort of dear being more extreme then an infinitely close object if you move on object with close to guys who can't focus on it and war and this sort of this light moving the object inside eyeball and still not I'm not focus on it anyway so are virtual images can always be seen since it can't stepped in front of their behind the figurehead let's talk now a convex mirrors so the Convention for a convex mirrors that we sign a negative curvature of the reviews of small and therefore the focal length small organs and I said earlier the images are always virtual and up pride in that case and we can go all right diagram just like we did before so the only thing now that we have to remember is that these focal point is on the other side so we draw of peril Ray this it will become a focal Ray and focuses on that side means dips reflected light that's straight line as if it came from the from the focus that we can't centigrade gets reflected on itself also just like before if we'd all be vocal rate from the object then again we we have to use this focal point we draw the line donned a year and then it will get reflected parallel just like it was for the concave so let me at all the formulas also still holders before so he I have my air convex mirror and and now plays an object of this and you can see the image being back here and no matter how close I move the image will always we may not right and it will always smaller than the object conjugate iii magnification and no magnification and we can change be would show off of and then the image will get smaller do that another interesting thing is if I could rid of concluded of the object instead of please mean that if I have a parallel being of a raise after they hit the memorable diverge as if they were coming from a point which is a focal point and that is true even if that means coming if it coming at an angle then will no longer Come from the focal point but it will come from a point in the focal plane from some point in spleen that's not all I calculate an example for the convex mirror so let's consider an external review column and those ought to be convex let's say it has a curvature of 16 meters and that means that we have the quality Murray creation will have to to assume that has a radius of curvature minus 16 meters because a it's convex mirror so they problem is to determine the location of the image and its magnification phone object that is 10 meters away from the and even tho we had to be in and rule that you should always draw diagrams in this case it is difficult to do so because of the scale of the problem it kind of looks like me an array diagrams that we had just before but this a difficult to draw to scale Saunders case dispensed with the exact read underground and a mold work directly To corrasion and against all 4 1 over the image distance which just 1 of the focal distance minus 1 all object and since it's a 16 meter courage Romero that means that the focal distance is my is what our 8 meters and therefore 1 always minus 1 so we have mine is 108 meters track miners 1 over 10 meters the distance of 1 over the object distance and we get

17:38

that the image distance is minus 4 . 4 4 and that means that the images on on the other side of the road which is always the case for a convex endeavor that is confirmed by this as an inaccurate and radar program which is not the problem then we can now determine the magnification the magnification as some minus the image distance divided by the object's distance or 4 . 4 4 meters divided by 10 meters and that means the magnification is . 4 4 4 so as see these powers of followed a 44 percent of the school it bird that is because Convex Murrow and that means that to be a focal length is minus 8 and now it's simply because it's a convex nor all convex Norris have negative focal length so so so that his convention otherwise equation will not work for Quebec's Of course negative a radius doesn't really make sense so it's is simply area signed a minus sign to make region correct kit that's why it's minus 1 plus 1 and the images are pride and a virtual before we continue with refraction I'm going to tell you the the solution of the little puzzle I gave the last lecture and the puzzle Wallace come back the cleaner and roads left and right but it doesn't end up and down and the answer that With that readily that remember me that converts left and right often down it front and back when you raise your your your right hand in the mirror image will also raised a hand that is on the rise it is just the imagined image being a person in their music sort of hour ahead we rotate the image around a around the vertical direction but in reality what is true is that the image has the face on the other side and the back the real Joe and therefore injured fondant back and not left and right now or up-and-down down and therefore cause of it's completely symmetric revenue to have sideways Bob put anything like that so now let's continue from a reflection tool refraction and as a sort of introduction to that these sequences again the speed of light so I came back the speed of light is the same in all frames of reference and the constant of nature of this cannot be changed as always 3 times and they need of Passaic 2nd even if you move vote with respect to the light source the personal watching however and of course there's no signals beat faster than have in this life however 1 c light travels in a medium like water or air or anything anything that is not your them add it slows down so the Lightspeed is no longer constant along with volume and how much it slows down will depend on on on the need and we can define an index of fraction which describes how much slower like that index of a fraction minutes or velocities and given speed of light and vacuum divided by that index of refraction and in a uh this index of refraction is close to what is a table off of index of refraction for various materials so vacuum of caused by definition exactly equal to 1 and you see that they it's slightly bigger than 1 by a would approximation it's also won and then out of water 1 . 3 alcohol is 1 . 6 and be a 1 of the allow largest index of the fact that you can find Diamond the index of refraction 2 . 4 2 0 0 0 the speed of light in diamond much slower and more than a factor of tools to describe a refraction reviews of the so-called snarls law solo wave that a boundary and the speed of propagation use different of both reflected and refracted so we can defying incident angles moves will still be defined and normal to the boundary surface for example we can air and water and we define an incident angle of the incidence rate with respect to be this normal and be defined for the reflected the way we can define a reflection angle and for the refractive parade redefined a refraction angle the normal and then the full list of it snarls not be index refraction the incident times the sign of the incident and equals an index of refraction and the need for the refracted been times the size of that Act and that means that day these index of refraction here smaller than that uh that banned the library toward formal and the other cases and away from from them and here is the reverse case we actually have a ray coming from water into air so we ran away from the normal and of course there incident index of refraction index of

24:19

refraction change position

24:22

so we can actually partner to list In reality so did I have a tank of water and a light beam that I can change the angle with us and the normal is given by this by this black line and if for example I have incident angle of 40 degrees when have our refractive and off of 30 degrees and moved to 80 degrees incident angle than I get refractive angle of 40 degrees and you see that he refracted and will always the small loss he have 80 degree angle then it's very difficult to see the refracted a beam at all because the close I get tool glancing incidence of the reflection refraction and he cannot also enlisted fixture let's say I have an incident angle water 30 degrees than I get about 45 degrees for be refracted angle or 20 degrees the incident and the union 30 degrees or so refractive angle and if I have normal incidents than the angle are still normal incidence and the same is true if I lose each normal incidence is not changed so because of snarls along a ridge can also are formulated in this they don't the index of refraction we can find it in terms of velocities and then you usually say the racial of incident refracted angle of the signings is equal to the ratio of velocities there you incident radiant over the human flesh this leads a bunch of

27:01

optical illusions in America water for example for example if you watch somebody else's lakes was halfway in the Lord of the seemed ready to shore and the reason for that is that you assume that like troublesome straight past but in reality of lightweight coming from the foot is refracted Beckett fans away from the normal and so you see the TO when in reality stone and by the same token as you always underestimated the depth of a body of water always looks shallower than men and really it's anybody was ever the dived and most of its true so let's say let's sculpted an example lists of the snails law long so let's assume we have a slab of and light strikes the glass over the incident and below 60 degrees and the question is what it is the angle of the old boring lightly after it passes through the glass back here and to answer that the apply smells law the 1st surfaced that gives us that this angle 8 of the size of that and favor must be equal to the signing off 16 degrees divided by a 1 . 5 because I want foreign fighters index of a fraction in glass and assume that the index of refraction and here's why and if we perform these

28:46

operations then we get that sign of favor a must be equal to . 5 7 of war and this corresponds to an angle favor 80 of 35 . 3 degrees so now we observe that this refractive angle favor it's the same angle the incident angle for the 2nd Circuit look so therefore we know what we incident angle is for for the 2nd surface and we can apply snarls again at the 2nd for this time multiply sign of 35 . 3 degrees I want to fight and die if we do that then we get . 8 6 6 for the has signed off of the out 1 that goes back out of it and that means that beat equals 60 degrees again and therefore we observed that if you have a slab of material even if it has an index of refraction that that's different from it doesn't change the direction of the race but it apparel shifts so instead of the going like this would normally gone it is now shifted by some by some distance s between me all regionally and effective this shift is actually given by an an hour the form of few so let's make both were another example of let's assume that sumo has dropped her goggles and pull and the pool was marked as being 1 meter deep however when you look at our Bible said on seem to be that deep the question is why and also how deep the goggles appear to be when you look straight down the answers we consider parade bundle from the goggles just small angles from the so we assume that she'll directly down and the world are from above and therefore the the only consider race that deviate from the the normal direction tight and if you do that then the angle theta while on the direction of respect the vertical which is also the normal is or is also the incident angle and we can apply snarls along but we do it approximating the sine function with the argument of the sine function we can't let it sufficiently small so in this case stayed at tool is approximately equal to sign is equal by smells not to end what times signed what it is approximately equal to wear and water at times don't want so smells law comes a lot simpler for the small angle approximation simply faded to equals and water watch and tool would be born in rate once it hits you if we assume that the position of the rail refract with respect to the position of it's called X than you observe the tangent of fatal won the award is given by this distance X divided by the depth of his excellent if we define Prime Minister apparent depth Of the pool meaning if it continued those raise interest rates power than they would needed a point that above the goggles and we have a similar relations are only now that we have deep prime and X so the tangent of faded equals XOT prime not only was again the fact that those angles of small and for small angles also the tangent function can be approximated by the argument of the function so we can say that they don't want equals X and faded to equals X. With prime so now we can actually solved the problem so deep frying equals X. overstated so that's using this equation and now we plugged in 4 x this equation of this means that we get Exel with I'm sorry for what they did to me now snails law that means that faded tool is approximately air and water times they don't want so instead of Exel with to get XO favor 1 divided by and lot is the depth divided by and what using the relation between fado 1 X and and since we know the index off a fraction of what which is 1 . 3 3 who appears to be 75 sending people got seem like the depth of 75 sending Sorin general if you look straight down the wobble water looks weak orders as steep Lee refractive index is a function on all of the frequency or wavelength of the light so therefore red light air refract differently from violent life and 1 can therefore splitter being consisting of many women's into separate monochromatic sold of for example these our users Is the index of refraction for fused quartz as a function of the wavelength you see that the index of refraction is becoming a bigger boat shorter wavelength and this is also true for various other materials all of this you and if we actually make tools surfaces at an angle and called for the weekend Split light of many Carlos many into a separate meetings which have only 1 color so that is also called the spectrum and the typical example for such a spectrum as a rainbow in the case of a rainbow on there's no president but we can replace the glass prisms picture that for example shown here with droplets of water and that if the sun is behind you and the index of refraction different for different wavelengths and therefore a red light debts or the red light in the sunlight gets refracted differently and violent life will be and therefore diabetes color separated and you see bands of color so

36:07

if Europe I about the ground and the Rainbow was actually a full circle depend see that if you look at clouds place where do need out of water droplets India for example rain and there's actually want reflection also from the far side of the draw so the Rainbow always appears if the sun is behind you and you are looking for example a waterfall and let's briefly discuss difference between them the spectrum and Carlos so just like for a fuller sound developed with things that physical phenomenon and there's a sensation and e-mail brain the latter it's not just determined by the physics but also by eyes or construct the soul of the spectrum is produced by different with a wavelength of frequencies for the however of 3 color receptors and time therefore I have free Priory Carlos the and see what we call Carlos the relative sensational those 3 receptors and in physics and we don't have 3 principal Carlos we we just have Cleveland and frequency as a consequence the air the Rainbow doesn't have all possible Carlos their color missing for example brawl and also the physical spectrum there's no connection between the and the red while Schumann beings with call on a

37:49

continuous scales are going from being ruined the violent from the violent into the that any shade of colors possible for the wavelength of course that is not possible for 109 leaders connect to 7 so I have a last remark about refraction as since just like for the pulse transmission the 2 discussed for waves on honor roll boundary at the the Bonn reader feels can only vibrated 1 particular frequency and therefore the frequency of the of the waves is not changed by the press and therefore the wavelength has to change because we waste speed changes since the Braves speech sealed and the wavelength has to be and have or a wavelength In ne in vacuum divided by the index of refraction so WaveLAN stitch sort of inside of me medium the outside a day let's

38:59

continue that thought the example next time

00:00

Höhentief

Parallelschaltung

Konfektionsgröße

Leisten

A6M Zero-Sen

Blei-209

Brennspiegel

Hobel

Brennweite

Überlagerungsempfang

Negativ <Photographie>

Elementarteilchenphysik

Speckle-Interferometrie

Multiplizität

Front <Meteorologie>

Stardust <Flugzeug>

Höhentief

Schreibstift

Eisenkern

MIR <Physik>

Puma <Panzer>

Rückspiegel

Front <Meteorologie>

Längenmessung

Intelligenter Zähler

Eisenbahnbetrieb

Paarerzeugung

Honen

Brennspiegel

Demultiplexer

Übungsmunition

Passung

Strahlung

Cocktailparty-Effekt

Jahr

Theoretische Mechanik

Ion

03:27

Gesteinsabbau

Anrufbeantworter

Wasserwiderstand

Parallelschaltung

Gürtelreifen

Konfektionsgröße

Diwan <Möbel>

Geokorona

Schwächung

Staustrahltriebwerk

Leitungstheorie

Abformung

Brennspiegel

Amplitudenumtastung

Breitbandübertragung

Grau

Brennweite

VHS-System

Wagenheber

Monat

Brennpunkt <Optik>

Dual-in-Line-Gehäuse

Höhentief

Array

MIR <Physik>

Kaltumformen

Bleibergbau

Rückspiegel

Längenmessung

Licht

Klopfen

Paarerzeugung

Brennspiegel

Gedeckter Güterwagen

Übungsmunition

Passung

Werkzeug

Führerstand

Spheric

Weiß

Satzspiegel

Atmosphäre

Jahr

Lineal

Rungenwagen

Optisches Filter

Anstellwinkel

Gewicht

Maßstab <Messtechnik>

Bergmann

Besprechung/Interview

Schusswaffe

Rootsgebläse

Hobel

Bildqualität

Steckkarte

Nanometerbereich

Rauschzahl

Überlagerungsempfang

Buick Century

Speckle-Interferometrie

Kraftfahrzeugexport

Klangeffekt

Parallelschaltung

Kraft-Wärme-Kopplung

Front <Meteorologie>

Potentiometer

Brennpunkt <Optik>

Stoffvereinigen

Minute

Munition

Telefon

Fehlprägung

Maske <Halbleitertechnologie>

Sprechfunkgerät

Fußmatte

Hochseeschlepper

Brennweite

17:38

Magnet

Mikrowellentechnik

Drehen

Radar

Interstellares Gas

Konfektionsgröße

Lichtgeschwindigkeit

Leistungssteuerung

Minute

Staustrahltriebwerk

Brennweite

Bildfrequenz

Fahrgeschwindigkeit

Endeavour <Raumtransporter>

Elektrisches Signal

Rückspiegel

Rollsteig

Licht

Längenmessung

Bildfrequenz

Energielücke

Übungsmunition

Werkzeug

Reflexionskoeffizient

Atmosphäre

Licht

Vakuumphysik

Interstellares Gas

Anstellwinkel

Elektrisches Signal

Leitrad

Blechdose

Diamant <Rakete>

Erdefunkstelle

Schusswaffe

Nanometerbereich

Rückspiegel

Rad

Brechzahl

Lichtbrechung

Überlagerungsempfang

Brechzahl

Speckle-Interferometrie

Vakuumphysik

Tagesanbruch

Kraftfahrzeugexport

Stardust <Flugzeug>

Stunde

Tag

Band <Textilien>

Dampfbügeleisen

Lichtbrechung

Nassdampfturbine

Mikrowelle

Kit-Car

Material

24:22

Atmosphäre

Konfektionsgröße

Gas

Gauß-Bündel

Oberfläche

Optik

Leitungstheorie

Radialgebläse

Brechzahl

Fuß <Maßeinheit>

Lichtbrechung

Schiffsrumpf

Glasherstellung

Fahrgeschwindigkeit

Fuß <Maßeinheit>

Brechzahl

Flachstahl

Höhentief

Licht

Gauß-Bündel

Rotverschiebung

Schwarz

Proof <Graphische Technik>

Glasherstellung

Minute

Spannvorrichtung

Werkzeug

Atomhülle

Nassdampfturbine

Nassdampfturbine

Optische Täuschung

Reflexionskoeffizient

Diesellokomotive Baureihe 219

Schlagwerk

Edelsteinindustrie

Optische Täuschung

Licht

Grubenausbau

Hochseeschlepper

Anstellwinkel

Kampfflugzeug

Anstellwinkel

28:46

Rucksack

Anrufbeantworter

Nahfeldkommunikation

Flüssiger Brennstoff

Gauß-Bündel

Leistungssteuerung

Optisches Spektrum

Wasserbeckenreaktor

Trenntechnik

Snelliussches Brechungsgesetz

Sänfte

Längenmessung

Freileitung

Reihenschwingkreis

Übungsmunition

Farbcodierung

Werkzeug

Tinte

Regentropfen

Juli

Jeep

Reflexionskoeffizient

Schwimmer <Technik>

Licht

Anstellwinkel

Balg <Technik>

Quarzglas

Armbanduhr

Be-Stern

Brechzahl

Schiffsrumpf

Rotor <Drehflügel>

Glasherstellung

Gruppensteuerung

Brechzahl

Energielücke

Stunde

Relativistische Mechanik

Intelligenter Zähler

Farbton

Munition

Minute

Wellen-Naben-Verbindung

Siebdruck

Gleichstrom

Rundstahlkette

Pulsphasenmodulation

Schnecke <Maschinenbau>

Material

Summer

Wafer

Erder

Schlagwerk

Umbra <Astronomie>

Starkregen

Sonnenstrahlung

Stromschiene

Merinowolle

Optisches Spektrum

Schwächung

Oberfläche

Ampulle <Technik>

Boot

Himmel

Flachstahl

Dose

Wellenlänge

Schiffsklassifikation

Kaltumformen

Licht

Regentropfen

Atmosphäre

Schiffsrumpf

Direkte Messung

Anstellwinkel

Atmosphäre

Wolke

Tonfrequenz

Lichtbrechung

Elementarteilchenphysik

Starkregen

Wasserbeckenreaktor

Wälzfräsen

Stardust <Flugzeug>

Edelsteinindustrie

Steckverbinder

Schall

Sonnenstrahlung

Tonfrequenz

Umreifen

Eisenbahnbetrieb

Proof <Graphische Technik>

Glasherstellung

Rotverschiebung

Dampfbügeleisen

Lichtbrechung

Schmalfilm

Nassdampfturbine

Nassdampfturbine

Mischstufe

Buntheit

Grau

Trenntechnik

Photographische Platte

37:47

Naht

Maßstab <Messtechnik>

Besprechung/Interview

ELBE <Teilchenbeschleuniger>

Tonfrequenz

Leisten

Wellenlänge

Optisches Spektrum

Drahtgebundene Übertragung

Druckmaschine

Lichtbrechung

Fiat 500

Walzmaschine

Brechzahl

Seil

Elle <Maßeinheit>

Stardust <Flugzeug>

Schreibstift

Wellenlänge

Tonfrequenz

Optische Dichte

Feldeffekttransistor

Tag

Lichtbrechung

Farbcodierung

Abtriebswelle

Licht

Vakuumphysik

Mikrowelle

Buntheit

Direkte Messung

Segel

### Metadaten

#### Formale Metadaten

Titel | Basic Physics III Lecture 12 |

Serientitel | Basic Physics III |

Teil | 12 |

Anzahl der Teile | 27 |

Autor | Smy, Michael |

Lizenz |
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DOI | 10.5446/12948 |

Herausgeber | University of California Irvine (UCI) |

Erscheinungsjahr | 2013 |

Sprache | Englisch |

#### Inhaltliche Metadaten

Fachgebiet | Physik |