Expert answer:I need physics help with questions about light

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Ina conceptmapof physicsthe studyof lighcstandsat all the maiorintersections.
Insightsinto light illuminate
the whole of physics,just as scattered light rays illuminatea whole house.This article is not a scholarly history but
an illustrativeoverview written with hindsight,of the central role of Iight in makingconnections.
‘awakening
In 1267RogerBacon.with whom the post-medieval
began,”[2JpublishedOpusMalus.In BookV rhe
Oprlcssection of that encyclopedicwork Baconwrote,[3]
“lt is possible that some other science may be more useful, but no other science has so much sweetress
and beautg of utility. Therefore ir is rhe flower of the whole of philosophq and through it, and not
without it, can other sciencesbe known.”
Sevenhundredyearslater this motif was madeexplicitby JacobBronowski:[4]
“We see matter by light; we are aware of the presence of light bq the interruption of matter. And
that thought makesup the world of every great phgsicist, who finds that he cannot deepen his
understandingof one without the other,”
Letus beginat the beginning.
Ceometrical
Optics
‘About
10 monthsagoa rumor cameto our earsthat a
had beenmade . . . Thisfinally causedme to apply
sPyglass
myselftotally to investigatingtheprinciplesandfiguring
out the meansby whichI might arrive at the inventionof a
similarinstrument,which I achievedshortlyafterwardon the
basisof thescienceof refraction” -Galileo Galilei [5]
Navigationand surveyinghavelong dependedon the straightnessof light rays.Through the practicalexperienceprovidedby
theseactivities,the opticallawsof rectilinearpropagationand
20 Radiations Fall2014
reflectionbecameknown in antiquity.The first unifled theory in
physicscamefrom Hero of Alexandria(c. l0-70 CE), who set forth
the principlethat light raysfbllow the path of minimum distance;
rectilinearpropagationand the law of ref’lectionfbllow as consequences.
[6]
Refractionhas beenknown qualitativelyfrom time immemorial. A partially immersedstick appearingto be sharplybent at the
water’ssurfacewas mentionedin Plato’sRepublic(c. 360 BCE).
“Burning glasses,”
lensesfor startingfiresby focusingsunlight,
were part of ancienttechr-rology,
as documentedby artifactssuch
asa magnifierfound in the ruins of the palaceof AssyrianKing
(708-681BCE).Refractionwasmadea quantitative
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[ : l e g r r n t ( , o n r r c c t i < l n . si n I ) h ) ' s i c sI sciencein the Middle Agesby Muslirn scholarssuchas Ibn alHaytham(c. 965-1040),known to us asAlhazen,who introduced the practiceof measuringanglesfrom the normal for reflectedand refractedrays.Alhazen'scontemporaryAbu Sid al-Ali ibn Sahl(c. 940-1000)expressed the law of refractionin terms of the hypotenusesof right triangles.[7] Willebrord Snellius(or Snell)rediscoveredin 1621the law of refraction,which RendDescartesrediscoveredagainand publishedin its well-known sine form in 1637. Refractionmadepossiblethe lens,which made the cell and of the starsaccessible to human senses.Galileo'sStarryMessenger l6l0 arrdRobertHooke'sMicrographiaof 1665openednew worlds to investigation.They deepenedthe questions,and not only for scholars: . . . He burnedhis housedownfor thefire insurance And spenttheproceedson a telescope To satisfya li_felong curiosity About our placeamongthe infinities. -Robert Frost,"The Star-Splitter" Hero'sprincipleof rninimum distancedoesnot explainrefractior-r.That gap was rernediedby Pierrede Fermatin 1657through a broaderunifying principle:Of all possiblepathsconnectingtwo fixed points,the path followedby a light ray minimizesthe time for light to go betweenthe points. Fermat'sprinciple requireslight to travelat finite speed.Astronomy offeredthe first meaningful estimateof this speedin 1676when Ole Romer usedas a clock the periodic emergenceof Io from behind fupiter'sshadow (The moon hasan orbital period of 42.5hours.)During the time of year when Earth recedesfrom the |upiter-Io system,after eachorbit of Io around fupiter the clock is seenfrom Earth to run slow.Romer interpretedthe delayasthe time light took to travelthe additional infordistancebetweenEarth and Io. Astronomy,which possesses mation carried from the heavensto us by light, now gaveback from the heavensinformation about light itself. Lensesand Spectra "I procuredme a triangular glass-prisme,to try therewith the celebrated Phenomenaof Colours.. ." -lsaac Newton The edgeof everylensforms a prism. The rainbow of colors that emergesfrom prismswas familiar in Aristotle'stime. Received . doctrineheld that a prism somehowmodifiesthe color of light. IsaacNewton had to investigate. He made a hole in his window shutterto let in a fine beam of sunlight.The prism producedthe expectedcolorsof the rainbow,but Nervtonnoticedthe significanceof somethingelse:the circularbeam that enteredthe prism emergedas an elongatedellipse.Eachcolor refractedat a different angle.[8] With a secondapertureNewton could selectfrom this rainbow one color to entera secondprism. This prism did not changethe color.Allowing all the colorsto enterthe secondprism produced white light on its far side.A prism did not modify light but sepa'A ratedit. Newton wrote, naturalistwould scarceexpectto see ye scienceof thosecoloursbecomernathematical,and yet I dare affirm that there is as much certaintyin it as in any other part of white light into a specOptiksJ'[9]This imageof a prism separating trum and the inverseoperationof synthesizingdistinct colorsinto white light, illustratesvisuallythe mathematicsof synthesisand analysis,suchasthe harmonic seriesof Fourier'stheorem. William Herscheland his sisterCarolinemade someof the first catalogsof stars,discoveringmany binary systemsand the planet Uranus.While testinga red filter for observingsunspots,William happenedto placehis hand at the focal point of his reflectingtelescopeand noticed the region to be unexpectedlywarm. To study the temperatureof light, in 1800William insertedthermometers into the separatecolorsof the sun'sspectrum.He noticedthat in going from violet to red, the temperatureincreased.Intrigued,he placeda thermometerbeyondthe red, and there found the highest temperature.Herschelcalledthis warm invisiblelight beyondthe red'taloric rays,"which we know as infrared.Herschel'sresults were anticipatedby 63 yearsby Emilie du ChAtelet.This remarkable woman essentiallydiscoveredthe work-energytheorem,translated Newton'sPrincipiainto the Frenchtranslationusedto this day, and collaboratedwith Voltaireacrossmany years.Her opuswas Eldmentsde Ia Philosophie de Newton (1738),which went deepinto the philosophicalfoundationsof mechanicsand was influential in shifting Frenchscientistsfrom the mechanicsof Descartesto that of Newton. In 1737du Chdteletenteredan essaycompetition on the natureof fire. In her essay"Dissertationon the Natureand Propagationof Fire,"shearguedthat fire is not a materialsubstance,and differentcolorsof light transportdifferentquantities was to line up of heat.The way to demonstratethis, shesuggested, an arrayof thermometers,one insertedinto eachof the separated colorsof the spectrum,which was preciselywhat William Herschel did in 1800.du ChAteletwas not ableto perform the experiment herselffor lack of thermorneters.[10] fosephvon Fraunhofersupervisedglassmelting and grinding processes in his Munich optical institute.He neededto measure the refractiveindicesfor differentcolorsin variouskinds of glass. In one of his experiments,light from an oil lamp flame passed Fraunhofer through a prism to be viewedthrough a telescope. noted dark lines in the spectrum.Intrigued,he looked for generalizations.RepeatingNewton'sexperimenton sunlightwith his telescope-equipped prism,in l8l4-15 dark lineswererevealedin the solarspectrum. In 1857the "daring and resourcefulexperimenter"Robert Bunsen inventeda burner that produceda colorlessflame.Il 1] With Bunsen'sburner the spectraof chemicalsplacedin the flame could be cleanlyseparated.His collaboratorGustavKirchhoff added a prism to completethe basictool of modern spectroscopy, the Payoffscamequickly.In 1860Bunsenand Kirchhoff spectroscope. discoveredrubidium and cesiumin a sampleof Diikheim mineral from Franceand water.In 1868two astronomers,PierreJanssen Norman Lockyerfrom England,independentlyreporteda yellow line in the solarspectrumthat fit no known element.Interpreting it as an unknown element,Lockyernamedit after helios,Greek for "the SunJ'[12]Terrestrialhelium wasnot confirmeduntil 1895 when William Ramseyisolatedit as a byproductof uranium ore. In 1907ErnestRutherfordand Thomas Roydscollectedalpha particlesemittedby radioactivedecay,examinedtheir spectra,and showedthat the particleswerehelium. C l a s s i c aM l echanics "Followingin thefootstepsof Hero and Fermat,he IMaupertuisl thenproclaimedthat thissimplicitycausesnatureto act in sucha way as to rendera certainquantity,whichhe namedthe'action,'a ntinimum."-Wolfgang Yourgrauand StanleyMandelstamI l3] 2l F al l 2Ol 4Radi ari ons I ElegantConnectionsin Physics After Newton revolutionizedopticshe turned to mechanics. Generalizinginductively from specificproblems solved in quantitative detail [14]-Archimedes on the lever,Galileoon projectiles, Huygenson the pendulum,and Newton himself on gravitation-he postulatedin 1687three lawsof motion that turned mechanicsinto an axiomatic system.As the laws of geometricaloptics could be derived from Fermat'sleasttime principle, could the samebe done for mechanics?Severalproposalswere forthcoming. Theseincluded fohann Bernoulli's 1717principle of virtual work for statics,extended to dynamicsby |ean le Rond dAlembert in 1743. Around 1740PierreLouis Moreaude Maupertuis(who tutored young Emilie du ChAteletin calculus)suggestedthat a particle acted on by specificforcesmovesin a way that minimizes the "action." This approachwas successfullydemonstratedfor central forcesby LeonhardEuler in 1744.Inhis MicaniqueAnalytiqueof 1788,Joseph LagrangegeneralizedMaupertuis'principle to all conservative 'hction" forcesand clarified as the line integral of momentum. The generalizationof this principle to all of mechanics(later extended to most of physics)was published in two papersby William R. Hamilton in 1834-35.[15]Hamilton'sprinciple postulatesthat of all L r s e d b v p e r n r i s s i < - r nf r o n r A P I . 2 o l 4 t l i ( t l r S c l r o o l P h r s i t s P l r o t o C o r r t e s t . " (Ci k rxllliirrttqq R e f r a c t i o r r , " b v C l a i r e l r r r r : rl s a b e l l e S a l o f f - C o s t e . l t h a r a l l i q h S r l t o o l . the conceivabletrajectorieswhereby a particle might travel between two fixed points, the trajectory actually followed minimizes the time-averageddifferencebetweenthe particle'skinetic and potential energies.The principles of Hamilton and Fermat arosefrom similar motivations,but a logicalconnectionbetweenthem would haveto await generalrelativity. Ontology "From the multitude of experiences it [science]selectsa few simpleforms, and constructsfrom them, by thought,an objective world of things."-Max Born [16] "Youknow somethingand then the qualitystimulushits . . . , but to defineit all you'vegot to work with what you know. So your definition is made up of what you know. It an analogue to whatyou alreadyknow."-Robert Pirsig [17] A debateabout the ultimate realityof light beganin the time of Plato and the Sophists.By the time of Newton and Huygens,those arguingthe question"What is light?" faceda binary choice:What 22 Radiarions Fall 2Ol4 is light-wave or particle?Robert Hooke'sMicrographic describes how colors of thin films dependedon a film's thickness,suggesting a standing wave condition. Christaan Huygensarguedthat the tremendous speedof light would be feasibleonly if light was a disturbancethrougha medium, not the bulk motion of a medium. He gavethe wave hypothesispredictive power by postulating that each point on a wave front behavesas the sourceof another wave.If that were so, then light should radiate into regionsthat would otherwise remain in geometric shadow.Hooke and FrancescoGrimaldi had noticed diffraction in the fine structure of shadowscastby a needle. Initially ambivalent ("I make no hypotheses"),Newton eventually argued that light was a beam of particles.While acknowledging that somethingperiodicoccurswith waves(and discovering an interferencepattern called "Newton'srings"), he interpreted the periodicity as something that matter does fo light. To Newton, the diffraction reports did not require light to be a wave.Gravity acts betweenseparatedmassivebodies,so matter could bestow its periodic influenceon light from a distance. Refraction offered one way to decidethe question.When light passesfrom air into water the ray bends toward the normal. If light consistsof waves,the speedof light in water would be lessthan its speedin air. If light consistsof particlesthe reversewould happen. In 1800Thomas Young demonstratedthat the interferenceof light passedthrough a double aperture.Sucha pattern could be interpreted only as the superpositionof waves.Augustin Fresnel worked out a comprehensivetheory of diffraction basedon the assumptionthat light consistsof waves,and his predictions were vindicated, famously so with the notorious "Poissont spot,"a bright spot, due to wave diffraction, in the shadowbehind an illuminated disk. In 1850Ldon Foucault measuredthe speedof light in water and found it to be lessthan the speedof light in air. The riddle "What is light?" seemedanswered.[18] Lingering questionsremained,as they alwaysdo with important questionsthat have multiple layers.First, supposinglight to be a wave,what is waving?Second,acousticalwavesrequire a medium; what servesas the medium for light, the "aether"?Third, light had been found to be polarized by bifringent crystals.Reconciling polarization and the rapid speedof light with our ability to breeze freely through the aether offered a perplexing situation. Elecrromagnetism "Maxwell shewedlight to be an electromagnetic phenomenon, so that the wholescienceof Opticsbecamea branchof Electromagnetism. . .." -famesJeans[19] Hints at a connection betweenelectricity and magnetismcame when Hans Christian Orsted showedthat moving electriccharge makesmagnetismand when Michael Faradayshowedthat changing magnetismmakeselectricity.A unified theory of electromagnetism was written by IamesMaxwell in 1862.Action at a distance,which servedwell for staticinteractions,was replacedwith the dynamic conceptof the field, a function of spaceand time. The interactionsof matter proceedthrough fields.On one hand, local fields tell a particle of matter how to move. Newton'ssecond law with the Lorentz force,for instance,predicts the motion of a chargedparticle in responseto electromagneticfields.On the other hand, matter determinesthe fields around it. Maxwell'sequations relatethe electric and magnetic fields to their chargedparticle sourcesand relatethe fields to eachother. When a chargedparticle Maxwell'sequationssaythe fields it producesmust accelerates, I C t s ll c t f I r li tl s L,legantConnectionsin PhvsicsI change.A changingelectricfield producesa magneticfield that also changes,and the changingmagneticfield producesa changing electricfield. Togetherthe changingfields rnakea self-propagating wavemoving at the speedof light. In responseto the "What is waving?"question,light must thus field! The equationsdescribingthis be a wavein the electromagnetic wavehaveno restriction on the frequency,suggestingthe existence of a continuouselectromagneticspectrum of harmonics whose frequenciesrangefrom zero to infinity. The equationsalso saythat the propagatingfields are transverseto the direction of wavetravel,implying polarization and explaining the effectsof bifringent crystals. In 1886-89 Heinrich Hertz affirmed Maxwell by broadcasting and detectingradio wavesin the laboratory.While doing so the alert Hertz noticeda spuriousglitch in his apparatus.Radiationof low intensity but sufficiently high frequencyimmediately stimulatesan electriccurrent in certain materials;at low frequenciesthe incoming light producesno current even at high intensity.Dubbed the photoelectriceffect,this anomaly in the interaction of light with matter did not fit Maxwell'stheory. For two decadesit remaineda mystery. Maxwell had answeredimportant questionsabout light, but others remained.The equationssaythat electromagneticwaves need no medium, that they travel in empty spaceat the speedof light, c, but the equationsare silent on the frame of reference.In 1895l6-year-oldAlbert Einsteinwonderedwhat he would observe if he rode on a beam of light. Intuition said that Einstein'slightwave surfer should observea stationary crest of the electromagnetic wave.But Maxwell'sequationsinsist that electromagneticwaves travel at speedc even from the surfer'sperspective!This paradox, like all paradoxes,suggestedthat the question should be restated. Einsteinheld the questionin his mind for l0 years.Then the 26-year-oldEinsteinwrote "On the Electrodynamicsof Moving Bodiesl'noting that "Maxwell'selectrodynamics-as usuallyunderstood at the present-when appliedto moving bodies,leadsto asymmetriesthat do not seemto be inherentin the phenomena."[20] The relativemotion betweena magnetand a coil of conducting wire illustratesthe issue.Whatever the referenceframe, the relative motion resultsin a forceon the chargecarriers,driving an electric current in the coil. An observeraboardthe coil seesa changing magneticflux as the magnet sweepsby. Faraday'slaw saysan electricfield E getsinducedin the coil, producingthe force4E on the charges.An observeraboard the magnet seesa different picture. The coil sweepsby with velocity v, carrying the chargedparticles through the magneticfield B. Each chargeq feelsthe force qvxB. Thus do distinct mechanismsdescribethe sameresult,an asymmetry in the explanationnot inherentin the phenomena.Einstein wondered what principle would unify the two explanations. The thought experimentabout light surfing suggesteda clue in light itself.If you ride on the beam of light that bouncesoff a clock at 10:00am, then you staywith the information that says the time is l0 o'clock.[21]For the light-wavesurfer,time stands still. Newtonian relativity of inertial framespostulatesthe separate invarianceof length and time intervals;as a consequence,the speed of light must be relative.Einstein replacedthose assumptionswith the postulateof the invarianceof the speedof light betweeninertial frames,which requiresspaceand time intervals to be relative. Mechanicshad to adaptto light, insteadof the light adapting to mechanics. Specialrelativity,which linked light to spaceand time, also linked light to massand energy.Energy and momentum became the time and spacecomponentsof a vectorin four-dimensional space-time.Its geometrywas not Euclideanbut hyperbolic. The squareof the energy-momentum four-vector was given by a difference,not a sum, with the particle'smassas the vector'smagnitude. For a free particle,E - (pc)' - (mct)t. Thermodynamics and Quantum Physics "By 1906or 1908Planck had cometo seethat his compromise over cavity radiation had loosedsomethingbrand new and -J.L. Heilbron l22l menacinginto the world of physics." The thermodynamics of light motivated the extensionof Newtonianmechanicsto quantum mechanics.Macroscopic thermodynamicsservesas a boundary condition on microscopic statisticalmechanics.After many triumphs with enginesand phase changesand the kinetic theory of gases,statisticalthermodynamics confronted the question of finding the energy density of light as a function of frequency.Light and matter in thermal equilibrium was produced in the laboratory by a metal box held at temperature T. The atoms in the box walls are made o ... Purchase answer to see full attachment

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