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1、IntroductiontoIntroductiontoStatisticalMechanicsStatisticalMechanicsMinHuangChemicalEngineeringTongjiUniversityClassicalMechanicsClassicalMechanicsReviewReviewIntroduction•WhatisStatisticalMechanics?•Abranchofphysicsthatappliesprobabilitytheorytothestudyofthethermody
2、namicbehaviorofsystemscomposedofalargenumberofparticles.•Statisticalmechanicsprovidesaframeworkforrelatingthemicroscopicpropertiesofindividualatomsandmoleculestothemacroscopicbulkpropertiesofmaterials•Explainingthermodynamicsasaresultofclassicalandquantum-mechanicald
3、escriptionofstatisticsandmechanicsatthemicroscopiclevelFermat’sPrincipleinGeometricOptics•Inhomogeneousmediums,thelightraysgostraight.Attheinterfacebetweendifferentmediums,lightraysgetreflectedorrefracted.•1658theFrenchmathematicianPierredeFermatdemonstratedthatallth
4、reeofthelawsofgeometricopticscanbeaccountedforontheassumptionthatlightalwaystravelsbetweentwopointsonthepathwhichtakestheleasttime(or,morerigorously,theextremaltime)Fermat’sPrincipleinGeometricOptics•Fermatalsoassumed•lighttravelsmoreslowlyindensemediathanitdoesinair
5、•Theopticallength,isdefinedbytheactuallengthofthepathtimestheindexofrefractionofthemedium•Allowingtheindexofrefractiontovaryasafunctionofthepositionn(x),theopticallengthisgivenbyl=∫n(x)dl222wheredl=(dx)+(dy)+(dz)isthelinesegmentalongthepathFermat’sPrincipleinGeometri
6、cOptics•Fermat’sprincipleis•Inotherwords,timestatedmathematicallyastakenforlighttotravelalongitstrueoractualδl=0pathfrompointAÆBisalongtheactualpathofequal“infirstorderalightrayapproximation”tothetimetakenalongother(hypothetical)pathscloselyadjacenttothetruepath.Ferm
7、at’sPrincipleinGeometricOptics•1)Inahomogeneousmedium,theindexofrefractionisaconstant,andtheproblemisjusttominimizethepathlength,correctlychoosingthestraightlines.2)Iftherearetwomediumsattachedatz=0Choosingtheinitialpointas(xi,0,zi)(zi<0,theindexofrefractionn1)andthe
8、finalpoint(xf,0,zf)(zf•Possible>0,theindexofrefraction(hypothetical)pathsn2),theonlyparametertoconnectingpointsAbedeterminedistheva
