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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=0pathfrompointA?Bisalongtheactualpathofequal“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
