国际物理林匹克竞赛试题IPHO_1984

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ProblemsoftheXVInternationalPhysicsOlympiad
(Sigtuna,1984)
LarsGislén
DepartmentofTheoreticalPhysics,UniversityofLund,SwedenTheoreticalproblemsProblem1a)Consideraplane-paralleltransparentplate,wheretherefractiveindex,n,varieswithdistance,z,fromthelowersurface(seefigure).ShowthatnAsin??nBz=0
b)Assumethatyouarestandinginalargeflatdesert.Atsomedistanceyou
seewhatappearstobeawatersurface.Whenyouapproachthe“water”isseemstomoveawaysuchthatthedistancetothe“water”isalwaysconstant.Explainthephenomenon.
c)Computethetemperatureoftheairclosetothegroundinb)assumingthatyoureyesarelocated1.60mabovethegroundandthatthedistancetothe“water”is250m.Therefractiveindexoftheairat15?Candatnormalairpressure(101.3kPa)is1.000276.Thetemperatureoftheairmorethan1mabovethegroundisassumedtobeconstantandequalto30?C.The
atmosphericpressureisassumedtobenormal.Therefractiveindex,n,issuchthatn–1isproportionaltothedensityoftheair.Discusstheaccuracyofyourresult.Solution:
a)FromthefigurewegetnAsin??n1sin?1?n2sin?2???nBsin?
b)Thephenomenonisduetototalreflexioninawarmlayerofairwhen?=90?.This
gives