光栅衍射分光计教案Grating Spectrometer.docx
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光栅衍射分光计教案Grating Spectrometer.docx
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光栅衍射分光计教案GratingSpectrometer
Experiment2-6:
Gratingspectrometer
1.Aim:
Measurementofthewavelengthsoflightfromamercurylampusingagratingspectrometer.
2.Theory:
(Read:
CutnellandJohnson–Chapter27.7)
Fig.1.Structureofaspectrometer.
Aspectrometerconsistsofacollimatorthatproducesaparallelbeamoflightfromalamp,adiffractiongratingonaturntablethatdispersesthelightandatelescopetoviewthelight,asshowninFig.1.
Adiffractiongratingwillseparatelightintoitsconstituentcolours.Adiffractiongratingconsistsofalternateopaqueandtransparentlines.Dispersionoccursbecauseconstructiveinterferenceoccursforlightdeflectedincertainspecificdirections.Otherwisedestructiveinterferenceoccurs.
Thephysicsofadiffractiongrating.Diffractionpatternsofbrightanddarkfringesoccurwhenmonochromaticlightpassesthroughasingleordoubleslit.Fringepatternsalsoresultwhenlightpassesthroughmorethantwoslits,andanarrangementconsistingofalargenumberofparallel,closelyspacedslitscalledadiffractiongratinghasprovedveryuseful.Gratingswithasmanyas40000slitspercentimetercanbemade,dependingontheproductionmethod.Inonemethodadiamond-tippedcuttingtoolisusedtoinscribecloselyspacedparallellinesonaglassplate,thespacesbetweenthelinesservingastheslits.Infact,thenumberofslitspercentimeterisoftenquotedasthenumberoflinespercentimeter.
Fig.2.Whenlightpassesthroughadiffractiongrating,acentralbrightfringe(m=0)andhigher-orderbrightfringes(m=1,2,...)formwhenthelightfallsonadistantviewingscreen.
Fig.2illustrateshowlighttravelstoadistantviewingscreenfromeachoffiveslitsinagratingandformsthecentralbrightfringeandthefirst-orderbrightfringesoneitherside.Higher-orderbrightfringesarealsoformedbutarenotshowninthedrawing.Eachbrightfringeislocatedbyanangleθrelativetothecentralfringe.Thesebrightfringesaresometimescalledtheprincipalfringesorprincipalmaxima,sincetheyareplaceswherethelightintensityisamaximum.Theterm"principal"distinguishesthemfromother,muchlessbright,fringesthatarereferredtoassecondaryfringesorsecondarymaxima.
Fig.3.Theconditionsshownhereleadtothefirst-andsecond-orderintensitymaximainthediffractionpatternproducedbythediffractiongratingontheright.
Constructiveinterferencecreatestheprincipalfringes.Toshowhow,weassumethescreenisfarfromthegrating,sothattheraysremainnearlyparallelwhilethelighttravelstowardthescreen.Inreachingtheplaceonthescreenwhereafirst-ordermaximumislocated,lightfromslit2travelsadistanceofonewavelengthfartherthanlightfromslit1,asinFig.3.Similarly,lightfromslit3travelsonewavelengthfartherthanlightfromslit2,andsoforth,asemphasizedbythefourcoloredrighttrianglesontheright-handsideofthedrawing.Forthefirst-ordermaximum,theblow-upviewofslits1and2showsthatconstructiveinterferenceoccurswhensinθ=λ/d,wheredistheseparationbetweenslits.Asecond-ordermaximumformswhentheextradistancetraveledbylightfromadjacentslitsistwowavelengths,sothatsinθ=2λ/d.Thegeneralresult,ofprincipalmaximaofadiffractiongrating,is
m=0,1,2,3,...
(1)
Theseparationdbetweentheslitscanbecalculatedfromthenumberofslitspercentimeterofgrating;forinstance,agratingwith2500slitspercentimeterhasaslitseparationofd=(1/2500)cm=4.0×10-4cm.Betweentheprincipalmaximaofadiffractiongratingtherearesecondarymaximawithmuchsmallerintensities.Foralargenumberofslits,thesesecondarymaximaareverysmall.
Fig.4.Agratingspectroscope.
Thephysicsofagratingspectroscope.Aninstrumentdesignedtomeasuretheanglesatwhichtheprincipalmaximaofagratingoccuriscalledagratingspectroscope.Withameasuredvalueoftheangle,calculationscanbeturnedaroundtoprovidethecorrespondingvalueofthewavelength.Theatomsinahotgasemitdiscretewavelengths,anddeterminingthevaluesofthesewavelengthsisoneimportanttechniqueusedtoidentifytheatoms.Fig.4showstheprincipleofagratingspectroscope.Theslitthatadmitslightfromthesource(e.g..ahotgas)islocatedatthefocalpointofthecollimatinglens,sothelightraysstrikingthegratingareparallel.Thetelescopeisusedtodetectthebrightfringesand,hence,tomeasuretheangleθ.
Inamercurylamp,mercuryvapourisheatedtoahightemperature,andlightisemittedthatischaracteristicoftheatomicstructureofmercury.Thisislikeanatomicfingerprint.Thespectrumofmercuryconsistsofanumberofbrightlines,fourofwhichareeasilyvisibleusingasimplespectrometerandthenakedeye.Therearetwoviolet/purple
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