光栅衍射分光计教案Grating Spectrometer文档格式.docx

光栅衍射分光计教案Grating Spectrometer文档格式.docx

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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