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  • 7/29/2019 P2 Week 10 - Diffraction & Spectra

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    Singleslitdiffraction

    Youcans)llgetfringesevenifyouuseasingleslit Theslitbehavesasthoughithasalargenumberofpoint

    sourcesspreadevenlyacrossthewidthoftheslit

    Thewavefrontsfromthedifferentendsoftheslitwillbearrivingatdifferentpointsontheendscreenatdifferent)mes

    Yous)llgetconstruc)veanddestruc)veinterference Thenarrowertheslit,thegreaterthediffrac)on Thelongerthewavelength,thegreaterthediffrac)on

    1

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    Singleslitdiffraction

    AssumewehaveadarkfringeatP Pathdifferencecorrespondingtodarkfringesis(m+1/2 MCQandMOParesimilartrianglesso:

    OP/MP=MQ/MC=sin( MC=d/2(halftheslitwidth sin(=(/2/(d/2dsin(=[forfirstdarkfringe] 2

    B

    C

    d

    D

    O

    P

    M Q

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    Singleslitdiffraction

    Darkfringesoccuratdsin(=m(wherem=1,2,3 Sameequa0onasfordoubleslitsbuthereitcorrespondstotheposi0onsofdarkfringes!

    mherecannottakethevalueof03

    B

    C

    d

    D

    O

    P

    M Q

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    Example

    Lightofwavelength632.8nmfromaHe-Nelaserilluminatesasingleslitofwidth0.1mm.Whatisthewidthofthecentralmaximumformedonascreenplaced2.0mbeyondtheslit?

    [Lengthofanarcinradians:L=r,whereristheradius]

    4

    Darkfringesat:dsin(=m

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    Intensitydistribution

    Awidesingleslitproducesmorefringes

    5

    0slitwidthd

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    Intensitydistribution

    Singleslitintensitycomparedtodoubleslitintensity

    Highintensitypeaksbecomesharperiftheslitnumberisincreased6

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    Diffractionbycircularaperture

    Similarprincipletothediffrac)onbyaslit

    Angularposi)onoffirstminimum dsin(=1.22 7

    Airydisc

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    Diffractionbycircularaperture

    Refrac)ngtelescope d=objec)velensdiameter Thesizeoftheairydiscdeterminesthe

    resolvingpower

    smallerairydisc=moreresolvingpower

    Diffrac0onlimit:theminimumangularsepara)onbetweentwosourcesthatcanbedis)nguishedbyatelescope

    8=1.22/d(inradians

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    Example

    TheHubblespacetelescopehasadiameterof2.4m.AccordingtoRayleighscriterion,whatisthetheore)calangularresolu)onthatthistelescopecanachievewithvisiblelightofwavelength5500(1=0.1nm?Howmuchbeeristhisthantheangular

    resolu)onof0.5arcsecondsachievedbytelescopesonthesurfaceoftheEarth?

    [1degree=60arcminutes,1arcminute=60arcseconds]

    9

    =1.22/d

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    Example

    Twopointsourcesoflightareplaced12mmapartandemitlightofwavelength0.6m..Whatisthemaximumdistanceatwhichthetwosourcescanjustbedis)nguishedbyanobserverwithaneyepupildiameterof4.0mm?

    [L=r,L=distancebetweenthetwopoints,r=theirdistanceaway]

    10

    =1.22/d

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    Diffractiongrating

    Ahighnumberofparallelslitsarrangedcloselytogetheriscalledadiffrac0ongra0ng

    Insuchanarrangementthepeaksappearassharpthinlines Theloca)onofeachline(principalmaximaisgivenby

    disthespacingbetweentwoadjacentslits Diffrac)ongra)ngsareusedtomeasurewavelengthswith

    highaccuracy

    Transmissiondiffrac)ongra)ng:blackparallellinesontransparentplas)corglass

    Reflec)ondiffrac)ongra)ng:usesareflec)vesurfacebetweentheblacklinestoreflectincidentlight

    11

    dsin(=m

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    Example

    Adiffrac)ongra)nghas5000linespercen)meter.Whataretheangularposi)onsofthefirstthreeprincipalmaximaproducedbythisgra)ngwhenilluminatedwithmonochroma)clightofwavelength6500(1=0.1nm?

    12

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    Numberofdiffractedbeams

    Ifdandareknown:wecangetthenumberofdiffractedbeams

    sin(1m/d1 whichmeansthatmd/

    d/willgiveusthenumberofdiffractedbeams Thehighestordernumberisthevalueofd/roundeddown

    tothenearestinteger

    13

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    Example

    Aparallelbeamofmonochroma)clightofwavelength500nmisdirectednormallyatadiffrac)ongra)ngwhichhas600linespermm.Determinethenumberofdiffractedbeamsandtheangleofdiffrac)onofthehighestorder.

    14

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    Thevisiblespectrum

    Thevisiblespectrumistheregionoftheelectromagne)cspectrumconsis)ngofphotonswithwavelengthsfromapproximately400to700nm

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    TypesofSpectra

    Spectroscopy:isthestudyoftheinterac)onbetweenmaerandradiatedenergy

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    TypesofSpectra

    Spectroscopy:isthestudyoftheinterac)onbetweenmaerandradiatedenergy

    Threetypesofspectra: acon0nuousspectrumisasmoothdistribu)onofwavelengths

    andhasnogaps

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    TypesofSpectra

    Spectroscopy:isthestudyoftheinterac)onbetweenmaerandradiatedenergy

    Threetypesofspectra: acon0nuousspectrumisasmoothdistribu)onofwavelengths

    andhasnogaps anemissionlinespectrumisproducedbyexcitedatoms

    returningtotheirgroundstate

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    TypesofSpectra

    Band(emission)spectraareproducedbymoleculesratherthanatoms

    molecularbandspectraaremuchmorecomplexthanthespectraofsingleatoms

    Theytypicallyshowbroadbandsinsteadofnarrowlines Thelinesappearclosertogetherononesideoftheband

    19

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    TypesofSpectra

    Spectroscopy:isthestudyoftheinterac)onbetweenmaerandradiatedenergy

    Threetypesofspectra: acon0nuousspectrumisasmoothdistribu)onofwavelengths

    andhasnogaps anemissionlinespectrumisproducedbyexcitedatoms

    returningtotheirgroundstate

    anabsorp0onlinespectrumisproducedwhenphotonsfromasourcewithacon)nuousspectrumpassthroughadiffusegas

    cloud

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    TypesofSpectra

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    TheSolarspectrum

    Thehotdensecentreofthesunemitsacon)nuousspectrum Thecoolerouterlayerofthesun,theHeliosphere,absorbs

    someofthelightatspecificenergies

    Lookingattheabsorp)onspectrumwecanfindoutwhattheSunismadeof

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    TheSolarspectrum

    TheSunemitsprimarilyinthevisiblespectrumbutalsoatotherwavelengths

    MuchoftheUVradia)onfromtheSunisabsorbedbytheatmosphere

    TheSunatX-raywavelengths

    TheSunatUVwavelengths

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    ToDo

    Readsec)on18fromthebook[from18.3un)lendofchapterp.351-p.363PhysicalOp)cs]

    HomeworkAssignmentwk10:ques)ons18.1,18.3,18.4,18.11,18.14and18.16

    Handitinnolaterthan4:pmnextWednesday-LATEWORKWILLNOTBEACCEPTED

    24


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