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AY105LabExperiment#2Spectroscopy

PurposeThis week, you will work on one of the most important components of optical

astronomy--spectroscopy.Themaingoalwillbebuildingyourownspectrographandusingit to resolve theD-linesofneutral sodium(NaID1=5895.93Å, 2P1/2-2S1/2; andD2=5889.962P3/2-2S1/2). Youwill also investigate how spectral resolution depends upon spectrographdesignparameterssuchasgrating(orprism)dispersion,slitwidth,cameralens,etc.PartAmakesuseofagratingasadispersiveelementwhilePartBusesaprismfordispersion.

Unlike the first week, there are no drawings given to you in this week’s labinstructions, nor is the equipment and its setup described in as much detail. You arelearninghowtofigurethingsoutyourselves!

Pre-LabWork● Readtheentirelab!Figureoutwhatequipmentyouhaveonthetable.TRYNOTTO

TOUCHTHESURFACEOFGRATINGSEVENWITHGLOVES.● Review the spectroscopic concepts such as grating ruling and grating blaze angle,

“order”oflight,etc.(https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8626)

● Evaluate the equations as instructed in theBackground section in order toderiveusefulrelationsforlabworkandanalysis.

BackgroundSpectroscopyisaverypowerfultoolinastronomy.Bydispersingthelightreceived

by a telescopewe increase the spectral resolution and thus enablemore physical insightinto theprocessesoccurring inastronomicalsources.Modernspectrographsuseavarietyof dispersive elements, e.g. the Low Resolution Imaging Spectrometer (LRIS,https://www2.keck.hawaii.edu/inst/lris/)onKeckIusesgratingonredside,andgrism,acombinationofgratingandprism,onblueside.

Acriticalconceptforgratingsisthegratingequationwhichrelatespropertiesofthelight (wavelength, 𝜆, and “order”,𝑚) to properties of the grating including the distancebetweengroovesorslits,a,andtheopticalsetupwhichdefinesseveralangles.Itisgivenby

𝑚𝜆𝑎= (𝑠𝑖𝑛𝛼 ± 𝑠𝑖𝑛𝛽)

where𝛼and𝛽are the angles between the grating normal and the incoming rays and theoutgoingdiffractedrays.Notethattheplus-signindicatesareflectivegratingandaminus-sign indicates a transmissive grating. Show that the dispersive power (i.e., the angularchange in the direction of outgoing rays with a change in wavelength) of a diffractiongratingis:

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∂β∂λ

= ±m

acosβ

Forprism-basedspectrographs,theangleofdeviationcanbeexpressedas,

𝐷 = 𝑖 − 𝐴 + 𝑎𝑟𝑐𝑠𝑖𝑛(𝑛 ⋅ 𝑠𝑖𝑛(𝐴 − 𝑎𝑟𝑐𝑠𝑖𝑛(𝑠𝑖𝑛𝑖𝑛))),

where𝐴 is the internalangleof theprism(60° in this case), 𝑖 is theangleof the incidentlight,and𝑛istherefractiveindexoftheprism.ThelightpathisshowninFig.1.Forlightatacertainwavelength𝜆,theangleofminimumdeviationDhappenswhentherefractionangleisA/2andi=f=(A+D)/2.Inthisscenario,Dsatisfiesthefollowingrelation:

𝑛! =!"#(

!!!!! )

!"#(!!).

Figure1:therelationshipbetweentheangleofminimumdeviationandthelightentering

theprism.A derivation of these relations can be found at https://www.askiitians.com/iit-jee-ray-optics/prism/

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EquipmentWewillmostlybeusingtheThorLabsSpectrometerEducationalKit,whichincludes

thefollowingequipment:o ImagingOpticsandAssociatedMountingHardwareo VariableSlito 1200Lines/mmDiffractionGratingo 600Lines/mmDiffractionGratingo EquilateralDispersingPrismo ViewingScreeno LaserSafetyScreen

Wewillalsobeusing:

o SodiumArcLampo Iriso ThorLabVisibleAchromaticLensKit

EquipmentlistfortheThorLabsSpectrometerEducationalKit:Item # Description Qty.

LEDMF LED Mount 1

LEDWE-15b White LED, Pkg. of 5 1

ACL2520U Condenser Lens 2

FMP1 (FMP1/M) Ø1" Optic Mount 2

LB1471 Focusing Lens 1

LMR1 (LMR1/M) Ø1" Lens Mount 2

VA100 (VA100/M)

Variable Slit 1

LB1676 Collimating Lens 1

GR25-1205 1200 lines/mm Diffraction Grating 1

GR25-0605 600 lines/mm Diffraction Grating 1

CH1A Diffraction Grating Mount 2

PS858 Equilateral Dispersing Prism 1

KM100PM (KM100PM/M)

Adjustable Prism Mount 1

PM3/M Clamping Arm for Prism Mount 1

EDU-VS1 (EDU-VS1/M)

Viewing Screen 1

MB1824 (MB4560/M) Optical Breadboard 1

RDF1 Breadboard Feet 4

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TR3 (TR75/M)

3" (75 mm) Long Optical Post 9

PH3 (PH75/M)

3" (75 mm) Long Post Holder

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TR2 (TR50/M)

2" (50 mm) Long Optical Post

1

PH2 (PH50/M)

2" (50 mm) Long Post Holder

1

BA1 (BA1/M)

Post Holder Base, 1" x 3" x 3/8" (25 mm x 75 mm x 10 mm)

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BA2 (BA2/M)

Post Holder Base, 2" x 3" x 3/8" (50 mm x 75 m x 10 mm)

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TPS5 Laser Safety Screen, 12" x 12" (305 mm x 305 mm)

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LabactivitiesYour main goal for this lab is to understand the factors that contribute to the

resolutionofaspectrograph.

PartI:GratingSpectrographUsing the equipment on the optical table, setupwith theNa arc lamp as the light

source(youcanchoosetostartwiththeLED,whichhasabright“continuum”butdoesnothaveany lines).Yourgoal is touseoneof thegratings(between600lines/mm,and1200lines/mm) to form an image on the white screen. Some of the equipment may not benecessary.Youalsoneedtochooseyourlenseswisely(seethenotebelow).

Makesureaboutthefollowingissues:

1) TheNaarclampneedssometimetowarmup.2) Usethe iristo filteroutthescatteredlightcreatedbythe lightsource,butkeepas

muchusefullightaspossible.Donothesitatetousetheblackscreenforadditionalstraylightcontrol.

3) Usingoneormorelenses,formanimageofthelampbulbontotheslit. Theimageshould be as small and bright as possible, so that the spectrum is as bright aspossible. Be careful when adjusting the slit width. Do not force the slit jawstogether.

4) Placeanotherlensaftertheslit.Thislensshouldbesuchthatifnogratingexisted,itwould form an image of the slit at a suitably large distance from the lens,with acorrespondinglylargemagnification.

5) Placethediffractiongratingafterthelens. Thelightfromthelensshouldfillupasmanylinesonthegratingaspossible,sincethisistheultimatelimitonthespectralresolution. Youmaywanttosetupthegratingonarotationalstage(sameas lastweek)tomeasureitsangle.

6) Placeascreenatasuitablylargedistancefromthegrating,suchthatthelightfromthelastlenscomesintofocusatthescreen.

7) You should see the NaD doublet on your screen, possibly in addition to otheremissionlines.Ifnot,rotatethegratingandadjustthefocus.

Sketchtheconfigurationsofarinyournotebook.andrecordthecollimatingmirror

focallength,gratinggrooves/mmandblazeangle𝜃! .Markonyoursketchthegratingblazedirection.Giventhis,whereshouldthescreenbelocated?Whatblazewavelength,λB,doyouderive for your grating from the grating equation evaluated in first-order Littrowconfiguration (𝑚 = 1;𝛼 = 𝛽 = 𝜃!)? Is this reasonable? Inwhich orderwould you expecttheNaDlinestobebrightestwiththisgrating?

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Usefulformula:thelensequationTohelpyouchoose theright lens for the job, find itsoptimal locationwithrespect to theobjecttobeimaged(e.g.theNalampofLEDontotheslit,andtheslitontothescreen),aswellastheimagelocationitself,thelensformulaandcorrespondingmagnificationMmightcomeinhandy.

Figure2:LensFormula

PartIMeasurements:Determinethezeropointoftherotationalstagewhenthegratingisnormal to the incidentbeam.Moveback to thebest configurationwhere you can see theNaDlinesclearly.Identifythe0thand1storderofthedispersedlight.Measurethe𝛼and𝛽anglesandcalculatethewavelengthofthedoublet.Adjusttheslitwidth,anddeterminethepointwhenthedoubletisdistinguishable.Changethecameralensorthegrating(controlyourvariables),andrepeatthemeasurementoftheslitwidth.(Justforfun:Adjustthecameralenssothatthelightilluminatingthegratingiscollimated,i.e.imageatinfinityandobjectatfocus.UseyoureyetoobservetheemissionspectrumofNaI directly. You can even take a picture of the spectrum with you cell phone camera!Identifysomeofthespectrallinesthataretooweaktobeprojectedonthescreen.)Part I Discussion: Given the phenomena you see during the experiment, discuss thepropertiesthataffectsthespectralresolution.Isanarrowerslitalwaysbetter?

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PartII:PrismSpectrographUsetheNaarc lampasthe lightsource. (Still, ifyou found it isdifficult toalignor

focus with Na lamp, feel free to use the LED first, and then switch back.) Change thedispersiveelementtoprism.Reconfigureyourequipmentifnecessary.RotatetheprismandfindwheretheangleofminimumdeviationforNaDlinesisreached.Part IIMeasurements:Measure theangleofdeviationandcalculate the refraction indexforNaDlines.HowdoesyourmeasurementcomparetoFig.2.

Figure2:Therefractionindexoftheprismasafunctionofwavelength.

Sellmeier’sequationdescribesn(λ),therefractiveindexoftheprismmaterialasafunctionofwavelength𝜆inµm:

𝑛! λ = 1 +𝐵!λ!

λ! − 𝐶!+

𝐵!λ!

λ! − 𝐶!+

𝐵!λ!

λ! − 𝐶!

which isvalidoveroptical andnear infraredwavelengths. Theappropriate constants forthe prism can be found on the ThorLabs website:https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6973&tabname=F2Part II Discussion: Derive the dispersive power (!"

!") of the prism spectrograph we

constructed during the class, and compute its numerical value at the angle of minimumdeviation for theNa II doublet.Howdoes it compare to the gratings?Does itmatchwithwhatyousee?