SP212 Lab: Nineà Thin Lenses
Version: April, 2014
Physics II
Lab 9
SP212
ThinLenses
I. Introduction
A. Thinlenseshavemanyapplications;theyareusedinmicroscopes,
binoculars,eyeglasses,contactlenses,magnifyingglasses,camerasand
refractingtelescopes.Consequently,weencounterthemfrequentlyin
everydaylife.
B. Thephysicsofathinlensisrelativelysimplesincealensonlyformsan
image.However,imagescanbeeitherrealorvirtual.Complicating
thingsfurther,theimageformedbyathinlensescanevenbearealor
virtualobjectforanotherlens.Itisthereforeworthwhilespendingsome
timefirmingupourunderstandingofthinlenses.
C. Thelaboratoryisanexcellentplacetostudylensessincearealimage
canbedisplayedonascreen.Wecanmeasurewherearealimageis
relativetoalensandcompareitsactualpositiontotheposition
predictedbyourequations.
D. Wecanalsocarryoutexperimentsthatinvolvevirtualimages.Since
virtualimagescan'tbedisplayedonascreen,wewillstudy
combinationsoflenseswheretheimportantroleofthevirtualimage
canbeinferred.
E. Ifanobjectisadistancep(objectdistance)fromathinlensoffocal
lengthfandformsanimageatadistancei(imagedistance)fromthe
thinlens,therelationshipbetweenp,iandfisè1/p
+ 1/i = 1/f
F. Magnificationoftheobjectisgivenbytheequation:m=-i/p
M = M1 M2 for a combination oflenses.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
II. NeededEquipment
A. Theequipmentconsistsofalightsource,lenses(bluedot,reddot,andyellowdot),
spreadsheetforcalculations,aviewingscreenandanopticsbench.Theopticsbench
isaslottedaluminumtrackforfixingthelightsource,lensesandscreen.The"object"
willbetheilluminateddrawing(concentriccircles,perpendiculararrowsandscale)
onthefrontofthelightsource.Arealimageoftheobjectisvisibleonthescreenin
thenextpicture.
III.Objectives
Attheendofthisactivity,youshould:
1. Findthefocallengthofaconverginglensandseewhyadifferenttechniqueis
requiredforadiverginglens.
2. Practiceusinglensequationtopredicttheimagelocationgiventheobjectdistance
andthefocallengthofthelens.
3. Predictthemagnificationofanobjectbasedontheobjectdistanceandthe
theoreticalimagedistance.
4. Observethelocationoftheimageanditsmagnificationandseeiftheymatch
predicted.
5. Observetheresultsofatwolenssystemsimilartohomeworkproblems.
6. Observehowavirtualimagecanstillbeusedastheobjectforanotherlens.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
IV. Yourinstructorwilldemonstratehowtooperatetheinstrumentand
takethedata.
V. TurninyourHomework/Pre-LabAssignmentifassigned.
VI. Procedure
A. PreliminaryMeasurements
Note: You cannot find the focal length via the below method for a diverging lens.
1. EstimateofFocalLengthsofPositiveLensesUsingImageof
DistantObject
a. Sinceonlyconverginglensescanformrealimagesofrealobjects,wewill
usethisfacttodecidewhichofthelenseswithcoloreddotsare
convergingandwhichisdiverging.Usingthetechniqueshowninthe
followingdiagram,attempttoformanimageoftheceilinglights(real
objects)witheachofthelenses.Separatethelensesintoconvergingand
divergingandrecordwhicharewhich.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
b. Askyourinstructoriftheywantyoutodoprocedure(i)or(ii).Their
decisionisprobablybasedonhowsunnyitisoutside.Ilearnedlastyear,
thattakingaclassoutsidewhenitiscloudyisawasteoftheirtime.
i. Iftheobjectdistanceismuch,muchlargerthanthefocallength,then
theimagedistanceisverynearlyequaltothefocallength.According
toGoogleEarth,thehousesacrosstheSevernRiverareabout1km
fromChauvenetHall.Findtheimagedistanceforeachofyourlenses,
usingahouseacrosstheSevernasanobject,andrecordtheimage
distanceasthelens’sfocallength.Youmustdothisforeachofthetwo
converginglensesandrecordtheirfocallength.SkipstepiiandGoto
stepc.
ii. Yourinstructorwillplaceanimageontheoverheadprojector,standin
thebackoftheroomasfarawayfromthescreenwiththeopticsbench
onyourshoulder(almostlikeabackwards“bazooka”).Movethe
converginglensuntilyouareabletoformaclearimageonthesmall
screenattachedtoyouopticsbench.Youmustdothisforeachofthe
twoconverginglensesandrecordtheirfocallength.
2. DivergingLens:Sincevirtualimagescannotbedisplayedona
screen,wemustuseadifferenttechniquetodeterminethe
focallengthofadiverginglens.
Warning: Do not shine the laser beam into anyone's eyes. Permanent vision damage may
result.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
a. Putadiverging(negative)lensontheopticsbenchandalaseronthelab
jackasyourinstructordemonstrates.Itisnecessarytoadjustthelaserso
thatthelaserbeamliesonthelens’sopticalaxis.Thereisonlyoneray
thatisbothparalleltotheopticalaxisandisalsoavertexray,andthatisa
raythatliesalongtheopticalaxis.Therefore,adjustthelabjack,andthe
laseronthejack,until(1)thebeamisnormaltothelens,and(2),the
beamdoesnotdivertwhenitgoesthroughthelens.Ifbothoftheseoccur,
thebeammustcoincidewiththeopticalaxis.
b. Notethepositionoftheimageofthelaserbeamwhenitisalignedalong
thelens’saxis.
c. Now,holdarulernexttothelabjack,andturnthescrewtoraise(or
lower)thejackandlaseracentimeterorso.Measurethedistanceyou
shiftedthelasercarefully,andcallthisdistancee.Alsomeasurethe
distancebywhichtheimageshifts,andcallthisdistancey.
d. Finally,measurethedistance,L,fromthecenterofthelenstothescreen
onwhichtheimageisprojected.Sincethelaserbeamisstillparalleltothe
opticalaxis,itisrefractedthroughthelens’sfocalpoint.Alittlegeometry
involvingsimilartrianglesshowsthatf=L*e/y.Usethistocalculatethe
focallengthoftheyellowlens.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
B. TakingData:TheThinLensEquation:1/p+1/i=1/f.
1. Nowwearereadytotakedata.
a. Usethelampastheobjectforthisexperiment,asyourinstructor
demonstrates.Settheobjectatx=0.000monyouropticalbench.Setthe
screenatx=1.000m;thisiswheretheimagewillbelocated.Sincethe
lenswillbebetweenobjectanimage,forthisexperimentp+i=1.000m,
whichisconvenient.Notethatthediameteroftheouterringontheobject
is0.0200±0.0001m.
b. Now,placethebluelensonthebench,andadjustitspositionuntilyou
obtainasharpimageonthescreen.Notethattherearetwosuchpositions,
oneproducinganenlargedimage,theotherproducingareducedimage.
First,recordthelenspositionthatproducestheenlargedimage.Also
measuretheimagediameter.
c. Repeatforthepositionthatproducesthereducedimage.
d. Usetheresultsofyourmeasurementstomakethecalculationsindicated
onthespreadsheettemplateandtestwhetherornotthefocallength
determinedinthiswayagreeswithyourpreviousmeasurement.Also
checktoseewhetherbothwaysofdeterminingthemagnificationagree.
i
2. Repeattheexperiment(stepsa-cabove)usingtheredlens.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
C. Acombinationoflenses:
1. Inamulti-lensopticalinstrument,thelensclosesttotheobjectiscalled
the“objective,”andwewillcallthesecondlensthe“ocular,”or“eyepiece,”
eventhoughwewillnotlookthroughit.Insteadwewillcastitsimageon
thescreen,andobserveitthere.Theimageoftheobjectiveistheobject
fortheeyepiece,andtheoverallmagnificationoftheinstrumentisthe
productofthemagnificationsofeachlens.
2. Theobjectlampshouldstillbeatx=0.000m.Placetheredlensonthe
opticalbenchatx=0.200m.Adjustthescreenuntilyoufindanice,sharp
image,andrecordtheimagelocation.Alsomeasureandrecordtheimage
diameter.Useyourdatatocalculatethefocallength,andcomparewith
yourearliermeasurements,andcomparethemagnificationscalculated
bothways.
3. Now,placetheyellowlensatx=0.300m,andadjustthescreentofindthe
imagelocation.Recordtheimageposition,andmeasureandrecordthe
imagediameter.Usethesedatatotestthelensequationand
magnificationsasbefore.
4. Finally,findtheproductoftheindividuallensmagnifications,and
calculatetheoverallmagnificationastheratioofthefinalimagediameter
totheoriginalobjectdiameter,anddiscussagreement.
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SP212 Lab: Nineà Thin Lenses
Version: April, 2014
D. LabReporttohandin:
1. Spreadsheets,oneeachforPartsA,B1,B2,andCwith
discussions.
Don’tforgetuncertainties,units,annotationsanddiscussions.
VII.
Clean-Up
A. GoldenRule:“Dountoothersasyoudesirethemtodountoyou.”
ThisappliesasmuchhereinthelabasitdoesintheFleet.AspotentialNaval
Officers,howcanyouexpectyourenlistedsailorstomaintainacleanworkareaif
yourstateroom,workareas,messarea,etcisa“pigsty?”Soasofficersitis
imperativethatwecleanupafterourselvesnotonlytofollowtheGoldenRule,but
alsotoleadbyexamplefortheenlistedpersonnelunderourcharge.
1. EndofLabCheckout:Beforeleavingthelaboratory,pleasetidyupthe
equipmentattheworkstationandquitallrunningsoftware.
2. Thelabstationshouldbeinbetterconditionthanwhenyouarrivedandmore
importantly,shouldbeofanappearancethatyouwouldbePROUDtoshowto
yourlegalguardiansduringa“ParentsWeekend.”
3. Haveyourinstructorinspectyourlabstationandreceivetheirpermissionto
leavetheLabRoom.
4. YouSHALLfollowthisprocedureduringeverylabforSP212!
ManythankstoDr.HuddleandDr.FontanellafortheirassistanceinproducingthisLaboratory
procedure;specificreferencescanbesuppliedonrequest.LCDRTimothyShivok
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