Harvey Mudd Optics Lab Manual

134 Pages·06.581 MB·English

by  Saeta, Lyzenga, Gallicchio

Physics 134
Optics Laboratory
Spring 2018
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SemesterCalendar
The notation “1–1” indicates the first experiment of the semester, and the first week of three
weeks spent on that experiment. “3–2” means the third experiment of the semester, and the
secondofthreeweeksspentonthatexperiment.
Meeting Week Thursday Friday
1 Mon,Jan15toFri,Jan19 1-1 1-1
2 Mon,Jan22toFri,Jan26 1-2 1-2
3 Mon,Jan29toFri,Feb2 1-3 1-3
4 Mon,Feb5toFri,Feb9 2-1 2-1
5 Mon,Feb12toFri,Feb16 2-2 2-2
6 Mon,Feb19toFri,Feb23 2-3 2-3
7 Mon,Feb26toFri,Mar2 3-1 3-1
8 Mon,Mar5toFri,Mar9 3-2 3-2
9 Mon,Mar12toFri,Mar16 SpringBreak
10 Mon,Mar19toFri,Mar23 3-3 3-3
11 Mon,Mar26toFri,Mar30 TR-1 TR-1*
12 Mon,Apr2toFri,Apr6 TR-2 TR-2
13 Mon,Apr9toFri,Apr13 TR-3 TR-3
14 Mon,Apr16toFri,Apr20 TR-4 TR-4
15 Mon,Apr23toFri,Apr27 Reportsdue
*Becausethismeetingwouldoccuronaschoolholiday(CésarChávezDay),thismeetingshould
berescheduledindividuallywithProf.Saeta.
Summary reports are due by17:00twodaysbeforethefirstlabmeetingforthenextexperi-
ment.
The60-minutefinalexamwillbegivenonFriday,May4at1:30PM.
Physics 134 ii
Introduction
Thislaboratory/lecturecourseisdesignedto
1. reinforceandextendyourskillsindesigninganexperimenttotestahypothesis,andtofine-
tuneyourexpertiseinrigorouslyanalyzingtheresultsofyourmeasurementstodetermineif
thehypothesishasbeendisprovedorsupportedbyyourexperimentalstudies;
2. extendyourknowledgeoftheoreticalopticsandintroducenewexperimentaltechniquesin
optics;
3. engageyouinperforminginterestingandchallengingexperimentsinoptics,piqueyourin-
terestinexperimentalphysics,andinspireyoutopursueacareerinscience.
The course consists of 3 laboratory experiments, one technical report project, and roughly 15
lectureswithtwoassociatedproblemsets.Thereisalsoa60-minutefinalexam.Theexperiments
aretobechosenfromeightpossibleexperimentsthatarecurrentlysetupinthelaboratory.The
lectureswillbegivenduringthefirsthalfofthesemester,at10AMonMonday,Wednesday,and
Fridayofeachweek. Thefirstlabmeetingwillbeaworkingsession! Itisimportantthatyou
readthelabmanualandindicatetoyourinstructorbyemailwhichexperimentyouwouldlike
toperformfirst.
Ascheduleoflabmeetingsappearsonpageii. Threelaboratorymeetingsareallottedforeach
of the experiments. The lab instructions leave a good deal of room for your own creativity, so
you will need to think carefully about each experiment before coming to lab. References are
giveninthelaboratoryinstructionstobackgroundreadingmaterialwhichcanbefoundinthe
mainlaboratory,JacobsB121. Youareencouragedtobrowsethroughthebooksandreadthem
inthelab,butpleasedonotremovethesebooksfromthelab! Ifyouphotocopythesectionsor
chaptersofinterest,wecanallsharethebooksharmoniously.
Animportantlessoninworkingeffectivelyinalaboratoryistoarrivewell-prepared. Toencour-
age you to do this, we are requiring reading logs. That is, by noon of the day of the first lab
meetingforeachexperiment,youmustsendyourinstructorsemaildemonstratingthatyouun-
derstandthemainpointoftheexperiment. Inaddition,youshouldincludeanyquestionsthat
havealreadyoccurredtoyou. Atthediscretionofyourinstructor,theremaybeadditionalread-
inglogsrequiredforlaterdaysintheexperiment.
Laboratory notebooks are an important part of this lab course and will be primarily a diary of
what you do in the laboratory; they should also include an informal summary of results, data
analysis,andconclusionsattheendofeachweek’swork.Attheendofeachexperiment,aformal
summarywithdataplots,measuredvalueswithuncertainties,andanyfinalinsightsshouldbe
preparedusingReVTEX. SupportfilesareavailableonSakaiintheWritingfolder. Thesereports
aretypically7–10pageslong. ThesourcefileandapdfversionshouldbesubmittedonSakai,
andahardcopyshouldaccompanythelabnotebookforgradingandfeedback.Theseelectronic
“summaryreports”willbearchivedandsharedwithfuturestudentswhoarepursuingtopicsthat
overlapwithyourwork. Summaryreportsofanexperimentareduetwodaysbeforethefirstlab
iii Physics 134
meetingofthenextexperiment, sothatyouwillhavetimetoprepareforthenextexperiment.
Thatis,theThursdaysectionwillsubmitnotebooksonTuesdayby17:00,andtheFridaysection
willsubmitnotebooksonWednesdayby17:00;seethecalendaronpageii.
Therewillbeamultiplechoicefinalexaminationgivenattheendofthesemester.Questionson
theexamwillcoverthematerialinthelectures,problemsets,andallexperimentssetupinthe
laboratory. However,theexamwillbegradedsothatyoucanobtainascoreof100evenifyou
choosenottoanswerthequestionspertainingtotheexperimentsthatyouhavenotperformed.
Thegradesonthethreesummaryreports,thetechnicalreport,andthecombinedgradesinthe
homework, readinglogs, andfinalexamwillbeequallyweighted(1/5each)toderivethefinal
gradeinthecourse. Asageneralrule,thegradeforalatenotebookwriteupwillbereduced
basedonhowlatetheworkissubmitted. Exceptionswillofcoursebemadeforillness,natural
disasters,orsimilarunusualcircumstances. Pleasebesuretoappriseyourinstructorofpoten-
tiallyextenuatingcircumstances.
Thiscoursecarriestwounitsofacademiccredit,andhenceyoushouldbedevotinganaverage
of6hours/week(absolutemaximumaverageof8hours/week)tothecourse.Thisfigureincludes
the3-hourlabsessionand1.5hoursoflecture(averagedoverthesemester)eachweek. Ifyou
findthatyoumustspendmoretimethanthistocompletetheworktoyoursatisfaction,please
notify your instructor. We intend this course to pique your curiosity and provide an outlet for
your creativity, not to beat you senseless with a heavy load of required work. If you enjoy this
courseasmuchastheinstructorsdo,itwillbeahighpointofyoursemester.
Physics 134 iv
Contents
Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LabReports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 FraunhoferandFresnelDiffraction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 CircularAperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 FresnelDiffractionbyaStraightEdge. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Recording2-DDiffractionPatternswithaCCDCamera . . . . . . . . . . . 6
2 GratingSpectrometer 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 HydrogenorSolarSpectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 TheBalmerSeriesofHydrogen. . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 TheSolarSpectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 NaDoubletandCollision-BroadenedHg . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 TheSodiumDoublet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 TheMercuryLineWidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 AppendixtoExperiment2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 TheSPEX500MScanningGratingSpectrometer . . . . . . . . . . . . . . . 14
2.6 ControllingtheSPEXSpectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 RecommendedStartupProcedure . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.2 TakingSpectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.3 WherearetheData? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.4 RemakingaPlot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.5 WorkingonAnotherComputer. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.6 CalibrationLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 ScanningFabry-PerotInterferometer 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 HeNeLaser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
v Physics 134
Contents Contents
3.2.1 MeasuringtheModeSeparation . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 MeasuringtheWidthoftheDopplerEnvelope . . . . . . . . . . . . . . . . 32
3.2.3 MeasuringtheWidthoftheLambDip . . . . . . . . . . . . . . . . . . . . . 32
3.2.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 MeasuringtheZeemanSplittingofNeon . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.1 MoreAdvancedMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 MichelsonInterferometer 39
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 White-LightFringes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.1 GroupIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 HeNeWavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 IndexofAir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 RecordingFringes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5 FourierTransformSpectroscopy 49
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 SodiumDoublet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 HgGreenLine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 QuantumOptics 55
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 TheQuantumNatureofLight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.2 DemonstratingtheQuantumNatureofLight . . . . . . . . . . . . . . . . . 59
6.2.3 TheExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.4 MeasurementsDuringtheFirstLabMeeting. . . . . . . . . . . . . . . . . . 66
6.2.5 TestingtheQuantumNatureofLight . . . . . . . . . . . . . . . . . . . . . . 68
6.3 TestsofBell’sInequality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3.2 TheExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3.3 PerformingTestsofBell’sInequality . . . . . . . . . . . . . . . . . . . . . . . 72
6.4 QuantumEraser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.4.2 TheExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.4.3 NextSteps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7 GeometricalOptics 83
7.1 FocalLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 RayTracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.3 AligningOptics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.3.1 ImageCaptureSoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.3.2 MATLABImageToolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.3.3 SpecificationsforyourCamera . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Physics 134 vi
Contents Contents
7.4 Notesontheapparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.4.1 TheOpticalRailandtheThinLensEquation . . . . . . . . . . . . . . . . . 89
7.4.2 PreliminaryExploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4.3 QuantitativeMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.4.4 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.5 Warmupexercisestodoifyouwish . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8 FresnelCoefficients 93
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.2 TheoreticalBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.2.1 Snel’sLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.2.2 LawofMalus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.2.3 FresnelCoefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.2.4 Brewster’sAngle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8.2.5 TotalInternalReflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8.2.6 WaveplatesandCircularPolarization . . . . . . . . . . . . . . . . . . . . . . 97
8.3 ExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8.4 QualitativeMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.5 QuantitativeMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.6 AppendixA:AlignmentSuggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.7 AppendixB:SampleDataforFresnelCoefficients . . . . . . . . . . . . . . . . . . . 101
A DataAnalysisUsingIgorPro 103
B DataAnalysisUsingMATLAB 111
C DataAnalysisUsingOrigin 115
vii Physics 134
Reports Introduction
LabReportsasScientificPapers
YourlabreportsforPhysics134maybequitedifferentfromtheshortlabsummariesyouhave
prepared for other courses. A Physics 134 report should be in the style of a scientific research
publication: a self-contained exposition of the question, the approach you took to answering
it, andtheresultsyouobtained. Thereportshouldbeunderstandableandconvincingto, let’s
say,afuturejuniorphysicsmajor,withoutreferencetoeitherthelabmanualoryourlabnote-
book. Yourlabreportisbothascientificinvestigationandapieceofwriting,sogoodwritingis
important.
YourreportshouldrespecttheconventionsdescribedintheAmericanInstituteofPhysics“Guide
for Metric Practice,” which is available on the department website at writing. Please write in
LATEXusingthedocumentclassrevtex4-1touseRevTeX4.1,thestandardforsubmissiontoAPS
andAIPjournals. SeetheDepartmentLATEXpageformoreinformationongettingstartedwith
LATEXandforusingRevTeX.
Suggestionsforwritingthereport
• Rememberyouraudience,andmakesureyourpaperisclearandcompellingtoareader
who is unfamiliar with the Physics 134 experiments. You might ask a friend who isn’t in
Physics134toreadyourdraftandtellyouwhattheythinktheylearnedfromit.
• Theheartofaphysicspaperisthegraph(orgraphs)thatsummarizeyourprincipalresults.
Everythingthatappearsinyourpaperbeforethisfigureleadsuptothefigure,andevery-
thingthatappearsafteritdiscussesitssignificance. Toleaduptoyourcentralfigure,you
mustmotivateyourinvestigation(answerthe“sowhat?” question),explaintheapproach
youtookinyourinvestigation,andexplainyoursetupandprocedureinenoughdetailto
clearlydefineallthedatashowninthefigure. Todiscussthesignificanceofyourcentral
figure,youmustexplainthelogicalortheoreticalbasisforyourinterpretationofthefigure,
interpretthefigure(includinguncertainties!) fairly, andsuggestpossibleextensionsand
applicationsofyourwork.
• Refertothespecificcontentguidelinesonthenextpage.
• Examinepastlabreportsorsamplescientificarticles,payingattentiontostyleandformat
choices. For example, all figures should have figure numbers and informative captions.
Figuresshould“float”tothetoporbottomofapage,andshouldthereforebereferenced
inatleastoneappropriateplaceinthemainbodyofthepaperbynumber, notposition.
Thatis,donotreferencethe“figurebelow,”sinceitspositionmayshiftduringtypesetting.
Numberedin-textcitationsshouldrefertoentriesinalater“References”section.
• Yourlabreportshouldbeself-contained, sothatareadercanfinditclearandconvincing
withoutreferringtomaterialthatisonlycontainedinthelabmanualoryourlabnotebook.
Physics 134 viii
Introduction Reports
• ReportsshouldbesubmittedtoyourSakaidropbox,bothinsourceandpdfformat. Pre-
pareafolderforeachreport,andplacefiguresandsourcefiles(.texor.ltx)inthefolder.
• The scientific community and funding agencies place increasing importance on data
archiving. In that spirit, you should upload your data to the same drob box folder that
contains the corresponding report, in the format(s) you employ (typically spreadsheets
andIgorexperimentfiles).
Specificcontentguidelines
Exceptforthetitleandabstract,thesearemerelyguidelinesfortheinformationyourreport
shouldcontain,NOTrequirementsorevensuggestionsforsectionheadingswithinyourre-
port. Organizethemainbodyofyourreportinanywaythattellsthestoryofyourinvestiga-
tionclearlyandlogically.
Title Yourreportshouldbeginwithatitle.
Abstract Next comes a 2–5-sentence abstract saying what you set out to measure/investigate,
whatmethodyouused,andwhatresultsyoufound. Thisissomethinglikethethumbnail
versionoftherestofyourreport. Aftertheabstract, startthetextofthereportitself; the
mainbodyshouldnotreferbacktotheabstract.
Introduction/Motivation
• Whatquestionareyouinvestigating? Donotassumethatthereaderisfamiliarwith
Physics134experimentsalready,sobesuretogivesomecontext.
• Whyisthisinvestigationinteresting? (forexample,illustrationofanimportantprin-
ciple? relationshiptoatechnology? Discrepanciesthatmanygroupshaveseenand
youcanexplain?Particularchallenge?Other?)
• What if any expectations and/or hypotheses did you have as you started the data-
taking?Why?
TheoryandMethods
• Writethisforareaderwhodoesnotknowwhatyoudidinlaborwhatequipmentyou
had available to you. This should be a logical exposition of what you did to obtain
thefinalresult, andwhy eachstepwasimportantorrelevant. Attentiontodetailis
important.
• Makesureallsymbolsaredefinedattheirfirstuse;useacronymssparingly.
• Carefullylabeleddrawingsareveryhelpful.Theseshouldbereferencesfromthetext
byFig.#andpushedtoeitherthetoporbottomofthepage.
ix Physics 134
Reports Introduction
• Considerpresentingsometheoreticalbackgroundforyourinvestigation. Youneed
notshoweachstepofaderivation,butthestartingpoints(includingapproximations
andassumptions)shouldbeclearlysetup,andthefinalresultshouldbeprominently
reported.
Results/Discussion
• Makesurequantitiesarewelldefined.Unitsanderrorsarealsoimportant.
• It is not necessary (or desirable!) to include all your raw data in the paper, but it
shouldbeclearhowtherawdatawereprocessedtoobtaintheincludedgraphs. For
example, howmanytrialscontributedtoeachdatapointanderrorbar? Howwere
importantquantitiesmeasured?
• Explainthesourceofanyquoteduncertaintyestimates(statisticalvariation,instru-
mentprecision,etc.)
• Data should be analyzed (plotted, fitted, compared with theory, etc.) logically and
understandably. Graphs should include titles, axis labels, units, and error bars. Fit
formulas should correspond to appropriate theory. Data should be properly com-
binedtogivefinalanswersthataddresstheoriginalquestionasfaraspossible. Un-
certaintiesshouldbereasonablytreated.
• Clearly state comparisons to theory or to “known” values, and include source cita-
tionsorderivationsifnecessaryforthetheoryorknownvalues.Discussthestatistical
significance(orlackthereof)ofyourresult(s).
Conclusions
• Whatlightdoyourdataandanalysisshedontheoriginalquestion/hypothesis?
• Ifthereisafirmtheoreticalprediction,doestheexperimentagreewiththetheory?If
so,withwhatprecisioncanyouconfirmtheory?Ifnot,byhowmuchisitoff(relative
touncertainty)?
• If the experiment was designed to measure an unknown quantity or effect, what is
yourresult?Howprecisecanyouclaimitis?
• What are the major sources of systematic and random error in your experiment?
Whatextensions/improvementssuggestthemselvesifyouhad1or 2morelabses-
sions?
• PointouttherelevanceofyourworktofuturePhysics134labsortoothersituations
ifappropriate.
Citereferenceswhereappropriate e.g., lab manual, textbooks, and other sources of inspira-
tion.Eachreferenceyouincludeinalistattheendofyourpapershouldbecitedatoneor
moreparticularpointsinthebodyofthepaper.
Physics 134 x