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BuildaSunFunnelforGroupViewingoftheGreatAmericanSolarEclipse
ofAugust21,2017*
Version3.2•June2016
RichardTreschFienbergAmericanAstronomicalSociety
ChuckBueterNightwise.org
LouisA.MayoNASAGoddardSpaceFlightCenter
*andotherfascinaJngsolarphenomena,too!
Thissimple&inexpensivedevicemakesiteasyformanypeopletoobservetheSunsimultaneously—andsafely!
OriginoftheSunFunnel:AmateurastronomersGeneZajacandChuckBueteradapted(hAp://bit.ly/1raqocH)anexisKngdesignfora2003GreatLakesPlanetariumAssociaKonConferenceworkshop.Therear-screenprojecKonmaterialshownhereisanideaborrowedfromBruceHegerberg’sSunGun(hAp://bit.ly/23SVC5N).
ContentsSafetyFirst..........................................................4SafeSun............................................................5Supplies&Tools..................................................... 7MatchtheEyepiecetoYourTelescope.................................. 10AMaAerofSize&Degrees............................................ 15Step-by-StepAssemblyInstrucKons.....................................16PrepareYourSunFunnel&TelescopeforUse............................33HowtoAimaTelescopeattheSun..................................... 35SolarFiltervs.SolarProjecKon......................................... 37SunFunnelSafety....................................................38AddaSolarShadetoYourSunFunnel................................... 39WhyObservetheSun?............................................... 40TheGalileoscope&theSunFunnel..................................... 46MathemaKcalUnderpinningsoftheSunFunnelDesign.................... 48ContacttheAuthors................................................. 58
SafetyFirst!WheneveryouobservetheSun,withanytechnique,youmustputsafetyfirst.ConstrucJonoftheSunFunnelrequirestheskilleduseofasawandotherpotenJallydangeroustoolsandisthereforenotasuitableacJvityforchildrenexceptwhensupervisedcloselybyadults.OncecompletedbyfollowingtheinstrucJonsinthisdocument,theSunFunnelshouldbesetupbyaknowledgeableadultwhoisexperiencedintheuseofatelescopeforsolarobserving.ChildrenshouldneverusetheSunFunnelwithoutadultsupervision.NeverleaveatelescopeandSunFunnel—oranyothersolar-observingsetup—unaVended.
SafeSunYou’veprobablybeenwarnedmanyKmesnevertolookdirectlyattheSuntoavoidinjuringyoureyes.That’sgoodadvice!Also,mostcommercialtelescopeshaveasKckerwarningyounevertopointyourinstrumentattheSun—again,goodadvice,notonlytoprotectyoureyesbutalsotoprotectyourtelescope.ButexperiencedtelescopeusersknowthatthereareatleasttwowaystoobservetheSunsafely.Oneistouseaspecial-purposeaperturefilter—thatis,afilterthatfitsovertheinstrument’saperture,orfrontopening—toblockallbutaminusculefracKonoftheSun’slightandtherebycreateacomfortablybrightimageinthetelescope’seyepiece.Mostsuchsolarfiltersaremadefrommetal-coatedglass,metalizedpolyesterfilm,orasheetofblack-polymermaterial.
SomeKmes,though,itcanbehardtoconvincepeopletolookthroughafilteredtelescope;despiteyourmostsincerereassurances,they’reafraidthey’llhurttheireyes.Inanycase,onlyonepersonataKmecanviewtheSuninthetelescope’seyepiece.OnewayaroundtheseproblemsistoprojectanimageoftheSunfromyourtelescopeontoacardorscreen.Nownobodyhastolookthroughthetelescope(whichmeansnorefocusingandnobumping),andmanypeoplecanviewthesolarimageatthesameKme.Butthere’sariskthatsomeonemightaccidentallylookintothebrightbeamofsunlightemergingfromtheeyepiece.ThesoluKontothatproblem,andanevensaferwaytouseatelescopetoobservetheSun,isrear-screenprojecKon.That’sthetechniqueusedintheSunFunnel.Let’sbuildone!
SafeSun,ConJnued
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Supplies&Tools
Rednumberscorrespondtoitemslistedonthenexttwopages.
Supplies1.Blitz/HopkinsSuperFunnel#05034,17.75-inchx5-inchx5-inch(roundtop),$2to$6atyourlocalhardwareorauto-partsstore.Online:hAp://amzn.to/1VzVYNP2.Largehoseclamp,2.5-inchx5.5-inch,e.g.,Breeze#62080;$1to$2atyourlocalhardwarestore.Online:hAp://bit.ly/qBbvRK3.Smallhoseclamp,13/16-inchx1.5-inch,e.g.,Breeze#62016;$0.50to$1atyourlocalhardwarestore.Online:hAp://bit.ly/oTDjRR4.8-inchx8-inchorlargerpieceofDa-LiteHigh-ContrastDa-Texrear-surfaceprojecKonscreen#95774(hAp://bit.ly/1qX3yEW,$12for1sq.r.)orCarl’sRearProjecKonFilm(hAp://amzn.to/1SsLTRN,8½x11inchsheet,availableaspartof$3to$4samplepack).Ifyoucan’tordon’twanttobuyeithermaterial,asuitablealternaKveistousetwolayersofagrayorwhitevinylshower-curtainliner.
Supplies,ConJnued5.Inexpensive(e.g.,Huygens,Kellner,Plössl)all-metal-and-glasstelescopeeyepiece,1.25-inchbarrel,focallength~5to~25mm(KpsonchoosingtheopKmumfocallengthfollowonsubsequentpages).Useonethatyoualreadyhavelyingaround,aslongasithasnoplasJcinit,whichwouldmeltorcatchfire.Ifyoudon’thaveone,they’reavailablefromnumerousmanufacturersanddealers—justtype“telescopeeyepieces”intoanyinternetsearchengine,andyou’llfindmanytochoosefrom.AnothergoodsourceisSurplusShed(hAp://bit.ly/1SRnm2H).Tools6.Flat-headscrewdriver7.Smallhacksaw
8.Medium-tofine-gritsandpaper
9.12-inchruler
MatchtheEyepiecetoYourTelescopeWhattypeoftelescope?Refractor!
Eyepiece(noplasKc;allmetal&glass)
UsingaNewtonianreflectororacatadioptric(mirror-lens)telescopeisstronglydiscouraged,asconcentratedsunlightcandestroysuchinstruments’secondary-mirrorholders.
ObjecKve(mainlens,glass)
Photo:ExploreScienEfic
Stardiagonal(noplasKc;allmetal&glass)
Thatsaid,youcanuseareflectorifyou“stopdown”theaperturebyplacingapieceofcardboardoverthefrontendwithasmall(1-to2-inch)holecutofftoonesidetoletinonlyaliAlebitofsunlight.BesuretoinstalltheaperturemaskbeforeaimingthetelescopeattheSun!
Aperturemaskfastenedsecurely
Photo:Chu
ckBueter
Focallength(f)
Arefractor’sfocallengthisusuallyindicatedonthebarreloftheobjecKve(front)lensinmm.
Or,youcancalculatethefocallengthofyourtelescopefromitsdiameter(D)andfocalraKo(f/raKoorf/number):
FLtelescope=Dtelescope×f/raJo
Example:Forthe66-mmf/5.9refractorshownonthepreviouspage,FLtelescope=66mm×5.9=389mm(closeenough;round-offerror!)
Besteyepieceforafull-disk(~100mmdiameter)solarimage:
FLeyepiece(mm)≈FLtelescope(mm)÷43
(ThederivaEonofthisformulaappearslaterinthisdocument.)
Example:FortheGalileoscope,a50-mmf/10refractor(FLtelescope=500mm),theeyepiecethatwillproduceafull-disksolarimagehasafocallengthofFLeyepiece=500÷43=11.6mm.Therearemanyinexpensive12.5-mmeyepiecesavailable;anywouldmakeagoodchoice.
AneyepiecewithashorterfocallengthwillproducealargerSunimage;aneyepiecewithalongerfocallengthwillproduceasmallerSunimage.
Telescope Eyepiece(FLtelescope) (FLeyepiece)
300mm 7mm400mm 9mm500mm 12mm600mm 14mm700mm 16mm800mm 19mm900mm 21mm1000mm 23mm
SamplePairsofTelescope&EyepieceFocalLengthsforaFull-DiskImageoftheSunontheSunFunnel
Don’tworryaboutge}ngtheeyepiecefocallength“exactlyright.”Dependingonwhatyouhaveavailableorwhatyoucanbuycheaply,aimtogetaneyepiecewhosefocallengthiswithin±10%ofthe“ideal”valueofFLtelescope÷43.
TheSunFunnelwasdesignedwithsmallrefractors,suchasthosewithaperturesintherangeof50to90mm(2to3½inches),inmind.There’snothingtokeepyoufromscalingituptoamuchbiggersize,exceptthatyou’relimitedbytheamountofsunlightyoucollect,soifyoumakeamuchbiggerfunnelforasmallrefractor,you’llendupwithadisappoinKnglydimimage.
Ifyouwanttodoublethediameterofthefunnelsothatyoucandoublethediameterofthesolarimage,you’llneedtodoublethediameteroftherefractortomaintainsimilarimagebrightness.That’snottoopracKcal,assuchrefractorsaretypicallyquitelarge,heavy,andexpensive.AbeAersoluKonistouseashorter-focal-lengtheyepiecetoincreasethemagnificaKon.ThiswillblowuptheSun’simagesothatit“overfills”theSunFunnelscreen,butit’llmakesunspotsorthesilhoueAeofMercuryduringatransitappearlargerandmorevisible.
Mostrefractorsincludea90°stardiagonalwhosepurposeistomaketheviewinganglemoreconvenient.Useit!ButiftheSunislowinthesky,it’sperfectlyOKtoleaveoutthestardiagonalandvieworproject“straightthrough”thescope.
AMaVerofSize&Degrees
OK,nowthatwehavealloursuppliesandtools,
includingasuitableeyepiece,let’sbuildaSunFunnel!
Step1.ThefunnelhasasharpliAlepieceofplasKcprotrudingfromthesideabouthalfwaydownitslength.
Usingthesandpaper,grinditsmoothsoitdoesn’tscratchyourhands.
NomoresharppieceofplasKc!
Step2.Usingthehacksaw,cuttheliAleflattaboffthewideendofthefunnel.
Itworksbesttocuthalfwaythroughfromoneside,thenhalfwaythroughfromtheother.
Roughedge!Sanditsmoothnoworinstep5.
Step3.Usingthehacksaw,cutabout7inchesoffthenarrowendofthefunnelsothatwhat’slermeasuresabout10incheslong(usetheruler).
10inches
7inches
Trytomakethecutperpendiculartotheaxisofthefunnel,butdon’tpanicifitendsupslightlyKlted.Rotatethefunnelasneededtocompletethecut.
Don’tbothersandingthisroughedgeyet.
DiscardthispieceofplasKc.
Step4.Standthefunnelonitswideend.Usingthehacksaw,cutstraightdownacrossthemiddleofthenarrowopening,makingyourcutabout1to2inchesdeep.
ThenarrowendofthefunnelwillnowhavetwosemicirclesofplasKcratherthanasolidcircle.
Step5.Usingthesandpaper,smoothallthecutsurfacesonbothendsofthefunnel.
Step6.Ifyoureyepiecehasarubbereyecupand/orrubbergrip,removeit/them.TheeyepieceshouldbemadeenKrelyofmetalandglass.
Notethatifyouhaveayellowthread-ineyepiecefilter,youcanscrewitintotheeyepiecebarreltoproduceayellowSun.Butnote,too,thatthetruecoloroftheSunis...white!(Youknewthat,right?)
Step7.Inserttheeyepieceintothenarrowendofthefunnel:lensin,chromebarrelout.Youmayneedtopryapartthetwosemicircularhalvesofthefunnel’sopening.
Remember:TheeyepiecemustcontainnoplasEc,whichwouldmeltorcatchfire.Useaneyepiecewithonlymetalandglassparts.
IftheeyepiecesKllwon’tgoin,cutawayaliAlemoreofthefunneltowidentheopening,thentryagain.
Aimtogetatleastahalfinchofthelengthoftheeyepieceintothefunnel.
Step8.Placethesmallhoseclampoverthenarrowendofthefunneland,usingthescrewdriver,Kghtenitaroundthefunneltosecurelyholdtheeyepiece.
Step9.Turnthefunnelwideendup(youmightfinditeasiesttositinachairandholdthefunnelbetweenyourknees).Placetherear-projecKonscreen(ortwolayersofvinylshower-curtainliner)overthewideopening;itdoesn’tmaAerwhichsidefacesdown.Lowerthelargehoseclampoverthewideendofthefunnel...
...and,usingthescrewdriver,Kghtenitaroundthefunneltosecurelyholdthescreen;astheclampbeginstogetpurchaseonthefunnelandscreen,gentlypulldownallaroundthelooseedgeofthematerialsothatthescreenendsupflatandtautoverthefunnel’swideopening.ThisisaniteraKveprocess;you’llneedtopulldownonthematerialarereachturnofthescrewtokeepittaut.
TheSunFunnel
CongratulaKons!YouhavesuccessfullybuiltaSunFunnel!
Step10.InspectyourSunFunneltomakesuretherearenoholesintheprojecKonscreen.ItisimportanttodothiseachandeveryKmeyougotouseyourSunFunnel.Ifyoufindanyholesordeepscratches,youwillneedtoreplacetheprojecKonscreen.Step11.Removeorcoveryourtelescope’sfinderscopeorred-dotfinder,ifany.BrightsunlightenteringafinderscopewillquicklymeltitscrosshairsandcouldburnanyoneoranythingposiKonedbehindit.Ifyoucoverratherthanremoveyourfinderscopeorred-dotfinder,makesurethecoverissecureagainstwindandthepryingfingersofsmallchildren.
PrepareYourSunFunnel&TelescopeforUse
Step12.WithyourtelescopeNOTpoinKngatorneartheSun,inserttheSunFunnel’seyepiecebarrelintothe1¼-incheyepieceholderandsecureitwiththethumbscrew(s).ThenaimyourtelescopeattheSun(seethenexttwopagesforKpsonhowtodothis),focus,andenjoygroupviewingwithyourSunFunnel!
WARNING!ALWAYSSUPERVISEUSEOFTHESUNFUNNEL.NEVERPOINTANUNFILTEREDTELESCOPEATTHESUN.SEVEREEYEDAMAGEMAYOCCUR!
Cover(orremove)yourfinderscope!
YourstardiagonalshouldcontainnoplasKcparts,onlymetalandglass!
HowtoAimaTelescopeattheSunHowdoyouaimatelescopeattheSunwhenyou’renotsupposedtolookthroughit,andwhenyou’resupposedtoremoveorcoveryourfindersothatyoudon’tlookthroughthateither?!OnesoluKonistowatchyourtelescope’sshadowonthegroundandadjusttheaimunKlthetube’sshadowisassmallandasroundasyoucangetit.AnothersoluKonistoaddaspecial-purposeSunfinderthatprojectsashadoworaspotofsunlightontoatarget.Thereareseveralcommercialunitsavailable,includingthese:
• FarLaboratoriesHelioPod:hAp://bit.ly/pcILOW• TeleVueSol-Searcher:hAp://bit.ly/nkhyOk• MeadeCoronadoSolRanger:hAp://bit.ly/1ThEIc5
YetanothersoluKonistomakesomethingyourselfbasedonthedesignofoneoftheseproducts.Seethenextpageforanexample.
Rick’shomemadeSunfinder:AshortlengthofplasKctubingwithapieceofScotchMagicTapestuckonthebackend.TheassemblyisaAachedwithVelcroparalleltothetelescope.Whensunlightpoursdownthetubeandfallsonthetape,thetelescopeispointedattheSun.Easy!
SolarFiltervs.SolarProjecJonIfyouhaveanaperturesolarfilterforyourtelescope,youdon’tneedaprojecKondevice—justlookthroughtheeyepiecetoseeacomfortablybrightimageoftheSun.Conversely,ifyouwanttouseaprojecKondevicesuchastheSunFunnel,sothatmanypeoplecanviewtheSun’simageatthesameKme,youcan’tuseasolarfilter,becausethentheimagewouldbetoodimtoshowuponthescreen.
Whatdowemeanby“toodim”?Atypicalsolarfilterblocks99.999%oftheSun’slight,sothattheimageintheeyepiece—orprojectedbytheeyepiece—isonly1/100,000thasbrightasitwouldbewithoutthefilter.That’sverygoodfordirectviewingintheeyepiece,butverybadforprojecKon.
SomesolarfiltersaremadetoshowtheSuninthelightofspecificatoms,suchastheredlightofhydrogen(Halpha,orHα),orthevioletlightofcalcium(Ca).Theseproducecomfortablybrightimagesintheeyepiecebut,likefull-spectrum(“whitelight”)filters,arenotsuitableforusewithprojecKonsystemsliketheSunFunnel.
SunFunnelSafetyThekeytosuccessfulsolarprojecKon,includinguseoftheSunFunnel,istousetherightkindoftelescope—onethatcantoleratehavingfull-strengthsunlightpassthroughtheopKcaltrain—andtouseaneyepiecethatdoesn’thaveanyplasKcinit.We’llsayitagain:Werecommendusingarefractor(atelescopewithafrontlens)—notareflector(unlessyoustopitdowntoa1-or2-inchaperture),andneveramirror-lenstelescope—withadecent-qualitycommercialeyepiece.AlwaystaketheutmostcarewhenpassingunfilteredsunlightthroughanyopKcs,asyou’lldowhenusingtheSunFunneloranyotherprojecKondevice.Ifyouseeorsmellsmoke,yourequipmentisunsuitableorsetupincorrectly—getitoutoftheSunimmediately!DoyoursolarobservinginshortsKnts.Don’tleaveatelescopepointedattheSun—orevensi}ngoutintheSunpointedelsewhere—forhoursataKme.And,asnotedearlier,neverleaveasolar-observingsetupunaAended.Whenyou’refinishedwithanobservingsession,aimyourtelescopeawayfromtheSunbeforeremovingtheSunFunnel.
AddaSolarShadetoYourSunFunnel
ToimprovetheviewontheSunFunnel’sscreen,ithelpstogetitoutofdirectsunlight.Aneasywaytodothisistomakea“solarshade”outofa16-by-20-inchpieceofblackfoamboard,availableonline(e.g.,hAp://amzn.to/25D3CfE)oratyourlocalart-oroffice-supplystore.CutaholethesamesizeasyourtelescopetubeusinganX-actoknifeandsliptheshadeoverthetubeasshowninthephotoshere.Tip:Useyourlenscapasatemplateforthehole,butcuttheholealiAlesmallerthantheinsidediameterofthecapsothattheboardfitssnuglyaroundthetubeandwillstaywhereyouputit.)
WhyObservetheSun?WitheitheranaperturefilteroraprojecKonsystem,thereareallsortsofinteresKngthingstoseeontheSun,includingthese:Sunspots.TheSunhasan11-yearmagneKc-acKvitycyclemarkedbysunspots,darkblotchesthatarecoolerandthereforedimmerthantheirsurroundings.Therearegenerallymoresunspotsatthepeakofthecycle,calledsolarmaximum,andfeweratsolarminimum.Thelastmaximumwasin2014,andthenextwilloccuraround2025.Bigsunspotshaveadarkinnerpart,theumbra,andalighterouterpart,thepenumbra,andthesecantakeonmanydifferentshapesandsizes.SolarrotaJon.IfyouobservetheSunfromdaytoday,you’llnotethatitsrotaKoncarriessunspotsabout15°easteachday.BecausetheSunspinsonceaboutevery25days,ittakeslessthantwoweeksfornewspotstoappearonthewesternlimb(edge),marchacrosstheSun’sface,anddisappeararoundtheeasternlimb.Theimagesonthenextpageshowabigsunspotoverthecourseofseveraldays.
Sunspot,April13,2016
UmbraPenumbra
Twodayslater(April15)
Twodayslater(April17)
Limbdarkening.TheouterpartsoftheSun’sdisk,towardthelimb(edge),lookdarkerthanthecenter.TheSunisaballofhotgas,soitdoesn’thaveahardsurfacelikeaplanetormoon.Whenyoulooktowardthecenterofthedisk,yourgazepenetratestodeeper,hoAerlayers.Whenyoulooktowardtheedge,you’relookingthroughhigher,coolerlayers,whicharen’tquiteasbright.Planetsintransit.Occasionallyoneoftheinnerplanets,VenusorMercury,crossesinfrontoftheSunasseenfromEarth.Thisiscalledatransit,andwhenithappens,youcanseetheplanetinsilhoueAemovingacrosstheSun’sfaceoverseveralhours.VenustransitedtheSunonJune8,2004,andJune6,2012,butitwon’tdosoagainunKlDecember11,2117,soifyoumissedthelasttwo,you’reoutofluck.TransitsofMercuryaremorefrequent;recentandupcomingtransitsofMercuryincludeNovember8,2006;May9,2016;Nov.11,2019;Nov.13,2032.TofindoutwhentransitsofMercuryoccur,andfromwhereintheworldagiventransitisvisible,seehAp://bit.ly/1WGafaw.
WhyObservetheSun,ConJnued
TransitofVenus:June6,2012
SilhoueAeofVenus
NotethattheSun’slimb(edge)islessbrightthanitscenter.Thisiscalled“limbdarkening.”
SizeofMercuryatsamescale:
Alltheseotherdarksplotchesaresunspots.
ParJalsolareclipses.AsolareclipseoccurswhentheMoonparKallyortotallyblockstheSun.OnMonday,August21,2017,asolareclipsewillbevisible(weatherpermi}ng)acrossallofNorthAmerica.ThewholeconKnentwillexperienceaparKaleclipselasKng2to3hours.Halfwaythroughtheevent,anyonewithina~65-mile-widepath(hAp://bit.ly/26�ZvJ)fromOregontoSouthCarolinawillexperienceabrieftotaleclipse,whentheMoonwillcompletelyblocktheSun’sbrightfaceforupto2minutes40seconds,turningdayintonightandmakingvisiblethespectacularcorona—theSun’setherealouteratmosphere.LookingdirectlyattheSunissafeduringthebrieftotalphaseofasolareclipse(“totality”),whentheMoonenKrelyblockstheSun’sbrightface.AtallotherKmesyoumustfollowthesafetyadvicethatappearsthroughoutthisdocument.TheSunFunnelwillbeuselessduringtotality;itissuitableonlyduringtheparKalphases.Tofindoutwhensolareclipsesoccur,andfromwhereintheworldagiveneclipseisvisible,seehAp://bit.ly/1VFZhCz.
WhyObservetheSun,ConJnued
SolarEclipseofMarch9,2016ObservedfromtheMoluccaSea,Indonesia
Thesequencegoesfromupperright(beginningofeclipse)tolowerleS(endofeclipse).
Totalsolareclipse:theonlyphaseyoucanobservesafelywithyoureyes,i.e.,withoutaspecial-purposesolarfilter,aSunFunnel,oranotherprojecKonmethod.
TheGalileoscope(hAp://galileoscope.org)isafinetelescopetousewiththeSunFunnel.Withsome250,000oftheseinexpensive,high-qualitytelescopesinusearoundtheworld,itwouldbeashamenottousethemforpublicviewing,forexample,duringtheparKalphasesoftheAugust21,2017,solareclipseintheAmericas.Buttherearetwoproblems:(1)thesuppliedeyepieceisplasKcandwouldmeltifusedforsolarprojecKon,and(2)theGalileoscopeisdesignedtobeused“straight-through,”withoutastardiagonal,whichleavestheSunFunnel’sscreenawkwardlypointedattheground.Tosolvethefirstproblem,notethattheGalileoscopehasastandard1¼-incheyepieceholder,soitcanusestandard1¼-inchmetaleyepieceswithglasslenses,preferablyonewithan11-to12.5-mmfocallength.Ifyoudon’talreadyhavesuchaneyepiece,checkSurplusShedoranotherdealer.
TheGalileoscope&theSunFunnel
There’snotmuchyoucandoaboutthesecondproblem,excepttoviewtheSunwhenitappearslowinthesky,i.e.,intheearlymorningorlatearernoon.AtsuchKmes,withthenearlyhorizontalGalileoscopeonafullyextendedphototripod,theSunFunnelcanbeconvenientlyplacedforgroupviewingoftheprojectedsolarimage.
MathemaJcalUnderpinningsoftheSunFunnelDesign
Onthefollowingpageswegothroughthe(relaKvelysimple)mathbehindtheSunFunnel.ItrelatesthefollowingquanKKesoverwhichwehavesomemeasureofcontrol:
• Telescopefocallength• Eyepiecefocallength• ProjecKondistance• Projectedimagediameter
andthefollowingquanKtyoverwhichwehaveabsolutelynocontrol:
• Sun’sangulardiameter
A
A/2
A/2S/2
S/2çObjectofangularsizeA(veryfaraway)
Telescopeoffocallengthf
ImageoflinearsizeS
f
Telescopeoffocallengthf(mm)producesimageoflinearsizeS(mm)ofobjectwithangularsizeA(radians).
RelaKonshipbetweenthesequanKKes:
tan(A/2)=(S/2)/f
Rearrange tan(A/2)=(S/2)/ftoget ftan(A/2)=S/2andfinally S=2ftan(A/2)Notethatfortheverysmallangleswetypicallyencounterinastronomy,
tan(A/2)≈A/2sowehave S=2fA/2whichreducesto S=fA (S,finmm;Ainradians)
WeneedtoknowthesizeoftheSunimageproducedbythetelescope,sincethat’swhatweplantoprojectontotheSunFunnelscreen.DoyouknowtheSun’sangularsize,A,inradians?Probablynot,solet’stweakourformulatoputAintodegreesinstead.
Thereare180°inπradians(thearcofasemicircle),so
S=fA×(180°/π)
or S=fA/57.3 (Aindegrees)
TheSun’saverageangularsizeisjustover½°(youknewthat,right?),i.e.,A≈0.533°.
So,withA=0.533°,weget
S=fA/57.3
S=f(0.533/57.3)
S=0.0093f (Sinmm,finmm)
ConsidertheGalileoscope,whichhasafocallengthof500mm.WhenaimedattheSun,itproducesanimageofdiameterS=0.0093×500mm=4.65mm.
You’renotgoingtohavemuchlucktryingtoseesunspotsorMercury’ssilhoueAeonsuchaKnyimage!
That’swhyweuseprojecKon,i.e.,toproducealargerimageonwhichwecanmoreeasilyseesunspotsandotherfeaturesofinterestontheSun’sdisk.
Thegeometryissimilartowhatwesawearlier:
P
D/2
D/2B/2
B/2
ProjecKondistance,PProjectedimagediameter,D
Angularsizeofprojectedimage,B
tan(B/2)=(D/2)/PEyepiece
Rearrange tan(B/2)=(D/2)/Ptoget Ptan(B/2)=D/2andfinally D=2Ptan(B/2)Again,fortheverysmallangleswetypicallyencounterinastronomy,
tan(B/2)≈B/2sowehave D=2PB/2whichreducesto D=PB (D,Pinmm;Binradians)
ButwhatisB,exactly?RememberA?It’stheangularsizeoftheimageproducedbythetelescope.Well,BisjustthatanglemulKpliedbythemagnificaKonproducedbythetelescope’seyepiece.Andthat,inturn,isthefocallengthofthetelescopedividedbythefocallengthoftheeyepiece,i.e.,
B=A×magnificaKon=A×(FLtelescope/FLeyepiece)so D=PBbecomes D=PA(FLtelescope/FLeyepiece)withD,P,andthetwoFL’sinmm,andAinradians.
Butremember,A(theSun’sangulardiameterinradians)isequalto0.533/57.3,or0.0093.Soourformulaforthediameteroftheprojectedimage,
D=PA(FLtelescope/FLeyepiece)becomes D=0.0093P(FLtelescope/FLeyepiece)withallquanKKesinmm.ThiscanberearrangedtosolveinsteadfortheprojecKondistance,P:
P=107.5D(FLeyepiece/FLtelescope)againwithallquanKKesinmm.
AlternaKvely,eitherformulacanberearrangedtosolveinsteadfortheeyepiecefocallength:
FLeyepiece=0.0093P(FLtelescope/D)
againwithallquanKKesinmm.FortheSunFunnelasdescribedhere,P≈10inches≈250mm,andthedesiredimagesizeforafull-diskSunisD≈100mm(sincethewideendofthefunnelisabout5inches,or127mm,across).Thus,
FLeyepiece=0.0093×254÷100×FLtelescope
or FLeyepiece=0.023FLtelescope=FLtelescope÷43
QuesJons?Comments?
Youmaycontacttheauthorsbyemail:
RickFienberg:rick.fienberg@aas.org
ChuckBueter:bueter@nightwise.org
LouMayo:astronomer2go@verizon.net
NowthatyouhaveallthemathemaKcalrelaKonshipsbetweentelescopefocallength,eyepiecefocallength,projecKondistance,andprojectedimagesize,youcandesignyourownsolar-projecKondeviceusingmaterialsotherthanthosesuggestedhere.
Exceptwhereotherwisenoted,allphotosare©2011-2016byRichardTreschFienberg.
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