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

1

32

5

4

9

76

8

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.