Astronomy3130
DayAssignment3–Spring2016
DueTuesdayMarch1
1)Supposeyouconstructa30cmtelescopeobjectivefromasinglepieceofBK-7glass
(refractiveindexcurvesvs.wavelengthforthismaterialcanbefoundfairlyeasily).Ifthis
lensisplano-convex(flatononeside,curvedtomakeitapositiveconverginglensonthe
other)witharadiusofcurvatureof2000mmontheconvexface:
a)Calculatethefocallengthofthislensat500nm.
b)Whatistheplatescaleinmm/arcsecforthistelescope?
c)Calculatetheimageblur(diameteroftheoutoffocusimage)atawavelengthof
400nminarcsecondsduetochromaticaberrationassumingthefocalplaneisin
focusforawavelengthof500nm.
d)Howdoesthechromaticaberrationat400nmcomparetothediffraction-limited
imagesizeforthistelescope?
e)WhatwillthepixelscaleofanAndoriXon888CCDcamerabeifplacedatthe
focalplaneofthisonelenstelescope?Whatisthefield-of-viewofthiscamera?Is
thispixelscaleagoodmatch?
f)Inordertosolvethechromaticaberrationissueyoudecidetoconstructa
reflectingtelescopewiththesamefocallength.Whatistherequiredradiusof
curvatureofthetelescopemirrortocreatesystemwithidenticalfocallength?
2)Consideran8.4-meterdiametertelescopeaperture(oneoftheprimarymirrorsonthe
LargeBinocularTelescope).Giventherulethat1”seeingcorrespondstoanr0of10
centimetersatawavelengthof500nmestimatetheapproximatenumberofactuators
required(thenumberofr0'sintheaperture)tocorrectattheinfrared“H”bandat1600nm
whenthe500nmseeingis0.8”.Comparethisnumbertotheactualnumberofactuatorson
theLBTsecondarymirrors(whichyouwillneedtodigupandreference).
3)Thecoursehomepagehasavarietyofexposuretimecalculatorslistedinthetools
section.Exploretheseinordertoanswerthequestion,“Howlongdoyouhavetoexpose
onthe31”telescopeatFanMountaintodetecta21stmagnitudestaratSNR=10throughan
R-bandfilter.”Thepathtotheanswerrequiresthatyoumakesomeassumptions.Make
anythatarereasonable,butbesuretobeexplicitaboutthoseassumptionsinyouranswer.
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