17 geometric opticshkpho.phys.ust.hk/protected/lecture2016/17 geometric...learning goals looking...
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GeometricOptics
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LearningGoals
Lookingforwardat…• howaplanemirrorformsanimage,andwhyconcaveandconvexmirrorsformimagesofdifferentkinds.• howimagescanbeformedbyacurvedinterfacebetweentwotransparentmaterials.• whataspectsofalensdeterminethetypeofimagethatitproduces.• whatcausesvariousdefectsinhumanvision,andhowtheycanbecorrected.• howmicroscopesandtelescopeswork.
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Introduction
• Thissurgeonperformingmicrosurgeryneedsasharp,magnifiedviewofthesurgicalsite.• Toobtainthis,she’swearingglasseswithmagnifyinglenses.• Howdomagnifyinglenseswork?• Howdolensesandmirrorsformimages?• Weshalluselightraystounderstandtheprinciplesbehindopticaldevicessuchascameralenses,theeye,microscopes,andtelescopes.
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Reflectionataplanesurface
• LightraysfromtheobjectatpointP arereflectedfromaplanemirror.• ThereflectedraysenteringtheeyelookasthoughtheyhadcomefromimagepointP’
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Imageformationbyaplanemirror
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Imageformationbyaplanemirror:Signrules
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Characteristicsoftheimagefromaplanemirror
• Inaplanemirror,theimageisvirtual,erect,reversed,andthesamesizeastheobject.
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Theimageisreversed• Theimageformedbyaplanemirrorisreversed;theimageofarighthandisalefthand,andsoon.
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Sphericalmirrorwithapointobject
• AsphericalmirrorwithradiusofcurvatureR formsarealimageP’ ofthepointobjectP.
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GeneralSignconventions(mirror&lens)
• IftheobjectpointP isonthesamesideastheincidentlight,thens ispositive.• IftheimagepointP’ isonthesamesideasthereflectedlight,thens’ ispositive.• IfthecenterofcurvatureCisonthesamesideastheoutgoing light,thenR ispositive.
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Focalpointandfocallength• Whentheobjectisveryfarfromthesphericalmirror,theincomingraysareparallel.• Thebeamofincidentparallelraysconverges,afterreflectionfromthemirror,toafocal point,pointF.• Thedistancefromthevertextothefocalpoint,denotedbyf,iscalledthefocal length.
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Focalpointandfocallength
• Withtheobjectatthefocalpoint,thereflectedraysareparalleltotheopticaxis.• Thereflectedraysmeetonlyatapointinfinitelyfarfromthemirror,sotheimageisatinfinity.
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Imageofanextendedobject:Sphericalmirror
• Shownishowtodeterminetheposition,orientation,andheightofanimageformedbyaconcavesphericalmirror.
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Imageformationbyaconvexmirror• Ifthemirrorisconvex,sothatR isnegative,theresultingimageisvirtual(thatis,theimagepointisontheoppositesideofthemirrorfromtheobject),erect,andsmallerthantheobject.
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Focalpointandfocallengthofaconvexmirror
• Whenincomingraysthatareparalleltotheopticaxisarereflectedfromaconvexmirror,theydivergeasthoughtheyhadcomefromthevirtual focalpoint F atadistancefbehindthemirror.• Thecorrespondingimagedistances isnegative.
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Focalpointandfocallengthofaconvexmirror
• WhentheincomingraysareconvergingasthoughtheywouldmeetatthevirtualfocalpointF,thentheyarereflectedparalleltotheopticaxis.
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Graphicalmethodoflocatingimages
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Graphicalmethodoflocatingimages
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Imageofapointobjectatasphericalsurface
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Apparentdepthofaswimmingpool
• Whenlighttravelsthroughaplanesurfacebetweentwoopticalmaterials,theimagehasthesamelateralsize(m =1)andisalwayserect.• s’=-s/1.33• Theapparentdepthofapoolislessthanitsactualdepth.
R→∞
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Lensmaker’s equation
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Magnification
m = y 'y= −s 's
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Typesoflenses• Shownbelowarevarioustypesoflenses,bothconverginganddiverging.
• Anylensthatisthickeratitscenterthanatitsedgesisaconverging lenswithpositivef ;andanylensthatisthickeratitsedgesthanatitscenterisadiverging lenswithnegativef.
1f= (n−1) 1
R1−1R2
"
#$$
%
&''
R1 > 0 > R2R1 =∞0 > R2
0 > R2 > R1 R2 > 0 > R1
f > 0 f < 0
R1 > R2 > 0R1 =∞R2 > 0
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Thinconverginglens
• Alens isanopticalsystemwithtworefractingsurfaces.• Thesimplestlenshastwosphericalsurfacescloseenoughtogetherthatwecanignorethedistancebetweenthem;wecallthisathin lens.
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Thinconverginglens• RayspassingthroughthefirstfocalpointF1 emergefromaconverginglensasabeamofparallelrays.
• fiscalledthefocal length.
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Imageformedbyathinconverginglens
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Thindiverginglens• Whenabeamofparallelraysisincidentonadiverging lens,theraysdivergeafterrefraction.• Thefocallengthofadiverginglensisanegativequantity,andthelensisalsocalledanegative lens.
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Thindiverginglens
• Incident raysconvergingtowardthefirstfocalpointF1ofadiverginglensemergefromthelensparallel toitsaxis.
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Graphicalmethodsforlenses
• Shownbelowisthemethodfordrawingthethreeprincipal rays forarealimageformedbyaconverginglens.
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Graphicalmethodsforadiverginglens
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Example
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Cameras
• Whenacamera isinproperfocus,thepositionoftheelectronicsensorcoincideswiththepositionoftherealimageformedbythelens.
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Cameralensbasics
• Thefocallengthf ofacameralensisthedistancefromthelenstotheimagewhentheobjectisinfinitelyfaraway.
• Theeffectiveareaofthelensiscontrolledbymeansofanadjustablelensaperture,anearlycircularholewithdiameterD.
• Photographerscommonlyexpressthelight-gatheringcapabilityofalensintermsoftheratiof/D,calledthef-numberofthelens:
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Theeye• Theopticalbehavioroftheeyeissimilartothatofacamera.
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Defectsofvision
• Anormaleyeformsanimageontheretinaofanobjectatinfinitywhentheeyeisrelaxed.• Inthemyopic (nearsighted)eye,theeyeballistoolongfromfronttobackincomparisonwiththeradiusofcurvatureofthecornea,andraysfromanobjectatinfinityarefocusedinfrontoftheretina.
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Nearsightedcorrection
• Thefarpointofacertainmyopiceyeis50cminfrontoftheeye.• Whenadiverginglensoffocallengthf =−48cmisworn2cminfrontoftheeye,itcreatesavirtualimageat50cmthatpermitsthewearertoseeclearly.
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Farsightedcorrection• Aconverginglenscanbeusedtocreateanimagefarenoughawayfromthehyperopiceyeatapointwherethewearercanseeitclearly.
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Angularsize
• Themaximumangular sizeofanobjectviewedatacomfortabledistanceistheangleitsubtendsatadistanceof25cm.
𝜃 ≈ tan 𝜃 =𝑦
25𝑐𝑚
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Themagnifier• Theangular magnification ofasimplemagnifieris:
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Thecompoundmicroscope
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Theastronomicaltelescope
• Thefigurebelowshowstheopticalsystemofanastronomicalrefracting telescope.
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Thereflectingtelescope
• TheGeminiNorthtelescopeusesanobjectivemirror8metersindiameter.
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Example:Inatelescope,theobjectivelensformsareal,reducedimageIoftheobject.Thisimageistheobjectfortheeyepiece,whichformsanenlarged,virtualimageofIwhichisatinfinity(formastcomfortableviewingbyaeye).
ϑ =−y 'f1
and ϑ ' = y 'f2
angular magnification M =ϑ 'ϑ= −
f1f2
(-ve for the inverted final image)