eye_lens facts paperl11

Phys531 Lecture 11 7Octob er2004 Survey ofOptical Systems Lasttime: Develop edtoolstoanalyze optical systems -raymatrix technique -thicklenspicture Today,lookatseveral common systems Won'tusematrix metho dsexplicitly butmany lenses thick: implicitly usethicklenspicture 1 Outline: theeye eyeglasses magnifying glass microscop e These andmoreexamples: Hecht 5.7 Nexttime: advice fordesigning systems ofyourown 2 TheEye(Hecht 5.7.1) Mostbasicoptical system Components: -cornea: n=1:376 -vitreous humorwater: n=1:33 -lens: n=1:391:41 indexvaries:highincenter, lowatedges -iris:variable aperture stop diameter 2-8mm -retina: detecto r Again, usethicklenspicture lenssystem haswelldened focallength 3 4 Note:detecto risinmedium ni=1:33 Lensequation becomes 1 so+ni si=1 fo=ni fi fo=object focallength fi=image focallength Irrelevant forraymatrix Modiesthicklenspicture: foapplies tofrontfocalpoint fiapplies tobackfocalpoint 5 System focallength variable maxobject distance =1(\relaxed") minobject distance 25cm(varies) What focallengths? Distance fromlenstoretina 24mmsi Relaxed eye:so=1)fi=si Forso=25cm:ni fi=1 so+ni si)fi=22mm Sofi=2224mm Called \accommo dation" 6 Mostfocusing powerfromcornea-air interface fi=n n1R R9mm)fi33mm Remaining surfaces: 1 ftotal1 fcornea+1 frest So 1 frest=1 241 33=1 88mm forrelaxed eye frest=66mmforaccommo dated eye 7 frestadjusted bysqueezing lens muscles relaxed: flong muscles tense: fshort Minimum achievable so=nearpoint dependson exibilit yoflens varieswithage Question: Whycan'tyouseewellunder water? 8 Capabilities oftheeye Resolution: angula rresolution
0:017=0:3mrad Justadequate toresolve crescent ofVenus Correpsonds toabout5monretina Atso=25cm, spatial resolution =so
=75m Also,wideeldofview: correspondsto100Mpixels! Resolution bestincenter 9 Sensitivit y: Fullyexpanded pupil, canseeI1010W/m2 frompointsource Power=IA Area=(4mm)2)P1014W Maximum irradiance: sunlight I250W/m2 pupilarea(1mm)2 Maxpower=103W But:sunisnotpointsource powerspreadoutonretina 10 Sunsubtends angle10mrad 30
 Same intensit yfrompointsource: illuminate area302smaller onretina 1000higher image irradiance Maxpowerfrompointsource 106W (damage threshold forlaser) Dynamic range ofeye:1014to106W eightordersofmagnitude Instantaneous range lower: veordersofmagnitude 11 Bestarticial detecto rs: photographic lm high-end CCDs dynamic range fourordersofmagnitude 10worsethaneye Upshot: Can't buildadetecto rnearlyasgoodastheeye 12 Eyeglasses (Hecht 5.7.2) Common problem: focallength ofeyeisn'tright Toostrong =nearsighted =myopic: relaxed eyehasfi<24mm 1 somax=n fin si>0 socan'tfocusat1 Maximum distance offocus=farpoint Easytomeasure Forme,farpoint25cm 13 Alsomoves nearpointcloser: formesomin7cm What ismyrange off?(assuming si=24mm) 1 fmin=1 1:33
70mm+1 24mm )fmin=19mm and 1 fmax=1 1:33
250mm+1 24mm )fmax=22mm 14 Fixwitheyeglasses Relaxed eye: 25 cm Addlenstoputimage of1at25cm: 15 What focallength required? wantso=1,si=25cm Sof=25cm Thisismyprescription: D=1 f=4diopters Howcloseisnearpointwithglasses on? sosuchthat si=-7cmforf=25cm 1 so=1 25+1 7=1 10cm 16 Other vision problems: Farsighted =hyperopia: eye'slenstooweak Correctwithpositive lens Astigmatism: asymmetry inlens f'sdierent along x,y Correctwithcylindrical lens Question: Ifyouwanttostartarewithyourglasses, should youbenear-sighted orfar-sighted? 17 Magnifying glass (Hecht 5.7.3) At25cm,typical eyecanresolve 75m Usealenstoseesomething smaller. .. whatkind? Wanterect, magnied image ofrealobject Realobject: so>0 Erect: m=si=so>0sosi<0 Magnied: m>1sojsij>jsoj 18 Have 1 so+1 si=1 f Want1=sopositive andlarge 1=sinegative andsmall Means fshould bepositive Recall: getvirtual image withpositive lens when so<f 19 Picture: sosi Seeimage ismagnied Butalsofurther away... Resolution improved ifimage onretina isbigger 20 Notesizeofimage onretina proportional toangula rsizeofobject α Sizeonretina =f Don't reallyknowf,justconsider  21 Dene magnifying powerofsystem (MP) =angula rmagnication =withlens without lens WriteasMP=5,etc. Could makewithout lensverybig: holdobject rightuptoeye Butcan'tfocusifso<nearpoint 22 Formagnifying glass, microscop e,etc (nottelescop e) Dene forstanda rddistance so=25cm Example: IfItakeomyglasses, nearpointis7cm Object at7cmsubtends =y=7cm Object atstanda rd25cmsubtends 0=y=25cm Magnifying power= 0=25 7=3:6 MybareeyeshaveMP=3.6 23 What isMPofglass? sosi d L Expressinterms ofpractical parameters d=distance fromeyetoglass L=distance fromeyetoimage f=focallength ofglass Haveobject sizeyo image sizeyi 24 Angula rsizeofimage =yi L=myo L magnication m=si=so: =si soyo L Without glass 0=yo do SoMP= 0=si sodo L 25 Eliminate so,si: Have si=dL and1 so+1 si=1 f Sosi so=si f1=dL f1 Gives MP= 1+Ld f! d0 L 26 Tworeasonable waystouse: MakeL!1 Achieve bymaking so!f(sosi!1) Viewimage withrelaxed eye,ddoesn'tmatter GetMP!d0 f LargeMPforsmall f 27 Other metho d: Lensclosetoeyed!0 MP!d0 1 L+1 f! TogetlargeMP,wantLsmall minimum L=nearpoint=d0 ThenMP!1+d0 f Largeiffissmall 28 Where doweneedtoputobject? 1 so=1 f1 si =1 f+1 d0 =1 d0 1+d0 f! Soso=d0 MP Recall eyeexample: MP=d0=so...same 29 Object looksasitwouldifyoucould focusatso Lensmakeseyestronger likebeingnear-sighted Workswellifyoucanholdobject uptoeye 30 Either metho dworksuptoabout4 fdownto6cm Forhigher MP,notparaxial: -lensaberrations important -requires morecomplex lens Stillworks: Metho d2:Jeweler'sloupe GetMPupto30 Impractical ifobject position xed orMPsohighyoucan'tholdsteady Already aproblem at10 31 Metho d1:putlensveryclosetoobject since sofandfissmall Problem: exitpupilissmallandfaraway -can'tseeverymuch Question: Where istheexitpupilinthiscase? Solution: compoundmicroscop e 32 Microscop e(Hecht 5.7.5) Usetwolenses: objective: shortf,closetoobject eyepiece: collects light,match toeyepupil Typical system: objectiveeyepiece 33 Typically don'tcareaboutinversion: -object creates realinverted image Objective collects raysatsteepangles: -importanttocontrol aberrations Eyepiece: putsnalimage at1 -viewwithrelaxed eye provides additional magnication matches exitpupiltoeye Aberrations lessimportantthaninobjective 34 What ismagnifying power? Objective: magnication =si=so Angula rmagnication notappropriate: intermediate image notviewedbyeye Evenso,thereisastanda rdlength scale Wantobjectives interchangeable: standa rdposition forobject, image Setbytubelength =distance frombackfocalpointtoimage =160mm 35 Then si=160mm+f 1 so=1 f1 si MP=si so=si f1 =160mm+f f1=160mm f Thisismagnication written onobjective So20objective hasf=8mm 36 TotalMP=MPobj
MPeyepiece =160mm fobj
250mm feyepiece where MPforeyepiece followsstanda rdconvention Typical objective: 5to60 Typical eyepiece: 5or10 Warning: Fancymicroscop esdon'tfollowtheseconventions 37 Summa ry: Eyesareimpressive instruments, bothfor sensitivit yandresolution Eyeglasses/contacts workbyadjusting location ofnearandfarpoints Eect ofmagnifying glassisreallyangu- larmagnication -Measure withmagnifying power Microscop eusestwolenses toprovide moreMPthanglass 38