OPT 305(ophthalmic optics).pdf

Ki 9i144 COURSEOUTLI NE Lec tur e1…………………………………. Int roduc tion Lec tur e2………………………………..... Manuf act...

Ki 9i144 COURSEOUTLI NE Lec tur e1…………………………………. Int roduc tion Lec tur e2………………………………..... Manuf act ureOfOpt icalGl ass Lec tur e3…………………………………. PowerSpec ifi cat ion Lec tur e4…………………………………. For mOfLens Lec tur e5……………………………. ……PowerMeas urement Lec tur e6…………………………………As tigmat icLens es Lec tur e7…………………………………Tr ans pos iti on Lec tur e8…………………………………Rel ati ons hipBet weenLensPowerAndThi cknes s Lec tur e9…………………………………Opht hal micPr ismsAndDec ent rat ion Lec tur e10……………………………..…Spec tac leFr amesAndFi tti ng RECOMMENDEDTEXTS: 1.I ntr oduc tiont oOpht hal micOpt icsbyDar rlyMei sterandJ amesE. Sheedy. 2.Geomet ric ,Phys ical ,andVi sualOpt icsbyMi chaelP. Keat ing. LECTURE1 I NTRODUCTI ON SI GNCONVENSI ON Thes ignconvention/ rul esusedi nopt icshaveal readybeenment ionedi nOPT203and OPT215butwillberevi si tedher e. 1) I nci dentl ightwi llbec ons ider edast ravel li ngf roml eftt ori ght 2)Alldi stanc es( obj ectdi stance,i magedi stanc e,foc all engt hs,et c.)ar emeas ured fr om t heoptic alsyst emconcer ned. a)I fthedis tanc ei smeas uredinthesamedir ecti onast hati nwhi chi nci dent l ighti dtr avel li ng,i twil lbecons ider edasposi ti ve. b)I fthedist anc eismeas uredi ntheoppos itedi rec tiont othatoft ravelof i nci dent l ighti twi llbec ons ider edasnegat ive. 3)Ver tic aldis tancesmeas uredfr omtheopt icalaxi stoapoi ntabovear econs ider ed pos iti ve, andt hos emeasuredt oapoi ntbel ow, ar enegati ve. 4)Theanglebetweenar ayandt heopt icalaxi sismeas uredf rom t her ayt othe opt icalaxi s. 5)Angl esofi nci denc e,r efl ect ion,andr efr act ionar emeas uredf rom t henor malt o ther ay.. 6)Vengeancecanbedes c ribedasthespreadofl i ghtraysasas pec ifi cdis tancef rom thei rfocus.Li ghtraysmovi ngtowardstheirfocusareconvergi ng(posi ti ve), and thos emovi ngawayfromt heirf ocusarediverging(negat ive). Theunitofmeas urementofver gencei st heDioper.Thever genceofapar ticul ar raysystem i st hereci proc alofthedi stancefr om thewavef rontt othecenterof curvat ur e( focus) ,inmeters. NOMENCLATURE( NAMI NGSYSTEM) a) A rayisani maginaryli neextendingf rom t hef oc ust othewavef r ont.I t repr esentst hedi r ecti onofpropagati on( movement )ofthewavef r ont.Ar ayis consi deredt oemanat efrom poi ntsources,anobjectoffini te(measur able)si ze, orfr omanobj ec ts ol arge,i tssi zecannotbemeas ured(inf ini te- siz edobject). b) Apenc ilofl ighti sabundl eemanat ingf romapoi nts our ceaf terpas sing t hroughali miti ngapert ure(f orexampl e,apinhol e).Thec hiefr ayi napenc ili s t heraypas singthr oughthec entr eoftheaper ture. c )Abeam ofl ighti sacoll ect ionofpenci lsar isi ngf rom anext ended( inf ini te- siz ed) s our ce, orfr omas our ceoffini tes ize. d)Anobj ecti saphys icals our ceofl ight ,ornol ight ,exi sti ngi nobj ects pac e. Anobj ec tmayber ealorvirtual.Ar ealobjec tisonefrom whic hlightisr ays diver georarerefl ectedfrom.Avi rt ualobjectisonetowardswhic hl i ghtisa convergi ngbef orei nterrupti onbyt hesurfac eofanoptic alsys t em. e) Ani mage,producedbyanopticalsyst em,isthepr oject ionofanobj ectinimage space.Iti sformedbyl i ghttravell ingfr om anobject ,inimagespace,af teran opti cals ystemhasactedonthelight Ani magec analsober ealorvirtual.Ar ealimagei soneformedbyt heac t ual convergenceofraysrefractedorreflect edbyanopt i calsyst em.Arealimagec an be‘caught’onas cr eeni fthescreeni splacedini magespace.Avirtualimageis for medbyl ight ,whichappear stobedi vergi ngf rom poi ntsinanopt i calsyst em aft err ef lec t i onofrefr ac ti on.Avi rt ualimagewi llnotfocusonascr eenpl acedin images pace,butitcanbec onvertedint oar ealimageand–pr ojectedontoa screen–bypl aci ngac onvexlensint heopt i calsystem. Thisr efer stoallt hes pac einwhichl ighthas ,orwoul dhave,t ravel edbef ore beingi nter rupt edbytheopti cals yst em.  f ) Obj ectSpac e Thisi sthespacewithinwhi c hlightt ravelsaf terbei ngact eduponbyanopt i cal syst em.Li keobjec ts pace,itencompassesspaceonbothsidesoftheopti cal syst em:t hesi deonwhi c hi tist ravel li ng;andt hesi def rom whichi tappear st o havecome. g)I mageSpac e Thewordpri marywhenusedtoget herwit hfocal ,pri ncipal,andnodalpoi nts , appl iest opoi ntsi nobj ects pace.Whereassec ondaryappli estopoint sinimage spac e. OPHTHALMI CLENSMATERI ALS Lenseshavebeenus edasvis ualaidsi nonef or m oranotherf orhundredofyear sbutup unti ljustunder300yearsago,allsuc hlensesweremadeofgl ass.Further more,fr om 300yearsagoupt il ltheperiodbetween1918and1938( betweent hefi rstandsecond worldwar),vir tual lyallsi nglevi sion(asopposedtopresbyopic )l ensesweremadeofa part icul arvarietyofglassknownasOpht halmicCrowngl ass,whichhasani ndexof ref racti onof1.523. NoteForanyr efr acti ngmat erial(suchasgl assorpl ast ics)wit hauni for mr efr act ive i ndex, t hepowertobend( r efr ac t)l ightraysincreaseswiththethi c knessofthemater ial. Also,ass umingauniformthicknessofdif f erentrefrac tingmaterials,t hemat er ial swith thehighestr efr acti veindexwillref r ac tlightmor epower f ull y. Othervar iet iesofgl as sl i kef li ntglasswerefir stusedforspec ialpurposessuchasfor makingreadings egmentsinbifoc als.Morerecentl ythough,numer ous‘hi ghindex’ l enseshaveper vadedt hemarketforgener aluseins i ngl evi s ion,biandmul ti -foc al l enses. TheSecondWorl dWars er vedasas ti mulusfort heproduct ionofplasticmater ialsof opti calqual it yandthedevelopmentofplasti copht hal micl ensesdevelopedrapi dly aft erthewar.Wit hint heintr oducti onands ubsequentpopulari tyoflargelenss izesin t he70s,plast iclenseshaveassumedanevengr eaterrol einlensmanufact uret hati s st il levi denttoday.Thisi sinspit eofthef ac tthatglassl ensesoff erbet teropt icsandare moredurabl ethantheirplas ticcount erparts. REFRACTI VEERRORSANDLENSES Spec tac lel ens esar ethemos tcommonmet hodofc orr ect ingr efr act iveer ror sand enabl ingpeopl etos eewel l.Cont actl ens esandr efr act ives urger yar eot heropt ions. Ref rac tiveer ror sinc ludemyopi aornear -si ght ednes s,andhyper opi aorf ar- sight ednes s. Myopi aandhyper opi aar ecor rec tedwi ths pher icall ens esofmi nusandpl uspower r espec tivel y.As pher icall enshasc irc ularc urves.Whi lel ooki ngs trai ghtatas pher ical l ensasi tiswor nbef oret heeye,anyr adi alc ros ssec tionoft hel ens( i. e.ac ros ssec tion t hati ncl udest hec ent eroft hel ensal soc all edamer idi anoft hel ens )wi llhavet hes ame l ensc urvat uresandt hes amepower.Thi sisi ll ust rat edi nFi gur e1. 1.Ar esul toft hisi s t hatt her otat ionalpos iti onoft hel ensbef oret heeyei snoti mpor tant.Inot herwor ds, whi lel ooki ngatt hewear erandas sumi ngt hatt hel ensi spr oper lyc ent eredi nfr ontof t heeye,i fthel enswer etor otat e(s ay,wi thi nac irc ulareyegl assf rame) ,itwoul dhave noef fec tuponvi si on.Whenpr esc ribi ng,f it ting,ormanuf act uri ngs pher icall ens est he l ensmus tbepr oper lyc ent eredbef oret heeye,butt her otat ionalpos iti onoft hel ens bef oret heeyei suni mpor tant.Spher icall ens esar espec ifi edbyt hei rspher icalpower onl y. FI GURE1. 1As pher icall enshast hes amepoweri never ymer idi an As tigmat ismi sanon- spher icalr efr act iveer rorandc anexi stal ongwi thmyopi aor hyper opi a.As tigmat ismi scor rec tedwi thas pher o-c yli ndr icall ensi nwhi cht hepoweri s di ff erenti ndi ff erentl ensmer idi ans ,ass howni nFi gur e1. 2.Mos tcommonl y,s tigmat ism i scaus ed byanon- spher icalc orneaoft heeyeand r equi resas pher o-c yli ndr ical c orr ect ioni nwhi cht hepowervar iesbyl ensmer idi an. Fors pher o-c yli ndr icall ens es, the l ensc ent ermus tbepr oper lyl ocat edbef oret heeyeandi tsr otat ionalpos iti onbef ore t heeyei sal soc rit ical.Spher o-c yli ndr icall ens esar espec ifi edbyt hei rspher icalpower , t hei rcyl indr icalpower( eff ect ivel ythemer idi onalpowervar iat ion) ,andt her otat ional pos iti onoraxi soft hel ens. FI GURE1. 2As pher o-c yli ndr icall ensvar iesi npowerf rommer idi ant omer idi an Myopi a,hyper opi aandas tigmat ism,byt hems elves ,requi rec orr ect ionbys ingl evi si on l ens.Si ngl evi si onl ens esar edes ignedt ohaveas ingl espher icalors pher o-c yli ndr ical poweri nthel ens.Mul ti foc all ens eshavemor ethanonedes ignedpoweri nthel ens. Ex ampl esofmul ti foc alsi ncl udebi foc als ,tr if ocal s,andpr ogr ess iveaddi ti onl ens es,as i ll ust rat edi nFi gur e1: 3.Mul ti foc all ens esar emos tcommonl ypr esc ribedf orpr esbyopi a, anage- rel atedc ondi ti oni nwhi chpeopl elos etheabi li tyt ochanget hef ocusoft hei reye t oseec lear lywi thi nar ms’ lengt hus ual lyoc cur ringi nthemi d-t o-l atef ort ies.Mul ti foc al l ens eshaveanear -poweraddi ti ont oenabl epeopl ewi thpr esbyopi atos eec lear lywhen t heyvi ewnearobj ect s. Thepoweraddi t ionislocatedinthelowerportionoft hel enssinc epeoplemos t commonl yl ookdownwar dwhenviewi ngnearobjects.Obviousl y,iti simpor tantthata multi focall ensbeproperl ycenter edandproper lyrotatedinfrontoft heeyesothatthe nearpowerisl ocateddownward LECTURE2 MANUFACTUREOFOPTI CALGLASS Glas smakingessenti all yentai lsmelt ingtoget hertheneces sar yi ngr edi entsathigh temper atures.Foll owingar es t epsf orthemanufac tur eofgl assus ingthebat chproc ess.  Theingredients(whichar eusuallyoxi desors al tsofmet al s,i ncl udings i li ca, sodi um,pot assium,calci um andaluminum)areputint oal argemelt ingpot.An addit ionalingredi entc ul let(whi chi swast eglassfr om pr eviousmelts)i sadded topreservevaluablerawmat eri alsandtoprot ectthei nsi deoft hepotfrom t he corr osivemol t englass. Thepottemperat urei srais edt obet ween800 Cand1000 candi skeptatt hat temper aturef or3-5days.  Thepoti sthengl azed( prot ect ed)byus ings mal lpi ecesofc ull et.  Thevari ousingr edi ents(dependi ngont hetypeofgl assbei ngmanufactur ed)are thenaddedatfi xedint ervalsunt ilt het emperat ureofthepothasr isentoabout 1400C.  Bubblesofgases capeatthes etemperatur esandimpuri ti essuc hass tonesfl oat tothesurf aceofthemolt englassandcanthenbesi evedoff.Thispr oc es stakes sever alhours.  Ther emai ningmol tengl assi sst irr edc ons tant lybyhandorbyamec hani calar m.  Themoltengl assisall owedtocoolsl owlytoatemperat ureof1200 Candt heni t ispour edandrol ledintos heetsofvar ioust hic knesses.  Eachs heeti sthenplac edi nan( anneal ing)ovenwher eiti sgr adual lyc ool edt o roomt emperat ure.  Thegl assi spr ess edormol dedi ntor oughbl anks.  Theroughblanksar einspec tedandthent hef irs tsurf acei sgr oundandpoli shed. Shor tlyaft eranotheri nspecti on,t hes ec ondsurfac eisals ogroundandpol ished tocr eateanophthalmi clensofapart icul arpower.  Mostgl assnowadaysismadebytheconti nuousflowprocess. I nthi smet hod,the gl assisnotpouredintosheet sbutisautomati call yext r actedbyaconti nuous pr ocess, andpressedi ntomoldsthatf ormtheroughblanks. TypesofOpt icalGl ass Thecriti calpr oper tiesofglas s(ori ndeed ot herr efr act ing medi a),i sit sindexof ref rac tionandi tsdi spers ion. Disper sioni sdefi nedasthevar iat ionofr efr act ivei ndexwi thwavel engt h.Di sper sioni s quanti fi edbytheAbbenumberVd,whi chi sknownasnuval ue. Themai nvar iet iesofgl assar e: Ophthal mi cCr own:I tismadeupof70% si li ca( sand) ,14-16% sodi um oxi de,11- 13% calci um oxi deandsmallper cent agesofpotas sium,borax,ant imonyand ars enic. Ophthalmi ccr ownisusedforthemajori tyofsi ngle- vis ionglassl ens esavai labl e todayandf ort hedi stanc eport ionofmostglas sbi -andtri -foc als. Fli ntGlass:Thi scontai ns45-65% l eadoxide,25- 45% si li caandabouta10% mixtureofsodaandpotassi um oxide.Fli ntglasshasahi gherref racti veindexthan ophthalmi ccrown.Iti susedmainlyforbif ocalsegment sinsomefusedbif ocals. Barium Cr ownGl ass:Thi scontains25-40% barium oxide( whi chi nc reasesthe refr acti veindexjustl ikel eadoxidebutdoesnotincreasechr omaticdi sper s i onas muc hasleadoxidedoes).Iti smai nl yusedforthes egmentpor tionofas peci fi c typeoffusedbi focal. Table2. 1Opt icalpr oper tiesofhi ghi ndexgl assasc ompar edwi thopht hal mic crown.  Gl ass Ref rac tiveI ndex NuVal ue Spec if. Gravi ty Opht hal micCr own 1. 523 58. 9 2. 54 Dens eFl int 1. 616 38. 0 3. 53 Ex tra- dens eFl int 1. 690 30. 7 4. 02 Bar iumCr own 1. 701 31. 0 2. 99 I nr ecentyears,spec ifi cvari etiesofglas shavebeeni ntroducedwit hs pecialpr operti es suchashi ghindexlensesthathaver efr activeindicesof1. 6to1.8.Thes etypesof glassesus ual lyhaveahi ghc ontentoft i tanium oxide( rat herthanl eadorbar i um oxiddes)andareusefulf orreducingthethi cknes sofhi ghpowerl enses. Addingmetal li coxi dest other aw mat eri alsmakeGl assf orabs orpt ivel ens es.For example:  Cobal toxi der esul tst oabl uel ens  Chr omi umoxi dec aus esagr eenl ens  Magnes iumoxi dec aus esavi oletl ens  Ur ani umoxi dec aus esayel lowl ens I naddit ion,ceri umoxi deandot hermat eri alshaveul travi olet( uv)abs orpt ionpr oper ties. I ronabsorbsinf rar edr adi ati on. Photoc hromicl ens escontai ns i lverhal idecr yst alsthatsepar ateandt henaggr egateon exci tat ionbyUVr adiati on(i ns unli ght)tomakethelensdark.Si lverhali derecombi nes toli ghtent helensi ntheabsenceofUVexcit ati on. Des irabl eQual it iesofOpht hal micGl ass 1.Homogenei tyi nbot hchemi calandphys icalandphys icalc ompos iti on. 2.Cor rec tref rac tivei ndexandc hromat icdi sper sionval ues. 3.Fr eedomf romc olour. 4.Ahi ghdegr eeoft rans par enc y. 5.Ahi ghdegr eeofc hemi calandphys icals tabi li ty.  PLASTI CLENSES These are made up from pol ymeric( usual ly organic) mat eri als and t he manufact uri ngproces sesforplasti csi nvolvetheus eoforgani cchemic alasoppos ed totheminer alnat ure/manufac t ur eofglas sl enses. Plasti clensesaremuc hl es sdur ablethanglassonesandpr ovidedec i dedlyinf erior optic sc omparedwi thglass.Themai nadvantageofplast icsi sthatsincetheyhave lessspecif icgravit yvalues,theyar eli ghterthanglass.I fpr operlymanufactureda lotofthedisadvantagesofplasti csmaybeover c ome.Sot hatt heygainmor eofthe attr ibutesofglasslens eswhi lesti llmaint aini ngtheirl ightweights uperi ori ty. Morerecentl y,t ranslati ngdes ign(phot ochromic)l enseshavebeenint roducedtot he marketthusshatter ingthemonopolythathasbeenheldbygl as sfordecades.This wi llreaf fir mt hefoothol dofplas tic sintoday’ sophthal miclensmarket. Manuf act uri ngPr oces sesf orPl ast ics General ly,plas tic sc anbes epar atedi ntot wogr oupsbas edont hephys icalpr oper ties ofthefi nishedproduct.  Ther moplast icMat eri als :Thes esof ten when heat ed and t her efor ecan be remol ded.  Ther moset tingMat er ial :Onc ehar dened,t hes epl ast icsc annotbes oft enedeven athi ght emper at ures. Thermoplast icswhenheatedcanbes tr etched,press edormol dedintocompl exs hapes withnoappar entc hemi calchangeandwhenc ooled,theyr etai nthes hapeofthe contai nerinwhichtheywereheated. Thisproces siscalledinj ectionmolding. Examplesofthermoplas t i cmat er ial sincl udePlexi glas ,Lucit e,pol ymet hyl methac ryl ate (PMMAwhi chisfamousf oritsuseinmanuf ac tureof‘har d’cont actl ens es) ,cel lul ose acet ate(andnit rate) ,polycar bonate,pol ystyr eneandnylon. Thermosetti ng mat er ialsare manufac tured by a dif fer entproces sbutthei rreal dis tingui shing f actorf rom ther moplast icsisthatt he har deni ng oft her mosett ing material sisanir reversiblepr ocess. Examples oft hermosett ing mat er ialsi ncl ude epoxy resi ns ( used i nsuper glue) , phenoli cs(Bakeli te),andallyldi glycolc ar bonate(ColumbiaResi n39orCr-39t hatis now usedforthemanuf actureofas izablepropor tionofplast icl ensesont hemarket today. Opt icalandPhys icalpr oper tiesofPl ast icOpht hal micLens esCR- 39 1.CR-39 hasawei ghtofhalft hatofopht hal micc rown gl asswi th as imi lar presc ript ionandofi dent icals ize. 2.Theyar efai rl yimpac tres ist anti nthei rnat urals tat e. 3.CR-39l ensesar everyiner tandar er es istanttoal mos tal lsol vent sandc hemi cal s exc eptper harps,hi ghl yoxidi zi ngchemicals. 4.CR- 39i smor eres ist antt hangl asst opi tti ngf roms mal lhots ubs tanc es. 5.CR-39hasmuc hlowerther malc onduc tivi tyt hanglas sandisther efor eless pronetofoggi ngwhent helens- wearermovesbet weenenvi ronmentswit ha consi der atedif fer encei ntemperat ure. 6.CR- 39l ens esc anbet int edt oal mos tanyc olour 7.Becauseoft henatureofthemateri al,andspeci altec hniques,as pheri csurf aces forc at aractl enses,pr ogressi ve addit ion mult if ocals,and magnif ier s with aspheri cs urfacescannow bemanuf actur edinplasti cf or m.Thisreducesthe consi derablypriceofmanufac turi ngthesedesi gninglassfor m. Di sadvant agesofCR- 39 1.I tiss oftands crat cheseas ily, muc hmor esot hanOpht hal micc rown. 2.I thasafai rl ylowR. Iandt her efor eiti sthi ckert hanc rowngl assl ens esofs imi lar power. 3.Theyhavei nfer iorphot ochr omi cqual it ieswhenc ompar edwi thgl assl ens es. Pol ycar bonat es Advant agesi ncl ude: 1.Theyar evas tlys uper iort oopht hal micgl assandCR- 39i nter msofi mpac t resi stanc e. NoteOphthalmicc rown i snotnat ural lyhigh on i mpactresi stanc e.Us ual ly opht hal mi c gl assi smade moreimpactresi stantby Ther malorChemi c al Temper ing. 2.Theyhavear efr act ivei ndex( 1.586)s light lyhi ghert hant hatofopht hal micc rown glas ses 3.Theyhaveas peci fi cgr avi tyof1. 20( ascompar edwit h1.32forCR- 39)and theref orelensesmadeoft hesemater ial saretheli ght ests pec tacl elens esin producti ontoday. 4.Theselens esar eeasi lytintedandanabrasi onresi stantcoat ingwhi chal so absor bsUVr adi ati on, isappli edtobot hfr ontandbac ksur f aces. Di sadvant ages 1.I thasal ow nuval ueandhencegi vesr iset oahi gheramountofc hromat ic di sper siont hangl assorCR- 39. 2.Thesur fac esofpol ycarbonatel ensesaresuchthati tisdi ff icul ttomol dthem suc hthati mper fect ionsarecomplet elyel imi nated. Cor lonLens es Theseareas peci altypeoflensmadebyCor ni ngGlassCompany.Theyaremadeof bonded(joi ned)lenses,havingafrontl ayerofglassandabl acklayerofpl ast ic (pol yuret hane).Thes el ens esaremanufac turedasC-Li telens es. Theadvantagesoftheselensesacc ordi ngtothemanufact urerarethattheyare25% thi nnerthanconventionall ensesandupto25% l ight erthanall -glas slenses.  LECTURE3 POWERSPECI FICATI ONANDMEASUREMENT Thewayofanopht hal micl ens ,orl enss yst em, canbes pec ifi edi nmanydi ff erentways. 1.Approxi matepower:TheApproxi matepowerofalensisspec ifi edac cor dingt o i tsfr ontandbacksur facepowers, wit houtregar dtoi tsthi ckness. 2.Back Vert ex powerand Fr ontVertex power:BVP and FVP s peci fy power accor dingtothechangeinthevengeanc eofr aysc omingoutthebacks urfaceor thefr ontsurf aceofthelens. 3.Equival entpower:Equi valentpowerspeci fi est hepowerofat hic klenss yst em i n ter msoft hepowerofasinglethi nlens. 4.Ef fect ivepower:Thisr elat estothechangeinthepowerofal ensasi tismoved cl oser ,orfur theraway, fromthepat ient’ seye. Onl yBVPi sus edr out inel ybyopt icall absandpr act iti oner s. Thel ens omet er( ver tomet er)pr imar il ymeas uresBVP. PowerSpec ifi cat ion Refr act ingpowerisdef inedast hec hangeinver gencet hatoccur swhenl ightpas ses thr ough alens.Theunitforpowermeasur ementist heDiopt er. Thet erm‘ Diopt er’ hasvar ious lybeenus edt odes cri be: a.Thecurvat ureofasurf ace,wheret hedi opt er= ____________1___________ Radi us of Cur vat ure ( metres ) b.Thecurvat ureofawavef rontatas pec ifi cdi stance(r)f rom i tspoi ntsour ce (i ll ust rate).Int hisc ase,_____1______ i srefer redtoasVer genc e. r(met ers) Wet al kofr educeddistanceinanobjectorimagespac e,wemeant heact ual di stanc e(inmetres)di videdbytheref rac tivei ndexoft hemedi um wi thi nwhichthe 1 1 di stanc eismeasured(i.el/norl/n). n1/1 Reduc edver genc eis ____1______¬¬¬_____ i.e l or n/ l. Reduc eddis tanc e vepowerF=L1-L=n1/1 Ref rac ti l -n/ l= n1–n r yL1=f 1 Foranobj ectati nfi nit e, F=n1/1 Ther efor f = n1–n r Forani mageati nfi nit y,l=f. Ther efor e,F= - n/f= n1–n r F= n1/1 So, f =- n/f. Appr oxi mat epower FA=F1¬+F2---------------------------------------------------------------------------------------------------------------------------3.1 WhereF1 andF2 ar ethef rontandbac ksur fac epower sar emeas uredbyt he l ensomet er. F1 F2 FI GURE3. 1.Fr ontandbac ksur fac epower sofac onvexl ens Bac kVer texpower Thi sisdefi nedasther ec ipr ocaloft her educ eddi stanc efr om t hebac kpol eofal ens toi tssecondar yfocalpoi nt  BVP = ¬ ____1______¬¬¬_____ A2F1 Ther ear etwoequat ionst ocal cul ateBVP FV= ____F1____¬¬¬_____ - --- --- --- --- --- --- --- -3. 2 1–tF1 n Equat ion3. 2ist heexac tfor mul aforc omput ingBVP FV=F1¬+F2+F12 t /n - --- --- --- --- --- --- --- --3. 3 Equat ion3. 3isas impl if iedappr oxi mat efor mul aforc omput ingBVP. Tocalc ulat eF1,i tiseasi ertousetheexac tfor mul aforBVP,butt ocompl eteFv,t he appr oximat eformul aiseasi ert ouse. Themainadvantageofquot i ngpower sinBVPi sthatitall owsust oplac et helens anywher einfrontoft heeyej ustsolongast hes ec ondaryf oc alpoi ntoft helens coi nci deswi ththef arpointoftheeye. Thisisdonebyadjust ingtheFVPac cordingl y. Fr ontVer tex, orNeut ral izi ngpower I ti sdef inedasthenegati veofther eci procalofthedi stancef rom t hefr ontpol eofthe lenstothepr i maryfocalpoi nt(i llustrateandexplai n).I tistheFVPofalensthati s neutral izeddur ing“ HandNeut r ali zation’ofalens. FVPc anbec alc ulat edus ingt hef oll owi ngf ormul as: FN= ____F1____¬¬¬_____ - --- --- --- --- --- --- --- -3. 4 1–tF1 n FN = F1¬+F2+F22t - --- --- --- --- --- --- --- --3. 3 n Equat ion3.4istheexactfor mulaf orcomputi ngFVP(neut ral izi ngpower )whi le3. 5ist he si mpli fiedapproxi mat eequati onf orc alcul ati ngFVP. Sol vedExampl es 1.Gi venal enswher eF1==8D, F2=- 9D, thi cknes s(t )=3mmandn=1. 6. Fi ndFN, FNandFA. FA( Appr oxi mat epower )=+8- 9=- 1D. FN( BVP)=+8–9+640. 003 1. 6 =+8–9+0. 12 =- 0.88D FN( FVP)=+8- 9+81 0. 003 1.6 =+8- 9+0. 15 =- 0.85D 2.Givenalenswher eF1=+14D,F2=- 6D,t hic knes s(t )=5. 5mm andn=1. 523.Fi nd FN,FVandFA. Thes eexampl esdemons trat ethati nlow- power edr elat ivel ythi nlens es,t hedi ff erenc e i nAppr oxi mat epower ,Fr ontVer tex, andBac kver texpowerar erel ati vel ysmal l. ForMeni scusOpt hal micl ens es, theFVPi sles sthant heBVP. Equi val entPower Somet imeswehavet wor efr act ings urf acess epar atedbyai roranot hermedi um ofa di ff erentr efr act ivei ndexf romt her efr act ings urf aces. Tof aci li tat ethes tudyofi magef ormat ion ( sinc ethet wor efr act ing s urf acesar e ar rangeds ucht hatt hei rpr inc ipalpoi ntsl ieont hes ameopt icalaxi s),i tiseas iert o c ons idert hes esur fac esasas ingl ethi nlens. Thef ocall engt hoft het hinl enswhi chwi llpr oduc ethes amei mages izeandi mage pos iti onast het wor efr act ings urf acesi scal l heEqui edt val entf ocall engt h. Thenextr elevantques tioni s:wher eshoul dthi sthi nl