Chapter 32 Optical Images Aberrrations 32-4 Optical Instruments n blue > n red. Aberrations

Transcription

1 Lctur 25-1 Lctur 25-2 Chrmatic abrratin Abrratins Camras, Chaptr 32 Optical Imags crrct 32-3 Abrrratins 32-4 Optical Instrumnts n blu > n rd Sphrical abrratin Parablic mirrrr Larg tlscps, Lctur 25-3 Th Human Ey (1) Rractin at th crna and lns suracs prducs an invrtd ral imag n th rtina th y (th brain intrprts it upright!) Fr an bjct t b sn clarly, th imag must b rmd at th lcatin th rtina Th shap th lns cntrls th distanc th imag 2.5 cm Lctur 25-4 Th Human Ey (2) Th lns is hld in plac by ligamn that cnnct it t th ciliary muscl that allws th lns t chang shap and thus chang th cus th lns Th indx rractin th tw luids in th y ar cls t that watr with a valu 1.34; th indx rractin th matrial making up th lns is 1.40 Thus mst th rractin ccurs at th air/crna bundary. 2.5 cm 1

2 Lctur cm Th Human Ey (3) = d d 0 i Lctur 25-6 Exampl: Crrctiv Lnss (1) Qustin: A hyprpic (ar-sightd) prsn whs uncrrctd nar pint is 75 cm wishs t rad a nwspapr at a distanc 25 cm. What is th pwr th crrctiv lns ndd r this prsn? Answr: Th crrctiv lns must prduc a virtual, upright imag th nwspapr at th nar pint th prsn s visin as shwn blw dpnds n d 0 d 0 => t kp d i at 2.5 cm Th bjct and imag ar n th sam sid s th imag distanc is ngativ Lctur 25-7 Exampl: Crrctiv Lnss (2) Lctur 25-8 Th Camra cal lngth numbr = = aprtur diamtr D Thus th bjct distanc is 25 cm and imag distanc is -75 cm = d d 0 i = = D 0.25 m 0.75 m Th rquird lns is a cnvrging lns with a pwr diptrs r D (cal lngth m = 1/ 2.66 D) 2

3 Lctur 25-9 Th Micrscp (1) Micrscps xist in many rms Th simplst micrscp is a systm tw lnss Objct Objctiv Lns Eypic Th irst lns is a cnvrging lns shrt cal lngth,, calld th bjctiv lns Th scnd lns is anthr cnvrging lns gratr cal lngth,, calld th ypic Th bjct t b magniid is placd just utsid th cal lngth th bjctiv lns Lctur m m h, i di + = m = d d h d 0 1, ,2 i d d d d = m m = d d i i i i,1,2,1,2,1,2 (0.25 mtr) L Micrscp (2) Lctur Micrscp (3) Th magniicatin th micrscp is givn by 0.25L m = whr L is th distanc btwn th tw lnss and 0.25 rsults rm th assumptin that th inal imag is prducd at a cmrtabl distanc 0.25 m Nt that ral micrscps hav cmplicatd, cmpund lnss dsignd t vrcm prblms such as sphrical abrratin and chrmatic abrratin, but th principl th magniicatin prvidd by micrscps is givn by this analysis Lctur Exampl: Micrscp Assum that w hav a micrscp with an bjctiv lns and an ypic sparatd by 30 cm. Th cal lngth th bjctiv lns is 20 mm and th cal lngth th ypic is 20 mm. Qustin: What is th magniicatin th micrscp? Answr: L m m = = = 188 ( m)( m) 3

4 Lctur Th Tlscp Lik th micrscp, tlscps cm in many rms First w will discuss (1) th rracting tlscp and thn (2) rlcting tlscps Th rracting tlscp cnsists tw lnss Th bjctiv lns and th ypic In ur xampl w rprsnt th tlscp using tw thin lnss Hwvr, an actual rracting tlscp will us mr sphisticatd lnss Lctur Gmtry th Tlscp Bcaus th bjct t b viwd is at a larg distanc, th incming light rays can b thught as bing paralll (th bjct is at ininity) Th bjctiv lns rms a ral imag th distanc bjct at distanc Th ypic is placd s that th imag rmd by th bjctiv is at distanc rm th ypic Th ypic rms a virtual, magniid imag th imag rmd by th bjctiv Th imag is at ininity, again prducing paralll rays Lctur Magniicatin a Tlscp Th magniicatin th tlscp is dind as th angl bsrvd in th ypic, θ, dividd by th angl subtndd by th bjct bing viwd, θ θ mθ = = θ Bcaus th tlscp dals with bjcts at vry larg distancs, w cannt calculat th magniicatin th tlscp using th lns law Fr xampl, n might try t xprss th magniicatin th bjctiv lns using th lns quatin di di m = = = 0 d W can still gt th angular magniicatin, but w nd t us angls rathr than distancs Lctur Calculatin th Magniicatin a Tlscp (1) Lt s calculat th angular magniicatin a rracting tlscp Th angl θ is th angl subtndd by a distant bjct d θ tanθ = 4

5 Lctur Calculatin th Magniicatin a Tlscp (2) Th angl θ is th apparnt angl sn in th ypic d θ tanθ = Th magniicatin is θ d / θ = d / = m (invrtd) θ = Lctur Exampl: Rracting Tlscp Th wrld s largst rracting tlscp was cmpltd in 1897 and installd in Williams Bay, Wiscnsin. It had an bjctiv lns diamtr 40 inchs (1.0 m) with a cal lngth 62 t (19 m). Qustin: What shuld th cal lngth th ypic b t giv a magniicatin 250? Answr: = 19 m m = 250 m = 19 m = = = m = 7.6 cm m 250 Th 40-inch rracting tlscp at Yrks Obsrvatry Lctur Prblms with Rracting Tlscps Th bjctiv lns a rracting tlscp is larg and havy Th 40-inch rractr at Yrks wighd 500 punds Supprting a larg glass lns is diicult Must b supprtd by its dgs Cnstructing larg glass lnss is diicult Glass lnss ar thick and absrb light A glass lns has chrmatic abrratin Dirnt cal lngths r dirnt clrs Slutin: Rplac th bjctiv lns with a mirrr Lctur Th Rlcting Tlscp Mst larg astrnmical tlscps ar rlcting tlscps with th bjctiv lns bing rplacd with a cncav mirrr Larg mirrrs ar asir t abricat and psitin than larg lnss Th ypic is still a lns Varius typs rlcting tlscps hav bn dvlpd W will discuss thr xampls th gmtris rlcting tlscp Rlctr Nwtnian Cassgrain 5

6 Lctur Basic rlctr Basic Rlcting Tlscp Lctur Nwtnian Rlcting Tlscp In 1670, Nwtn prsntd his dsign r a rlcting tlscp t th Ryal Scity Th ida r a rlcting tlscp cam rm Jams Grgry Rplac th bjctiv lns with a parablic mirrr This dsign is impractical bcaus th bsrvr must b in th lin th incidnt light Nwtn slvd th bsrvr prblm by placing a small mirrr that rlct th light ut t an ypic This mirrr is small cmpard with th bjctiv mirrr and causs nly a small lss light rm th imag Lctur Cassgrain Gmtry r Rlcting Tlscp A urthr imprvmnt n th gmtry th rlcting tlscp is th Cassgrain gmtry (namd r th Frnch sculptr Siur Guillaum Cassgrain) irst prpsd in 1672 Lctur Rlctr Tlscp Hr a small mirrr is usd t rlct th imag thrugh a hl in th cntr th bjctiv mirrr This dsign and many imprvmnts t this basic ida ar th basis mdrn astrnmical tlscps N chrmatic abrratin Larg mirrrs can b mad (larg amunt light gathrd) Easir t supprt Viw cntr blckd Maginicatin m = θ (sam as a rracting tlscp) Whippl Tlscp 6

7 Lctur Th Hubbl Spac Tlscp (1) Th Hubbl Spac Tlscp (HST) was dplyd April 25, 1990 rm th Spac Shuttl missin STS-31 Th HST rbits th Earth 590 km abv th surac th Earth, ar abv th atmsphr that disturbs th imags gathrd by grund-basd tlscps Th HST is a Ritchy-Chrétin rlcting tlscp arrangd in a Cassgrain gmtry Lctur Th Hubbl Spac Tlscp (2) Th HST is a Ritchy-Chrétin rlcting tlscp arrangd in a Cassgrain gmtry This typ tlscp uss a cncav hyprblic bjctiv mirrr rathr than a sphrical mirrr and a cnvx hyprblic scndary mirrr This arrangmnt givs th HST a wid ild viw and liminats sphrical abrratin Th bjctiv mirrr is 2.40 m in diamtr and has an ctiv cal lngth 57.6 m Lctur Hubbl Crrctd Th riginal HST bjctiv mirrr was prducd with a law causd by a dctiv tsting instrumnt (dplyd n April 25, 1990) In Dcmbr 1993, Spac Shuttl Srvic Missin 1 (STS-61) dplyd th COSTAR packag that crrctd th law in th bjctiv mirrr and allwd th HST t prduc spctacular picturs Th tw imags th galaxy M100 shwn n th lt and n th right dmnstrat th imag quality th HST br and atr th installatin COSTAR Lctur Th Jams Wbb Spac Tlscp Th plannd rplacmnt r th HST is th Jams Wbb Spac Tlscp (JWST) This prjct is plannd r launch in th yar Th bjctiv mirrr r th JWST will b 6.5 m in diamtr cmpsd 36 mirrr sgmnts Th JWST will viw in th inrard, which allws mr distant bjcts t b viwd bcaus inrard light is lss attnuatd by intrstllar dust 7