Lecture Aberrations. Cameras, Chromatic aberration. correct. n blue > n red. Spherical aberration. Parabolic mirrror.

Transcription

1

2

3 Lctur 25-1 Abrrations Chromatic abrration Camras, corrct n blu > n rd Sphrical abrration Parabolic mirrror Larg tlscops,

4 Lctur 25-2 Th Human Ey (1) Rraction at th corna and lns suracs producs an invrtd ral imag on th rtina o th y (th brain intrprts it upright!) For an objct to b sn clarly, th imag must b ormd at th location o th rtina Th shap o th lns controls th distanc o th imag 2.5 cm

5 Lctur 25-3 Th Human Ey (2) Th lns is hld in plac by ligamn that connct it to th ciliary muscl that allows th lns to chang shap and thus chang th ocus o th lns Th indx o rraction o th two luids in th y ar clos to that o watr with a valu o 1.34; th indx o rraction o th matrial making up th lns is 1.40 Thus most o th rraction occurs at th air/corna boundary. 2.5 cm

6 Lctur 25-4 Th Human Ey (3) 2.5 cm d d 0 i dpnds on d 0 d 0 => to kp d i at 2.5 cm

7 Lctur 25-6 READING QUIZ 1 Which o th ollowing statmnts is incorrct? Th statmnts dscrib th optical charactristics o th human y. A A nar sightd y ocuss in ront o th rtina whn obsrving an objct locatd at ininity. B A ar sightd y ocuss bhind th rtina whn obsrving an objct locatd at ininity. C A convrging lns is usd to corrct th vision o a nar sightd y. D Astigmatism is a condition whr th y dos not hav cylindrical symmtry about th cntral optical axis. E A cataract opration o th scond lns insid th y rmovs th cloudd lns and rplacs it with a plastic implant.

8 Lctur 25-5 Exampl: Corrctiv Lnss (1) Qustion: A hypropic (ar-sightd) prson whos uncorrctd nar point is 75 cm wishs to rad a nwspapr at a distanc o 25 cm. What is th powr o th corrctiv lns ndd or this prson? Answr: Th corrctiv lns must produc a virtual, upright imag o th nwspapr at th nar point o th prson s vision as shown blow Th objct and imag ar on th sam sid so th imag distanc is ngativ

9 Lctur 25-6 Exampl: Corrctiv Lnss (2) Thus th objct 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 convrging lns with a powr o dioptrs or D (ocal lngth o m = 1/ 2.66 D)

10 Lctur Compound Microscop A microscop consists o two convrging lnss: an objctiv (th ront lns) and an ypic. An objct is placd nar th irst ocal point o th objctiv. Th sparation o th lnss is adjustd so that th imag producd by th objctiv is ormd just insid th irst ocal point o th ypic. Th latral magniication o th objctiv is Th ypic angular magniication (y nar point = x np ) m o y' y M L x o np Th ovrall magniying powr is dind as M m M o L o x np

11 Lctur Th Tlscop Lik th microscop, tlscops com in many orms First w will discuss (1) th rracting tlscop and thn (2) rlcting tlscops Th rracting tlscop consists o two lnss Th objctiv lns and th ypic In our xampl w rprsnt th tlscop using two thin lnss Howvr, an actual rracting tlscop will us mor sophisticatd lnss

12 Lctur Astronomical Tlscops Rractor Tlscop Sam combination (xcpt imag at ) as compound microscop: Objctiv crats a ral imag which allows th ypic to magniy. Th angular magniication M o th tlscop is dind as θ /θ o o y', o M o o y'

13 Lctur Gomtry o th Tlscop Bcaus th objct to b viwd is at a larg distanc, th incoming light rays can b thought o as bing paralll (th objct is at ininity) Th objctiv lns orms a ral imag o th distanc objct at distanc o Th ypic is placd so that th imag ormd by th objctiv is at distanc rom th ypic Th ypic orms a virtual, magniid imag o th imag ormd by th objctiv Th imag is at ininity, again producing paralll rays

14 Lctur Magniication o a Tlscop Th magniication o th tlscop is dind as th angl obsrvd in th ypic,, dividd by th angl subtndd by th objct bing viwd, o o m o Bcaus th tlscop dals with objcts at vry larg distancs, w cannot calculat th magniication o th tlscop using th lns law For xampl, on might try to xprss th magniication o th objctiv lns using th lns quation di di m 0 d o W can still gt th angular magniication, but w nd to us angls rathr than distancs

15 Lctur Calculation o th Magniication o a Tlscop (1) Lt s calculat th angular magniication o a rracting tlscop Th angl o is th angl subtndd by a distant objct o tan o d o

16 Lctur Calculation o th Magniication o a Tlscop (2) Th angl is th apparnt angl sn in th ypic Th magniication is tan d/ o d/ o m (invrtd) o o d

17 Lctur Exampl: Rracting Tlscop Th world s largst rracting tlscop was compltd in 1897 and installd in Williams Bay, Wisconsin. It had an objctiv lns o diamtr 40 inchs (1.0 m) with a ocal lngth o 62 t (19 m). Qustion: What should th ocal lngth o th ypic b to giv a magniication o 250? Answr: o m 19 m m 250 o o 19 m m = 7.6 cm m 250 Th 40-inch rracting tlscop at Yrks Obsrvatory

18 Lctur Problms with Rracting Tlscops Th objctiv lns o a rracting tlscop is larg and havy Th 40-inch rractor at Yrks wighd 500 pounds Supporting a larg glass lns is diicult Must b supportd by its dgs Constructing larg glass lnss is diicult Glass lnss ar thick and absorb light A glass lns has chromatic abrration Dirnt ocal lngths or dirnt colors Solution: Rplac th objctiv lns with a mirror

19 Lctur Th Rlcting Tlscop Most larg astronomical tlscops ar rlcting tlscops with th objctiv lns bing rplacd with a concav mirror Larg mirrors ar asir to abricat and position than larg lnss Th ypic is still a lns Various typs o rlcting tlscops hav bn dvlopd W will discuss thr xampls o th gomtris o rlcting tlscop Rlctor Nwtonian Cassgrain

20 Lctur Basic rlctor Basic Rlcting Tlscop Rplac th objctiv lns with a parabolic mirror This dsign is impractical bcaus th obsrvr must b in th lin o th incidnt light

21 Lctur Nwtonian Rlcting Tlscop In 1670, Nwton prsntd his dsign or a rlcting tlscop to th Royal Socity Th ida or a rlcting tlscop cam rom Jams Grgory Nwton solvd th obsrvr problm by placing a small mirror that rlct th light out to an ypic This mirror is small compard with th objctiv mirror and causs only a small loss o light rom th imag

22 Lctur Cassgrain Gomtry or Rlcting Tlscop A urthr improvmnt on th gomtry o th rlcting tlscop is th Cassgrain gomtry (namd or th Frnch sculptor Siur Guillaum Cassgrain) irst proposd in 1672 Hr a small mirror is usd to rlct th imag through a hol in th cntr o th objctiv mirror This dsign and many improvmnts to this basic ida ar th basis o modrn astronomical tlscops

23 Lctur Rlctor Tlscop No chromatic abrration Larg mirrors can b mad (larg amount o light gathrd) Easir to support Viw cntr blockd o o Maginication m (sam as a rracting tlscop) Whippl Tlscop

24 Lctur Th Hubbl Spac Tlscop (1) Th Hubbl Spac Tlscop (HST) was dployd April 25, 1990 rom th Spac Shuttl mission STS-31 Th HST orbits th Earth 590 km abov th surac o th Earth, ar abov th atmosphr that disturbs th imags gathrd by ground-basd tlscops Th HST is a Ritchy-Chrétin rlcting tlscop arrangd in a Cassgrain gomtry

25 Lctur Th Hubbl Spac Tlscop (2) Th HST is a Ritchy-Chrétin rlcting tlscop arrangd in a Cassgrain gomtry This typ o tlscop uss a concav hyprbolic objctiv mirror rathr than a sphrical mirror and a convx hyprbolic scondary mirror This arrangmnt givs th HST a wid ild o viw and liminats sphrical abrration Th objctiv mirror is 2.40 m in diamtr and has an ctiv ocal lngth o 57.6 m

26 Lctur Hubbl Corrctd Th original HST objctiv mirror was producd with a law causd by a dctiv tsting instrumnt (dployd on April 25, 1990) In Dcmbr 1993, Spac Shuttl Srvic Mission 1 (STS-61) dployd th COSTAR packag that corrctd th law in th objctiv mirror and allowd th HST to produc spctacular picturs Th two imags o th galaxy M100 shown on th lt and on th right dmonstrat th imag quality o th HST bor and atr th installation o COSTAR