Geometric Optics of thick lenses and Matrix methods

Transcription

1 Geomec Opcs o hck eses a Max mehos Mahemaca eame o eaco o hck eses shows he exsece o pcpa paes he paaxa appoxmao whch seve as eeece paes o he eaco o as eeg a eavg he ssem. Smme a shape o he es eeme he ocao o he pcpa paes.

2 o Fg. 6.4 hck-les geome Ae a aaca eame o eaco o a hck es geome: o h h h V h V a whee om Gaussa s s ; ; ; ), ( ough appoxmao o oa gass eses a: 3 / V V Compee evao ca be ou Moga, Iouco o Geomeca a Phsca Opcs. Aso, he Newoa om hos: x x o o o x x M a

3 Noe ha as, hs w e he h es esu. Coveo: h, h > he, s o he gh o V,V, a covese h, h < he, s o he e o V,V Aga, a ee o axa pos hough he pcpa paes. Now, cose a compou es cossg o wo hck eses L a L, wh he usua paamees s o, s, a s o, s a, as show o he ex se. M s s s o so s so s, s o ae mage a objec saces o he combao as a whoe a ae measue wh espec o a.,, a Noe ha he sg s mpoa a saces > cae ha o ae o he gh o o.

4 Equvae hck es epeseao o a compou es Fg. 6.5 A compou hck es. Noe ha he eses ae h, he pas o pos, a, coaesce o a sge po a becomes he cee o cee es sepaao.

5 Cose he exampe o a compou h es beow (vua eses ae h). = -3 cm, = cm, = cm. he, he eecve oca egh s Sce hese ae h eses he pcpa paes covege o sge pos O, O : O O (3)() 3 5 (3)() 3 cm cm cm A compou h es

6 Aaca a acg: 3: : kˆ uˆ kˆ uˆ s s Exampe o a compue pogam o a acg.

7 Fg. 6.7 a Geome o hck eses Cose a a acg aass usg he paaxa appoxmao, s A po P : s s / / / a

8 Le s cae he powe o a sge eacg suace. Fo a h es, Aso, om he geome a V V whee hs s oe o cosmec easos. hus, max om we ca we:

9 eveopme o Max Meho Iouce a vecos coum max: a a eaco max: a /, a so Aso hus, we ca ee a ase max: / : Noe hus a a P a a P

10 Coug wh he seco eace he gue (Fg. 6.7) a Le A Noe A max ssem he ee so a wh : Noe ha he eema mus be a s a check o he ssem max. Ae mupg ou he ssem max, s compoes ca be we expc: a a a a A Whee = s he es hckess a he eacve ex o he es s =.

11 Noe ha a examao o he ssem max A gves a a,, he es s ake o be a, as epesee b he powes a. a We obseve ha hs s jus he ecpoca o he oca egh o a hck es such ha a =/, a he es powe s /. Moe geea, he mea ae ee o boh ses we wou have: o ; Fa, V a a a a hus, he max meho vovg eaco a ase maces eabes a eemao o uamea opca ssem paamees such as he ssem oca eghs a poso o boh pcpa paes eave o he es veces. V a

12 mage a objec a he s opeao ases he eeece po om he objec (.e., P O o P ). he ex opeao A he caes he a hough he es. A a ase opeao I bgs o he mage pae, P I. = ase max = eaco max A = ssem max

13 Exampe o a compex es ssem aaze wh he Max Meho: A ; ; ; A Fg. 6. A essa es ssem. he esu o he max meho eas aows o he souo o he basc es paamees such as he oca egh a poso o he pcpa paes eave o he veces o he oue eses. 5.6 V V

14 As aohe exampe, cose a ssem o h eses whch. Noe ha he powe o a h es s + =. he ) ( / es h A Suppose ha wo h eses ae sepaae b sace : O O he, he ssem max ca be we as / / / / / / / A

15 emembe ha a o ; V a a a a V a Whee = = a V = O a V = O o a h es heeoe a, O, O Noe ha he ocaos o he pcpa paes a sog epe o, whch ca aec o whch se o he eses he paes ae ocae. I s woh og ha a es ssem compose o N h eses ca eas be eae he same mae o cacuag he oca eghs a ocaos o he pcpa paes. 3 N

16 A sma aass ca be peome o a mo he paaxa appoxmao. he esu s o o wh M so emembeg M, / Noe ha o a pae mo a he ssem max o a mo euces o M

17 Les Abeaos: evaos om he coespog paaxa appoxmao Chomac Abeaos: () a a compoes havg ee coos have ee eecve oca eghs Moochomac Abeaos: Spheca abeao, coma, asgmasm eca ha we use s (s oe heo he paaxa appox.) Icug ao ems s - 3 /3! eas o he h-oe heo whch ca expa he moochomac abeaos. emembe ha o a sge eacg spheca eace he s oe appox: s s o I he appoxmao o he OPL ( o + ) ae mpove, he 3 oe eame gves: o o o s s s s h s s Whee h s he sace above he opca axs as show he gue.

18 as skg he suace a a geae sace (maga as) ae ocuse cose o he veex V ha ae he paaxa as a ceaes spheca abeao.

19 Maga as ae be oo much a ocuse o o paaxa as. sace bewee he eseco o maga as a he paaxa ocus, F, s kow as he LSA (ogua spheca abeao). Noe: SA s posve o covex es a egave o a cocave es. SA (asvese SA) s he asvese evao bewee he maga a paaxa as o a scee pace a F. I he scee s move o he poso LC he mage bu w have s smaes amee, kow as he cce o eas couso, whch s he bes pace o obseve he mage.

20 ue o humb: Ice a w uego a mmum evao whe. emembe he spesg psm: Noe ha a paacovex es ca be appoxmae as wo psms. > a he owe psm esus a geae evao. Fo a objec a, he ou se o es acg he objec w sue a mmum amou o SA. Fg. 6.6 Spheca Abeao o a paacovex es boh oeaos.

21 Sma he objec a mage ae o be ea equsa om he eses (s o = s =), a Equ-Covex shape es mmzes SA. Maga as gve smae mage egave coma Maga as gve age mage posve coma Coma (comac abeao) s assocae wh he ac ha he pcpe paes ae ea cuve suaces esug a ee M o boh maga a cea as. Sce M = -s /s o, he cuve aue o he pcpa suace w esu ee eecve objec a mage saces, esug ee asvese magcaos. he vaao M aso epes o he ocao o he objec whch ca esu a egave (a) o posve coma (b) a (c), as emosae he e gue.

22 he magg o a po a S ca esu a come-ke a, kow as a coma ae a oms a comac cce o he scee (posve coma hs case). hs s oe cosee he wos ou o a he abeaos, pma because o s asmmec coguao.

23 Asgmasm: he Meoa Pae coas he che a whch passes hough he cee o he apeue a he opca axs. he Saga Pae coas he che a a s pepecua o he meoa pae. Fema s pcpe shows ha paes coag he e as w gve a shoe oca egh, whch epes o he () powe o he es a he () age o cao. he esu s ha hee s boh a meoa ocus F a a saga ocus F S. e as have a shoe oca egh.

24 Asgmasm: Noe ha he coss-seco o he beam chages om a cce () epse () e (pma mage 3) epse (4) cce o eas couso (5) epse (6) e (secoa mage 7). Foca egh eece F S -F epes o powe o es a age o as.

25 ) ( Chomac Abeaos: Sce he ex epes o he waveegh he we ca expec ha he oca egh w epe o he waveegh.

26 Cce o eas couso

27