Geometrical optics. Textbook: Born and Wolf (chapters 3-5) Overview:

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1 Gomal ops Txbook: Bo a Wol aps -5 Ovvw: Elomag pla wavs om maxwll's quaos. T Ekoal quao a s vao ops a o wavlg. Rao ll's law lo Toal al lo T psm Dspso T ls Imagg as a pojv asomao. Opal ssms a ABCD max. T pma opal abaos Coma abao.

2 . Fom Maxwll's quao oug wav quao o koal quao up o vao o ll's law. a w Maxwll's quaos a l mum o us o ags D xh B xe D B Alog w maal quaos: D E B H ubsug quao o B o so Maxwll's quao a akg a ul opao w g: H x xe x Fom w w g b applg so Maxwll quao: E x xe mulplg b a usg xuv U xv UxV w g: xxe x a usg x w g: E E xe E E xxe D om Maxwll's quaos w g: Fall w a g sul: E E E E E l xxe E l

3 o-mag ma = a vas bw a ~ a opal qus so las m s gall slowl vag. Fo omogous ma w g: E E Fom w w g sp o lg a mum pas vlo s as av x o maal v us

4 Hamo pla wavs a Ekoal appoxmao Clal a pla wav o om: kx E E s a soluo o wav quao k=v. smlal o H. Ts s a pla wav. W wll os o soluos o popagao spa la. L us ow v wav quao assumg a wavlg s small. Ts soul pov a appoxmao as log as w a ma wavlgs awa om sous o bouas. Fo s w a assum a Asa o om: k k H E w s a sala uo a w wav quao kpg ol gs o ms k assumg s small lav o all gas o. Fom s w g: E k E k E H k H k H k H E k T gs o m k lavs jus ga o a m amo m applg m vav w gvs: k Fom Maxwll s quaos s smpl o w Pog vo w s popooal o ExH. om abov: E k H

5 s a b sow o b qual o: w w <w > s m avag g l l. T pog vo s us o alog ga. Dg a a as a pa s popagag alog pog vo w a w: s Fom w w a v: s s s s o s s I paula o osa w g: s Cospog o popagao sag ls. Now os ou oos bw ma w av s. s s g s s ga o ollows a x s o agal ompo o s s osa aoss sua. Ts ams o

6 s s aoss a a w s ll's law o ao. Fo as o lo w smpl g qual o agls s av x s al. Wa also ollows om s s Fma's ppl: lg as ak sos auall xmal opal pa avalabl. Ts s s s a o a a s s alwas paalll o. I a ll's law a b asl v om Fma's ppl. Exampl: v v x a v L x v a x v x x a v L x L x a s v s v o s s No a:. All s s sala o polaao lg was os o b a logual wav lk sou wavs a m s was vlop.. Ts ps pomo o oal al lo gog om a g av x mum o a low av x o. Fo xampl s s wl us o g g boaba mos w g agl psms.

7 . Rao psm ls p magg a pojv asomaos smpl opal sums. T smpls opal sum w a b v om ll's law s psm. T vao agl o a psm sass: w s s s s Ls os a psm-bas opal sum w ls all as m om a po o a po bo alog sam l. Fo smpl os small agls. T:. Ls assum o smpl a plao-ovx psm. a w a s qus. w g: x W s jus spal ls. Clal s woks jus as wll w ag sam aus o uvau o bo ss.

8 A smpl alulao ls o ls a as om a ous a a sa su a: W a a o uvau o bo as. Now l's u o a somwa mo al spo o magg b a ls. T ls abov spo a las o small agls poj a po o a po bu ow os poj mo omplx objs o xampl o pos o a l? A p magg ssm s o w v uv s gomall smla o s mag. I paula ls a mag oo ls. Tus a p magg ssm s a pojv asomao. Fo x obj pla a x mag pla w soul g: b x a F F F F F F F x W a also w a vs asom o x usg pms. Clal pos lg pla F = wll b mag oo a a obj om wll b mag oo F' =. Ts a all oal plas o magg ssm. Fo spal as o a axall smm ssm w a assum x=x'= as wll as smm o ->- '->-'. T quaos u o: b w oas 4 p vaabls up o aos. T oal plas a gv b: a s plas ppula o op axs. Masug sas om spv oal plas: Z Z Y Y s asoms o: Z Z Z Y b Y g:

9 b b w asl g: Y Y Z Z w gvs magao a wo's quao: O mpoa mplao o op o p magg as a pojv asomao s a a opal ssm oag mo a o sua o voluo a b mamaall mol as asa pojv asomaos w s b sl a pojv asomao. As su s la a a s o spal opal lms paaxal lm a b mol b a sgl v lm. T smpls xampl s ls w s ompos o wo bak-obak spal lms a o w w g pvous sul. Howv paaxal lm a k ls o a s o lss a also b mamaall omula as a pojv asomao. T smpls xampl s o wo lss w a spag l bw m o w w a v: ZZ l Fo l= + s gvs -> as xp. Ts s a a lsop. Fo l= w g av o lss. W wll ow ps a smpl wa o alulag o povg s omula usg aag.. Ra-ag Imagg ssms a gall o ous o as p as sb b a pojv asomao. Fo a ull aalss o mo ompla opal ssms w av o ak o a g o oos bo pojv asomao. I ollowg I sa b sbg o o ommol us umal mos a smpl om o valua opal abaos a-ag a ollow b a omal am o ps o abaos opal ssms. Ra ag basall ollows soluo o koal quao o "pls" o as maag om o po o os. I ps a smpl om o w s applabl o paaxal moal as os w a a pla w op axs all "ABCD" max. Fo s as pu a aa b s sa om op axs a s agl a b sb b a smpl x max as a uo o pu. Dvaos om paaxal a b sb umall b oug a ola p o x mas. I smpls om w a w:

10 D C B A Fo a opal ssm. om lma mas a: Popagao oug spa o x : / Rao oug a plaa a bw maals w a : a ao oug a ls a mum o x : W a us s o v o o mos mpoa pops o paaxal magg: o popagao spa a magg all mas av a ma o u a magg sup mus also av a ma o u. W w av magg pu s p ol o a pu a o o agl. I s as mos gal ABCD max s: M C M T galao o s s kow as s oo o m-hlmol vaa: os s L us ow os a w xampls. ag w g magg oos o a ls o oal lg a a obj pla a. Up o ls w g max:

11 To g magg w qu spa popagao o =. T al sul s : / Cospog o vso w M=. L's ow w obj poso a. Up o ls w g max: To g magg w qu spa popagao o =/. T al sul s : / / / Cospog o vso w M=/. L's os ow a s o wo lss spa b a oal sa l as sb abov. Usg ABCD max omalsm quval ssm upo popagao om bak apu o s ls o o apu o so ls s jus mulplao o mas: l**l l l l l l T oal lg s pa b a = om w w g: l Fo as o a lsop l=+ w g: ospog o vso a magao.

4. Abaos l abaos: To lows o w a valua abaos as small vaos om a pojv asomao. Ls os a magg ssm w pojs a po x o a po x'' w Gaussa mag pojv asomao o po s x**. T a abao a b as sa bw x'' a x**.

12 4. Abaos l abaos: To lows o w a valua abaos as small vaos om a pojv asomao. Ls os a magg ssm w pojs a po x o a po x'' w Gaussa mag pojv asomao o po s x**. T a abao a b as sa bw x'' a x**. L us a usul qua wavo abao D om w mag abao a b v as palg bw aual wavo a a spal wavo ovgg a Gaussa mag as a uo o x pupl pla poso x. I a b asl sow a mag abao s jus vav o wavo abao a smpl xampl s a spal wavo mpgg o a ab po w palg s jus a la uo. I a lall smm ssm D s ol a uo o a obj pla a x pupl pla a agl o sala pou o wo. lows o ms a b 4 o a ao oa a xpl p o ol s volas assumpo a mag s a Gaussa mag gal om o s s: 4 4 D B C 4 D E F T mos gal om o mag abao a us b xpss as w loss o gal assum x'= a pla ' w smpl akg vav o pvous xpsso: x B s F s os D s B os F Ts os la o ollowg: os C D os E B s spal abao ous also o axs oal lg s p o a o F s oma smag aog o agl o

D s asgmasm oal lg o agal a saggal as C s Fl uvau mag ls

b sl. L us jus gv a v smpl xampl osg salg o logual spal

L us os a ls w a o uvau a a a obj poso a a sa om ls wos

13 D s asgmasm oal lg o agal a saggal as C s Fl uvau mag ls o a spal o E s soo magao s p o poso T lmao o abaos s a s b sl. L us jus gv a v smpl xampl osg salg o logual spal abao o a ls smpl o vso omplx. L us os a ls w a o uvau a a a obj poso a a sa om ls wos mag s a '. T logual spal abao s as s as: L s p w p s paaxal valu a valu o a a a g ls.

14 Expag o o o agl o o ls w a w: w a a o o o T vao agl om paaxal valu 6 6 s A smla xpsso a b w o ' a. Expag o a oal agula vao a a : a a a a W g las m glg g o ms : L T ull xpaso o s xpsso oag a ' all la oug a b smpl o om: 4 8 q p p pq q L s w o a gv p a b mm oosg a su a:

15 q p A oo all "bs om" ls. Og qu p av x Lo-Lo omula Fo a lomag wav a mum w a a lo moo a maal as a amp amo osllao a lomag l as vg o. Tus glg mag o o lo assumg s vlo s small: m q E w o a amo vg l gvs soluo: m E q m T obuo o los o polaao mum s mu lag a a o av ul so oma o gv appoxmal: P Np N N m E om Maxwll's quaos P=NE' w a a b a smpl asomao also polaabl w s o o popooal w xal l: a 4 : O vsg s lao: N 4 N 8 N 4 N 4N

16 W o ~ a b appoxma as: N m 4 o mos opal maals lo soas ou ol UV a MIR vbaoal sos a sogl u om vsbl go s mas a x o ao vsbl ag s a moooall asg uo o wavlg usuall gv b a pomologal quao o abov om m llm quao. Coma abaos Ao p o abao s oma abao: Du o vaao o av x w olo olos av oal lgs. Ts s o o usg Doubl aomas o wo glasss w spso: Fo a ombao o wo m lss w a av a soluo o wo quaos: F I a a a o uvau a ol wo quaos so a xa g o om a b us o u spal abaos. Ts a a b x o mo ompos su a aoal vavs o oal lg a o sulg apoomas vav also o a supaomas vav.

Part I- Wave Reflection and Transmission at Normal Incident. Part II- Wave Reflection and Transmission at Oblique Incident

Part I- Wave Reflection and Transmission at Normal Incident. Part II- Wave Reflection and Transmission at Oblique Incident Apl 6, 3 Uboudd Mda Gudd Mda Chap 7 Chap 8 3 mls 3 o 3 M F bad Lgh wavs md by h su Pa I- Wav Rlo ad Tasmsso a Nomal Id Pa II- Wav Rlo ad Tasmsso a Oblqu Id Pa III- Gal Rlao Bw ad Wavguds ad Cavy Rsoao