Physics waves


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Physics waves

  1. 1. |F*6{4nd!6**bfu*f,.:,.,.;".--!..nt,n+# nffclril1t {fl Li1cilf il Flc{.1ron (,rutls lirr ( lr:rJrlr,r "12 To do an overview of Maxwells equations and dhaptn32 electromagnetic waves To study sinusoidal electromagnetic waves To consider the passage of electromagnetic waves I: lcci tqrn ril l:t t(l ic. rittics through matter To determine the energy and momentum of electromagnetic waves POWe,PClni t-ac|.....s f : To observe uave addition. the formation of a Untve rc ;ly P hvs i cs IFet.&lr Frill.rf , stand in g electrom agnetic rvave - llrNh l) l),r,tt) i 4. , . 1 ! at I, r l,tt(. l,J,,rn c rrlc rr*Foir&i.-rr.Fbhi;rir!,n..i {.b141.u r,4 , ,,+frffi,.&B I rt { rollrrtl ilrr i{it xrr el Is cr1 rral iorr: . Ifan electric field vector propagates, it After Ampere and Faraday came James Clark Maxwell. FIe pennecl generates a nragnetic field vector. Or, a set offour equations that draw Gauss, Ampere, and Faradays is it the other way? laws together in a comprehensive description of the behavior of . The "chicken and the egg" argument electromagnetic waves. ofwhich disturbance causes the other aside, this is often a favorite portion of (29.r8) a first course in physics. O=0 (Craussr taw for magnerism) (29.19) Electromagnetic waves, at least in the fU. fonn of light, are common to many of {u.n = r"(r. " "j"),-, (Am*re,s raw) (29.20) our daily experiences. Even i.vithout vision, you can stand in the sun {not : -o!, (Faaday,sraw) (2e.21) wearing a dark shirt and perceive electronragnetic waves. ,!ildelri &rrci^onridrer-,r". arrm;.-r-.""iulJiil, l.lcc{ lrtrtut grtrl it rr :! 1 r. ;t t"{., rr !ri11 1; I llrrn Ii ltc I lrtrrre grrcl ir * ilvrs { re{: rr r. {n,t: t. ir n.irlc gc . If you tried to cite all Where -rrlr-.tlgrg1t; j"tJiu:grJl-rq.Uilr,1{:lJr,slnnll, the places you notice The range extends from low energy and frequency (radio and electromagnetic waves television) to high energy and small wavelength (gamma rays) in your classroom, you - l1tvelengths in nr rir ro i riri; irj-;;iiol ir) i, i; ii I would conclude in a /j ---Xriy(--- _ ----i----*- TV ts_Micr,$arc€ few minutes that they ullmvnrld > {__ oarmra rnvs**j are everywhere. (nrrilh(r ?rurcrFonrdtr.d,-r. a*run""*r."""iiri-^.n, __- (l$nchl{ c* xf c - 3.0 x 108 mls }n3lc:Fonldrcdn{lir.ntrttihii!iltclGoi ddi6-d[
  2. 2. l l,rpa gl I io n o I elcc( rorn:lgn cl ir: rvn r es | | The wave front moves at spccd c. eqLral lo -1.0 . 108 m;s t- - .*---*- l_E_: !:S$ygnetic wave in vacuum) ,,,u,,,, *",, :B_ - ..t| 1. ,:l o"l 3.0 x 108 m/s nnl l: = (l rt=0 L+ ll c l. l = --_--, (sIEd of eleuomagnetic B.l ..--- 1yKK-Yrnpn /KK^ wava in a diclectric) E:t t l; I tt : index of l - refraction r6ni.. sfc:.rG t.rn, l ht * ar c cr;ulrliorr The wave BQ,t) = jE ocos( kx - ot) rtQ,t) = i8.,,cos (*x - t,;t) rI I ,,| Electromagnetic rvave ii ..1. traveling in the +x direction l -r--/., J t: tr.t| I I ,l ,i B (.tr_ndr{ lfittrrron t:duqrin tE (on;3ir ? rlnff rli^oDr dil.rrr*."*,rn-s-u-^."iao^* The wave o . A coating of oil on water or a delicate glass prism can create a rainbow. A rainstorm among open T: l.6s patches ofdaylight can cast a conventional rainbow. Both effects are beautiful and arise from the horizontal axis - time axis wavelength dependence of refraction 1l angles. Eyeglasses or contact lenses both use refraction to correct imperfections in the eyeballs focus on tire retina and allow vision correction. horizontal axis - position axis r--. 4rnprr I IrR fc,-,n I an.r,.{ tR . nilFin! il I.qf.," .,J rm ^,r (bpn!fir r 2$xlk,non lih,lnnn tR.ruitnhii! i fciF.n.dd!6,bft
  3. 3. rlltrlintr :trtrl r1lj ;r1 t i,r1r r * ill r(ln:ii(lf t. slxrcrrlur l"clleclions The figure below illuslrates both rellection and refraction at once. fhe A real surface will scatter and reflect light. Diffuse reflection is the storefront windorv both slros5 ths passersbl their reflections and allows thent rule. not the ex.ception, We will use spe;ular reflection as we used lo see inside. rne rav approxtmatton, to Inake a very difficult problem manaseable. ..... t .>{-- . )<---. . -_-- c n: U ><LA-r.ll .Ttn*!. yr*ryr l.;trrs rrl rtlltrliorr iurrl r Yhr,shoultl lhc ruk:r al)[)ritt. lo ltc bcnl.l . Angle ofincidence = angle ofreflection The difference in index ofrefraction for air and water causes your eye ffi 0,: 0" (lawofreflection) be deceived. Your brain follows rays back to the originthey would to have had ifnot bent. " Snells Law of Refraction considers the slorving of ltght in a medium other than acuum . .. the inder of refraction nosinOo : nrsinO, (law ofrefraction) (b) vhr rlc n,lt rnrur Ierr (). r, 7 r,,,r,,,.- i, " " T---.. , rL.,L.l ,, ,.,-,1itr- t i ,i-i{rril: l.jr Itr,r.;.t,, i tt"r",i,,r ltll"f"t"i rr"3 l i, I ,,,,i,n - rirl r,,i:,i-.+ ,"1: lrrrrrirl.r | lrrrrirt /, !ll"r"l i Ilirrcl (hDiqhr+ rrhr - - *irilr. u"r,rn;. * w-...;:, c,Fin *. "-^_ I:tbulxtr:rl iudcrlr of rtIr.:rr.1inrr Quiz/u sheet of paper L Witc down the relationship of frequency and lhe wavelength of light in a vacuum. 2. lf an EM wave or light enters a dielectric, ii .: t |,rq,lrr 1r:y rrjrna i1s thr safrle. As il enters the malerial, the electrons in lhe material vibrate with a driving frequency equal to that of the EM wave but ils wavelenglh would differ. The speed of light in vacuum is c = 3.0 x 10s m/s, what wourd be irs speed in water if its index of refraciion is .1.33? 3. rUrite down the law of reflection andiefraction (Snell,s law) l)r.|t,j4rtj( t!1, As index ofrefraction increases, velocity of 4. Knowing Snells law ani the theory of index of refaction, rank the speed of light through each medium from l.easl lo greatest. light in the mediurn decreases iil[ ]l i(lll r!lli :rr I I l): I r, ! r,rr,{ (i 1,, r1 r!. ti.riL,. { ll: |1. 1l1. l iroplns6rs r,xrsft:noi fdc!i* r... ru"rl-, *L""".iim;u {r,Dn!frrrY)Nt,cnonrihrcnnhtnc ntrhrnhinsrrsF$.ddn6_{atdr
  4. 4. Quiz (by pair) >:) ?8. r : r.. r I rt it nrc ,: tr I rm l-,.r. -. : , r, r d,r ,r.1. . f , lt.0 flr, I I ibi:rr - -- r n ,,, r ,._.1 -r,. sb,c .il.d fi:. , , r;, r.lJLiur rN ui(j ti4. I r. -., i,- j.t.rrrd :p:shr or in I - t f.lrapfer"35 i I trlrr(trtrt qhs Fr .:il "ih iFr inArc O - nutrcn an8lc or in, ,Lj,.. ,j ti,r qtth fm.Bc il,. !,Jr(r ridc: . Irr1ulcrurcc t I I --J "FlSarnoin t L eiure j jrr Uhivereity phvsics. iltetfth Ediilon . - tlu;h tt | ,.,,-."nj R,,-;; 4.r,14.g,,1,,, f*rtura b] talres e".," ., . ".46. - * r!-*,*. g"*.iror.***,, r*m ( ioals lor.( hupltr-"l5 I rr I rorlucl ion To consider interference and coherent . Rainbows in the skv: been sources there, seen that. A t-hin-film . soap bubble: why should that To study two-source interference of light create a rainbow effbct? " To determine intensity in interference " This thin filrn is dispersing patterns white light and revealine i r.o.y.g. b.i.v. spectrum oicolor. . To consider interference ill thin films . To study the Michelson interferometer ;;rm;;6,,uffi; c.ri!h! { 7(n3 t{iFoi |dtr.dhi ln! pullrhins n tjdnoi{ Wlll. Ir"onls l)rrrrr :l rlirlrrrfrl:rn.r, lhink back "srra;rslroI" to our first slide on rvave motion rvhen the father The "snapshot" of sinusoidal waves spreading out from two thre, an object into the pool and coherent sources. the boy watched the ripples proceed outward from the disturbance. We can begin our discussion of interference from .lust such a scenario, a coherent a.- *tt source and the waves from it that can add (constructively or. destructi ve ly,). I 1 u tl ,i ll(;r$sir I ld,src.roi r:dkilr,-r"" n,,riu*,-^iiu***. ;;;;;;ilffi ffi ;;;r.h;ffi ;;,*N.-
  5. 5. ittlcrlcrcrtr:c ol lighl " The "snapshot" of sinusoidai war,es spreading out from two We consider coherent sources. (i)],,.,J ..,i I I rli l:ll11rlr: !1 r rr111 1;iq Single wavelength Best example is laser (..:olrer eitl .? ,,) 1 I tr,r.. ,t Same frequency I -.-.. ,",,, Definite constant phase relationship (not necessarily in . phase) ",,;, i{.:i; , . ,. ,,",i:q, ^ t, i .Trrsr , rnr rr,n"i I hn!. k*-;*; ^ "**""r. l)ou hlc slit iltIcrfcr*-.ncr nf IiIh1 l)oublc slif i rr lcrlcrurcc ol liglrt " Trvo rvaves interfering constructively and destructively, Two waves interfering constructively and destructively . Young did a sinrilar experinrent ith light . Young did a sinrilar experiment with light. ( tlrnilrir:rl lJ,rrl: lrorrr ri,,.lil r,i. lrirnl. i (b) ;ctLNl $r.orttn, {c( 0 lrln} thr. .i(|f;) (c) Af If,iitnirlc gc(nnctry {rnn lllrnrirl i( if i,1{&**; I i/ rirr d lir:h( - -/ t .l I !i = - T * -*r i orrnrhr 1 l0,r ltrF4 t Jtrrrih tk. rlFlthrr n t,cr^( i !t.r!i $r, (nfn9hrl]i)ili.i^onrh!niitn..ntr6tnhii!ntciAoi JdL6.brc s the lltr1cs inlcrlcrr:" trtrlur 1lr rrrlutr. As thc 1aves intcrlcrr, tlrcl produce li.ingcs 4i I .hr.ilrhr - I . ni H : I *[- I ,4 I *i.=l "0t1 ,i. ,, fi.,...-i: -ol I l -,H I : I J $ ftsins krcn dsi,n0 : m^ Consftuctive Interference dsin7: (m + l)r Destructive nterference I m is called the order number ornshr a 2fir3 Pd^o. fdnciin tN. roht(i;! r fo6oi,!kr,!D.!_r$ co+n,r2mrpsftoi*r,cri-r*.1,nrnn3-"*.^..ii[iilil
  6. 6. Irt(ufilcuce liorrr Iwo slils ol Irvo larlio sle{iolrs L, . l:r l,rsition of rn,ir lrright band In a trvo-slit interference experiment. the slits are 0.200 mm aDart fi E and the screen is at a distance of 1.00 m. The third bright lringb .q (not counting the central bright fringe straight ahead from the slits) to,rt),,,: !Jn, lL is found to be displaced 9.49 mm from the central frinse. Find the : .$1 .,, ttl rr avelerrgth of light used. i U,,:^t $fi lrrtr s1t;t.. r1t{ir.s ll:r4,,, : .s1r14,,, &s1 ,l lt brrL r1 sin.O,, : ry,), 3 2 m,A tan0-., = .sin]m - d, I ton?r,,: llruf L trt). _,. /T $,.,,,.: Um/t l - k_n = r---- -,- *it Screen .rt nr . rrr As=..!: ar^o f do.r,6 -fl f 1ru. N[L.hins il td^on dJnq.(!.., l rrlcllcrtrtr"tt lrr:lrr llri ntr,r ll:ut ir.:r l l lr,l l l * :t,l tc Thin Film Interfererrce I 80o phere No phase change changc {c) I r. ,r,f,rri..rr nr. n{:.. l. r --:. A .: - r,,rh..rnt,.l.nLr1(l l1 2 n. Air Constructive Interference ;.- A |Im i I 2nr= (nL+ t)I n= 0,1,2, 1f il t I Destructive Interference 2nt- mA rr = 0, |,2. { onlnthr r ?orr h,roi I dr.nnn Inc. nnHnhiir il IqlMo;ddnoi..Bkvlltin lilrrrs n ill irrlt:rlir,. Quiz. U nclerstanding interference(a) llrlcrlerfD.. hctvcfil r0y,l 1n,!r if(r$ o !r,t x thir llhl l. A lascr bc:ln (I = {i32,ll nrn) is in(:i(l(:nt ()n tw() slilll,,, fr,r.111,,,,,r|.,i.t,,r i, 1 ., i 1).2()0 rrrrrr apart. I lorv far apirrt arc thr bright intcrfer-. )r ,1., . ,: 1f- JrlIr i L, r.., tr,r lrrr r. !l crrr:e fringcs on a screcn 5.00 rn asal tiorn thc slits?/ ,rl t, r!r:I ... ,t.rl. fr. 3.1 lxrr rarlio rrrrcnr)as trcpiratcd l)1 3()() n as slrorvn in tigirrrr l37.3 sintultancorrslr br oadcast idcirical signal! at ih(: if,rnc $au:lcngtl) A rndi0 ir) r (rl trir(.litg (luc (b) lhc nifhd{ lriil!c, ol xr oil li(k oil srrcr north rcccilca thc signalr. (r) Il drc caf i! nr rhc posi" tion ol thr: sccond nruiorrrm, r,hlrt is thr: r,rrclcngrh ol thc signalsi (b) I lor mnch fartbcr nrusr rhc car rnrrcl lo cn(o(ultcr thc ncxt rninimunr in rcccptio0? (.olr l)o not usc thc small,lnglc approximation in thi. problcn).) 3u,n i.itoungs d{)ublc-stil cxfcimcnr is pcr{brmecl wirh 58$nm light an(l a sliLrGcrcen disbnce ol 2.00 m. lhe lcntll iDtcrfcrcncc ninimum is obsctlcd 7.26 mnr front thc ccDtrnl tr)axirnum. I)crenlinc thc spacing of dtc alib
  7. 7. (lltls J() . Fresnel and Fraunhofer diffraction Chapter 36 . Single-slit diffraction . Diffiaction gratings I)iIlllrrtiorr PORstr:i. 9:.i,-.:i-- Unl!er-cig, Pitlsirs. Ilreliii €rJarorr - i/rrs.r lt l.,u,ri ..! R,,., .t t..(,,11tt,t lcrlr,* l,r .lrxr lrlun c.r*. Fr b!i r&ji6 lR. FNnhiis i lrFoi l,Uion_6!. I lt l rorlucl iorr Ij les rttl a nrl Iira u n h o Icr ll i,{lra r:i ion , Its intuitive that sound can diffract According to geometric optics, a light source shining on an object (and travel around corners). Light in front of a screen will cast a sharp shadow. Surprisingly, this doesnt "shor.v its poker hand" so does not occur. easily. (lconrclfic optics l)rcdicts that rhis sjtuation . Ifyou shine light fronr a point shtrtrkl frrllrtr: il i){rp bonndtrrv hets$)t source to a ruler and look at the illurrination antl shado,uv, you11 see the edges are ... solid sltarl, rv i DOCST{T ,veli ... not sharp. A close Ihat s NOI $,hat HAPPTII inspection ofthe indistinct edge rcrrlly hrpp.rrr! rvill reveal fringes. . This phenomenon may not sound Point source useful yet but stay r.vith us until the end ofChapter 36. This line of thinking has shorvn the way fbr advances in DVD technology and applications in holographl,. StraighledgerbPflghr r ld)[itr.on ltrtrn{ lr I 4^nph, )m | !Ja,.r |,ii,.rr i tr. rurtnhrs.! I,uFr- drr n.ct l)iffilr1inn l)ilfiaeliorr lrorn a sirrglc slil Ifthe source and the screen are close to the edge causing the diffraction. the effect is called "near-field" or Fresnel diflraction. Ifthese objects are far o) wAri€atrY f,aPPlnr: apart, so as to allow parallel-ray rnodeling. the diffraction is called ..far- lffi m field diffraction" or Fraunhofer diffraction. Fffi PxiilkLnry .r)n(1v(mric li8hl .opnrnr. nrihrcon lilLrNrri Inc rahtniii! n p$rrn dd;on.!td
  8. 8. lrt /rllrh ll ltlll( ilt ilt:llr.ili{ rlrll,.r, r,,,11 I"l csrrcl ol lil-aunholt1.: The figure illustrates Fresnel and Frarrnholer oritconles . J,r !{r. {a), x. r L ,n trr, lfr. Differentiating Fresnel and Fraunhofer ll, l , ll *ril l I ll ""trl*:t .i .,fI.--- - _---- -:::=_lr :- I i.rr! ! rholc riir. r,r /, relrt,.{,nlr;i rtrrl liir!r i.l l..,ihrilitrr ftrLlr nrfiriili.i (d) lfr.rrrs I r.(,nh..f.r rhtr.,: rr .n (b) Enlargcd vicrv ot lhc h)p lrrlf ol thc srrr . rr " , .,r,rll .r, ,...j| Lr.- rrlr . , r rl: .,,. .,,r t1 t,,,, a " i r.t tj r! ., !r": . 1 ,r, .t.,!1. t.j.( i. (nrrsr . pr Rr^F r ar:{ir rr. n$tnhh! n tdroi etr,n ELr I"lir rr n holc r rf i fli.;ttt ic,r ra F rr n lrolcl. tli lli.aciion divide source into two eqLlal oa(s f,r,,o=f destructive interference il,*, bFqi : ll . - i divide source into four equal parts, 0 -l : ! rlf" Inconring Vl.u=?ll l.l I ano so on v (nnn8hr.z$eP.r^inFduc,ri6ts. .ruh[.r ier!t,o^oi djn,i !r il Iillr u rr lrofc r. rli,-.1 itrr I;raunhofcr rlilli-acliolr rrnrl arr cxalnplc of analvsis . A photograph ofa Fraunhofer pattern from a single slit. |] li II 4 ll sn9 211,, . i r< r3 " n!2. sin0 - A/ a ,A ,2 I 4 sirrd= o " a/2. sin9 - -7/ t a. / ll ,i, snr9 = -27/ t -_ ll i U- k-- /i- /r0nt I sin0=aI n-11,12,13, l---.-- I .ru,iirdiu" I conclition ror lintgrlgl*l9q _ *Jlottrghrt 2rr[lc,Fonr:acirirtx.nhtrh;!iit,E^r [fn,n.trsts 16 i8h r lm3 hBon lin,cir im I nc _ puilnfrin8 ,! lcrG.n ddr6_ b L!