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Quang học sóng

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Quang học sóng

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Quang học sóng

  1. 1. P . F . I . E . V GD . HACHETTE I NHA XliAT BAN GIAO out + Sllperiellr
  2. 2. "Cuo’n séch nay duqc xuéit bén trong khuon kho Chuorng trinh D510 tao Ki su Chat luqng cao tai Viet Nam. véri Sl_I trot gifip ciia Bo phan Van héa Va Hop lac ciia Dai Sir quén Phaip tai nuérc Cong hoa X5 hoi Chit nghia Viefzt Nam". "Cet ouvrage, publié dans le cadre du Programme de Formation d’Ingénieurs d'ExceIIence au Vietnam be’ne'ficie du soutien du Service C ulturel et de Cooperation de I'Ambassade de France en République . i‘ocialiste du Vietnam”.
  3. 3. C/ i_iu I/ ‘dc/ I I1I1i'z_‘nr_'mit / nili: ‘ chm rich HDQT kiém Téng Gizim doc Noo_ TRAN / xi Phé Tong Giiim doc kiém Tong bién ujip NGUYEN ouY’ TI-IAO Bié/ I tap mji dung : LE HUNG Trinh bay bia . ' LE HOANG HA1 Sita ban in . ' PHAM TH1 NGQC THANG CI1<"lniI1 . ' DOAN VIETQUAN ‘I94 — 20‘O6/CXB/17 — 323/GD Ma"! S6: 7K483T6 — DAI
  4. 4. Quang hoc song ( Tcii ban Irin tin? ’ nlrrit) Chit bién : JEAN - MARIE BREBEC Gitio su giéng day caic ldp dt_I bi dai hoc truoing Lixé Saint — Lottis ('5 Paris JEAN - NOEL BRIFFAUT Giéo su giétng day céc ldp dit bi dat hoc truong Lixé Descartes (3 Tours PHILIPPE DENEVE - , . Giéo sit giétng day czic ldp dit bi dat hoc truétng Lixé Henri - Wallon E1 Valenciennes PC* — THIERRY DESMARAIS Giéo str giéng day céc léip dt_t bi dat hoe I-PSI, ‘ trtrbng Lixé Vaugelas 6 Chambéry ALAIN FAVIER Giéo su gizing day czic lop dit bi dai hoc trtrong Lixé Champollion 6 Grenoble MARC MENETRIER Gizio su giitng day céc léip dit bi dat hoe truong Lixé Thiers (3 Marseilles BRUNO NOEL Gizio sir gieing day céc lop dit bi dat hoc trtrong Lixé Champollion (3 Grenoble CLAUDE ORSINI Gitio su giéng day céc lop dI. _I bi clai hoc truoing Lixé Dumont - d'Urville 6 Toulon Nguoi dich : PHUNG Quoc BAD NHA xuA'T BAN GIAO ouc
  5. 5. tique ulatoire sous la direction de 011 JEAN - MARIE BREBEC Professeur en Classes Préparatoires au Lycée Saint - Louis it Paris PHILIPPE DENEVE d I Professeur en Classes Préparatoires 2 e au Lycée Henri - Wallon it Valenciennes THIERRY DESMARAIS " PC* "’; ’.f°ZZ‘Z‘;23‘. ‘§; ZZZZ"£i, ‘2.iLi§; ?:; “ PSI-PSl* ALAIN FAVIER Professeur en Classes Préparatoires au Lycée Champollion 5. Grenoble MARC MENETRIER Professeur en Classes Préparatoires au Lycée Thiers it Marseilles BRUNO NO EL Professeur en Classes Préparatoires au Lycée. Champollion 5. Grenoble CLAUDE ORSINI Professeur en Classes Préparatoires au Lycée Dumont - d'Urville it Toulon : :: HACHETTE III Superteur
  6. 6. L853‘ oinoidau Bo szich nay viét theo chuong trinh moi cita céc lop dit bi dat hoc, bét déu rip dung vito dip khai truong thaing 9/1995 dot vol ceic lop nam tht’t nhat MPSI, PCSIVS1 PTSI, va khai truong thong 9/1996 dot voi céc lop nétm thi’! hai MP, PC, PSI. Phit hop vol tinh than cita chuong trinh moi, bo seich nay dé xufit mot sir doi moi trong vioc giéng day caic mon vat ii va hoa hoc it czic lop dt_. r bi. 0 Trzii voi truyén thong do an sou bén ré, theo no thi vat if hoc bi ha xuong hang mot sén phém phu cita toén hoc. ceic hion tuotng chi duoc khéo seit it khia canh tinh toén, czic teic gié do tim céch dat toén hoc vao vi tri dong cita no. danh ttu tién cho sir suy nghi vii bion luan vat it’, via nhah manh céc tham so co 3" nghia va czic quan ho gén bo chting voi nhau. 0 Vaftt lt’ hoc la mot khoa hoc thuc nghiom va phéi duoc gizing day vol tu' céch la nhu vzfty. Czic tzic gié d5. doc blot cham lo vioc mo té. ceic thiét bi thi nghiom. ma khong coi nhe khia catnh thttc hétnh. Mong rang SI. _I‘ co gting cita ho sé tht’tc ddy céc gizio stt va czic hoc sinh nétng cao czic hoat dong thtrc nghiom, hoac tht’tc déy ho thuc hion ceic hoat dong do. chitng bao gior cftng co tzic dung déto tao rat ion. 0 Vat ii hoc khong phéti IE1 mot mon khoa hoc téch tori Ihuc re‘, chi chfim Io nhfmg tit liou khong lien quan don thuc té' cong ngho. Moi khi dé tfti cho phép. céc téc gié dé danh mot vi Iri rong rat cho céc L'mg dung khoa hoc hozfic cong nghiop, nhzim gay himg tht’t cho czic nhii nghién ct’ru vii czic ki su tuorng lai. 0 Vat ii hoc khong phiti 151 mot mon khoa hoc céch ll vi bat bién, no 151 sén phiim cita mot thori dai va khong tL_r taich khoi pham vi hoot dong cita con nguori. Czic taic gié dfi khong coi nhe sl_I vion dan vé lich sit céc khoa hoc do mo tit sit‘ [I611 trién cita céc mo hinh It’ thuyét, cfing nhu dé dat lat céc thi’ nghiom Vito dting ngt'I cénh cita chting. Nhom tzic gié do Jean-Marie BRéBEC diéu phoi, bao gom nhfmg giaio su czic lop dit bi rat co kinh nghiom, ném duoc mot thuc tién lau dat vé czic ki thi tuyén sinh véto ceic truong dat hoc. V5. co uy tin khoa hoc duoc moi nguoi cong nhzfm. Nhom téc gié nay dfi git": quan ho chat ché voi caic teic giei cita bo séch cita DURANDEAU vii DURUPTHY viet cho czic lop cfip hai céc truoing trung hoc. Nhu vay céc szich cho caic lop dit bi tie'p not mot céch hoitn hrio céc szich cho céc lop trung hoe. vé hinh thiic cftng nhu vé tinh than. Chéc chain ring czic séch nay IE1 nhfmg cong cu hfru ich dot voi sinh vién dé luyon thi co hiou qué. cftng nhu dé thu nhifm dtroc mot trinh do khoa hoc vfmg chétc. LP. DURANDEAU Nhiéu énh chup, hinh mo phong va so do minh hoa la uu the’ cita cuon séch gizio khoa nay. Nhor do ma cite khéi niom quan trong duorc trinh bay mot céch gién di. Céc doc trung cita nguon sang va dfiu thu (xem chuorng l) cho phép do cap dé'n nhfmg hion tuong giao thoa nftm trong hai nhom: giao thoa do chia mat song (dién hinh I51 hai khe YOUNG) V5. giao thoa do chia bién do (dién hinh I51 giao thoa ké’ MICHELSON). Sau khi duoc nghién citu trong tinh song don séc, céc hion tuong giao thoa hai song nay duoc khéo sait trong tinh sang khong don sac. Tie'p theo, cuo'n szich nay trinh bay hion tuong nhiéu xa citng vol tat cit czic ho qua cita no. Ba chuorng cuoi citng la czic bat thitc tap vé: 1 Giao thoa ké' MICHELSON: Czic quy trinh diéu chinh vét thao téc dttoc not dé'n trong bat cho phép lam chit duoc thiét bi nay. ° Méy quang pho céch tit: céc daftc trimg via tinh chat co bén cita crich tit duoc khéo sét vii do doc. A A 1 Nghién cL’ru SL_I' phan CL_I‘C cita énh sting: vioc sit dung caic kinh phan cttc vii bén lam cham pha (3 va 2 ) cho phép tao ra va phén tich tinh saing phan cttc.
  7. 7. 1 2 0V'I~§N L(‘7i n0’i dcfu . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . M ye Inc . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . Song ainh séng . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. Dai euotng vé giao thoa trong quang hoe . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . Giao thoa do chia mat song . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . Giao thoa do chia bién do . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . Giao thoa hai song trong zinh seing khong don sée . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. Nhiéu x2_1 efia song tinh szing . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . Gizio trinh Ihl_IC tap: Giao thoa ké MICHELSON . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... IA Giéo trinh th1_Ie tap: Mziy quang pho etieh tit . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . Gizio trinh thl_IC tap: Nghién et’1'u st; phén cue efla song zinh sting . ... ... ... ... ... ... ... ... ... ... ... ... ... .. . . P/1z_4 lL_4c 1: Phép bién d6i FOURIER . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . Plug /1_4c2 . ' Giao thoa ké MICHELSON, kiéu Mich-2 (SOPRA) . ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 37 53 85 125 151 197 225 245 283 286 U’9.:
  8. 8. .9‘LJE)“»%v Mé Jain Muc Ttrau I Nhfrng khéi niom co bén vé ezic defte trung efia nguon szing vi diu thu énh sing. I Ca’u mic cita song zinh szing. E Nhfmg khéi niom bién do vii euong do. I Xée dinh pha cita song don site. I Quang lo. Mac dd dnh sdng dufgrc cd'u tqo tftnlnbzg s0'ng dién I12 nlnmg quang lz_oc klz0”ng don gidn Id m_0‘t ngimlz cfia dig? /1 tit h_0c. Tcfn s0"so'ng dnh sdng, bdn chit cfia nguén szing cfing nhu cfia cdc dciu thu dnh scing Id do‘? turgmg cfia m_0‘t mén lz_0c hodn todn déc lcjp véi nI1i1‘ng phu'0'ng phép riéng cu’a minh. Clurovzg ndy trinh bdy ve" song tinh scing vd nhL'mg céng Cl_A Cain tlziéi dé’ nghién cnu chting dim trén nhfing vdh dé‘ tlufc nglném. Nhfing vcjt mio plzdt xc_1 cinh scing vci /1071 Ihé'm? a Id ldmt/1é'n&0 mil cluing ta cdm nhcjn dmjc cinh scing? Dtéu CAN BIET TRUoc E Biéu dién phfre cita ham sin dong I Ceic dinh luefn SNELL-DESCARTES V51 khéi niém tuong diém.
  9. 9. 1 Mot véi thi nghiom 1.1. Mo hinh quang hinh hoc SL_r phin xi eua gtrong, Sl. _I chiou phim don ehiou, S1)’ nhin efia mit Ii nhfmg hién tuong quang hoe quen thuoc. Do mo ti nhfmg hion tuong niy, chting ta chi cin biéu dién inh sing bin g nhfmg tia sing tuin theo eic dinh luit SNELL-DESCARTES. Do 1:31 mo hinh quang hinh hoe (xem H-prépa, Quang hoe nim thti‘ nhat) m‘a duoi diy ehftng ta sé nhie Iii nhfmg diém ehfi you. ' Anh sing truyén theo nhfmg quy dao duoc goi IE1 nhfmg tia sing. ' Nhfmg moi truong trong suot duoe die trung bing ehiot suit n efia no. Chiét suit niy co thé phl_l thuoc vao miu sic cita inh sing. ' Trong moi truong dong chit, cie tia sing li nhfmg duong thing. Tii mat phin eieh gifra hai moi truong, mot tia sing toi co thé eho mot tia truyén qua (tia khtie xi) va mot tia phin xi. Phuong truyén eua nhfmg tia nay lién ho voi nhau theo eie dinh luit SNELL-DESCARTES (h.1a). ° Khi hai chitm sing et‘mg chiou vao mot vat, eong suit inh sing mi vit nhan duoc sé bing tong eic eong suit efia ttmg chum sing riéng biot. Tuy nhién, trong mot so truong hop, mo hinh quang hinh hoe to rat khiom khuyét. 1.2. Méu sic cfia céc bin mong Doi khi chting ta gap nhfmg bin trong suot eo do diy nho hon lumz bot xi phong (h. lb), ving diu trén mit nuoc, vot chit tiy n'Ia trén mit kinh v. v.. . Khi duoe chiou bing inh sing to nhién (inh sing tréng), nhfmg bin mong nay phin xi inh sing co métu sic tuy thuoc Vito do déty cita bin. Hiou (mg niy khong tho duoe giii thieh theo mo hinh quang hinh hoe: ching phii do st; bion thién efia ehiét suit theo miu sic ma efing ehing phii do Sl_I hip thL_1 mot so miu sic cita eie phin til trong bin. Do giii thieh dfing din nhfmg quan sit thL_re nghiom niy, ehting ta ein phii eoi inh sing nhu‘ mot song, nghia Ii nhu‘ mot dii luong dao dong theo thoi gian va theo vi trt’ trong khong gian. 1.3. Nhiéu xo énh séng Ban dém khi nhin mot vat sing qua mot tom luoi co mit luoi ding chfr nhit, ehting ta sé thiy inh cita vit sing eo thém nhfmg vot sing theo phuong vuong goe voi eie soi efia ta'm luoi (11.2). Khong thé co mot st; giii thieh quang hinh hoe thoé ding ; nguyén 1i vé Sl. _l' truyén thing cita inh sing trong moi truong dong chit khong eon dting nfra o nhfmg kieh thuoc nho eua mit luoi va ehting ta chi co tho giii thich hion tuong nhieiu xq niy being eieh xem inh sing Ii mot song. 1.4. Phén x: _:t trén maftt dia CD Anh sing phin xi trén mat dia CD co miu sic ciu vong: inh sing tring toti mit dia bi phin tieh giong nhu khi no di qua lang kinh nhtmg Sl_I tin sic o diy minh hon vi nguyén nhin tin sic efing khie. Anh sing phin xi trén bé mit mi efia dia CD trén do nhfmg thong tin duoe mi hoa dtroi dang thétnh nhfmg khie doc theo nhfmg duong song song voi nhau. Cie dinh luit quang hinh hoe vé phin xa inh sing khong do eip don st; lim loch ehttm sing do phin xi phL_t thuoc mau sic cfia inh sing toi. Mot lin nfra, chi co mo‘ hinh song cita inh sing moi gitip ehting ta hiéu duoc hion tuong nay. tia khtie xi Hinh la. Cdc djult lmjI. S'. NL‘t1_-Dt; s‘cAIm-; s.~ ° Mail plltiltg It? !" diff. /C xtic djnlz brii Iiu 101' wt phép Ittyéit ctiu mo! /tr(77tg ('hzi'I. ' Tia plttin X£_l vd tia kluic xq don mint trong rm}! pltdng 161. ° D[nItIm_iI pltdrzxg. ‘ 1‘, =1] . ' D_ittltIu(_3II: Ittic‘xg1.‘ I11 sin)‘, 2 I12 siniz . Hinh lb. Ming bong bong xd pltong. Hinh 2. Nggn dén I: lu' nltin qua trim ltm"t': élth sting dén bi I1/litfll xq but I¢i'm ltréi.
  10. 10. 1.5. Mot vai thi nghiém voi laser 0 Khi ehiou inh sing phit ra to mot laser vao mot to giay tring. Chang ta sé thay trén to giay co nhfmg dom sing va xen ké la nhfrng dom toi hon (12.3). Hion tuong nay, duoe goi la speekele; dac trung cita inh sing laser va hoan toan khong phai do st_r khong dong nhat cfia chum tia: vi trt’ va kieh thuoc cita cae dom phu thuoc vao dung cu quan sat va hinh anh nhin bang mat nay khong thay duoe trén inh chup. ' Tiop theo chting ta chié'u ehftm sing laser qua mot lo tron nho lén man quan sat. Chfmg nao duong kinh D efia 15 tron eon Ion hon 1mm thi vét sang tron man van gan nhu‘ la mot diém. Sau do, nou ta giam din ban kinh lo, vet sang trén man bi nhoe rong ra va tro thanh mot he van tron dong tam co do sang giam dan tit tam ra ngoai (h.4). Day la mot hion tuong nhié'u xq, gay ra do ban chat song cua inh sang. 2 Song 2.1. Cae vi do 2.1.1. Song nude Mot vién soi roi xuong diém 0 trén mat nuoc phang ling. Mat nuoc bi Chan dong, co xu huong lay lai dang can bang cfia minh Va do do dao dong. Su bion dang mat nuoe, khong dinh XL’! o diam chin dong ma dan dan lan ra toan mat nuoe. Mot song bion dang 1z(M ,1) duoe truyén di trén mat nuoe (11.5). Chimg nao song nay ehua gap vat can thi cae duong “dang huong” con la nhfmg duong tron dong tam. Chang ta dat mot thiét bi thu (<3 day la mot cai phao nho) tai diom M trén mat nuoe. Nou eai phao nay bat dau ehuyén dong thi ta co tho suy ra rang Iron do di co mot chin dong (Sl_I roi cfta vién sol) xay ra (3 each M mot khoang nao do. Hon nfia, thiot bi thu ban dau dttng yén nay da nhan duoe nang luong. Nhu vay song truyén di mang theo ca thong tin Ian nang luong. 2.1.2. Song am Am thanh duoe gay ra do sL_r1an truyén cita ap suat du trong khong khi. Dae tinh dao dong efia am thanh duoe cam nhan ro rot nou ta dat tay lén mang loa dang hoat dong hoac co hong khi noi. Am thanh duoe dae trtmg boi cuong do, cao do va am sac cita no. Cao do phu thuoc vao tan so dao dong am tharth, eon am sac cita no phu thuoc vao ding ham tuin hoan mo ti dao dong cfia ap suat du. Diéu nay duoe kiom chttng dé dang bang each cho dao dong efia may phat am tan ra loa: am phat ra, voi mot tan so xie dinh, co eong cao do (vidt_1 not La 3 cita quang tam thi’: nhat co tan so 440 Hz) nhtmg sé co am sac khae nhau nou may phat eho dao dong hinh sin, dang xung vuong hay ding xung rang cua. Hinh 3. Speckle. /inh speckle chup dttglc 0'! Irén mdn khi cltiéit clnlm laser qua nu}! Itfrn kinh mo. Hinh 4. Nhiéu xgz qua mo! 15 Iron: Itinlt quan mt dtrqc tréu mzin khi cltiéit cltum laser qua mo! [(5 Iron. Hinh 5. Cdc song bé nujt. Tdc dong ctia viélt . s'()'i I41 0 gdy ru mot song biéll dgutg mcjt mléc. M_o‘t [tic sau, song My dtrgc thu nIu_2/t 1441 M. Cltfmg mio song kltong ggip vcjt cdn, czic du()7tg "rluzng 1u((}1tg" déiu Id nIn77zg dtrong Iron.
  11. 11. 2.2. SL_r truyén tin hiéu trong Vilng nay, song 2.2.1. Khoéng thési gian truyén vé vén t6'c truyén Trong céc hién tuqng séng cc’) mot dai luqng vat I1’ ma ta goi la Iin hiéu duqc truyén din déin t1‘II1gtIo‘fi ra xa. Sl_I truyén tin hieu nay xay ra trong mét khoang thbi gian hfru han theo nhfmg duémg truyén ducyc goi la céc Iia. Chting ta hay theo d6i séng gay ra do viec séi roi trén m2_'1tnu6c. N6 la séng trbn Va dinh séng nam trén mét dufrng trbn c6 bén kinh p phL_1 thuéc vao khoéng thbi gian I tréi qua ké rt‘: khi vién séi roi gay chin dcfmg. Cac duimg truyén tu'o‘ng Lhich véi tinh d6i xting trbn la nfla dubng thang phat xua't ti: trong Vimg nay, song / duuc xcm la song phdng diém roi cita vién séi. Chting ta cc’) the dua them vao dai luqng van t6c truyén do U : __ , ngoéi nhfmg dai mung u. én_ Hinh 6. . S:6ng’gan Ilillfp/ Idllgi trong mie: n ‘ ' D, In: Iugu sang gan n/ ur den Iren loan nu_1!p/ Ming vming géc véi Iruc (Oz). D6i véi séng am, caic dubn g truyén séng am trong mt‘): chat léng d6ng Chat 151 nhfmg duétng thang, van t6c truyén am la hfru ham cé thé duqc nhan tha’y né’u nhu ngu6n am 6 cach xa. Chting ta nghe tha’y sa'm sau khi da nhin tha'y chép va moi ngu'€1i déu biét phucng phép xaic dinh khoéng czich den vi tri cita sét: Khoéng cach = Khoéng thbi gian (tinh bang giay) x 340m. 2.2.2. Séng phaing Nhu vay mOt séng duqc dac tnmg being met tin hieu phl_l thuoc vao vitr1'M tai thbi diem I : s(M. I) hay trong he toa dcf) Descartes s(x, y,z, t). Mot séng duqc goi la séng pluing né'u nhu n6 chi phL_1 thu(f)c vao mét loa dc) Descartes khéng gian. Nhu vay s(M, I) = s(z, I) la biéu thfic cfia séng phang. Trong tnximg hqp nay, s(M. I) la nhu nhau trén toan mat phzing vuong géc véi truc (Oz). Do vay, n6 (:6 tén la séng phing. Hinh 7a. Tnra‘ng / WP b'<5"8 43'" M 56113 M6 hinh séng don gian nay chi la gan dting béti vi né ngalm dinh rang hien tuqng Ch‘-‘V’ séng lan truyén ra vé cfing. Tuy nhien, trong mét mien khong gian 9 him ban 6 xa ngufin, mt“) hinh gin dting nay la hoan loan c6 the ap dung duqc (h.6). Han nfra séng phéng cbn la mot séng chay vi tin hieu duqc truyén di theo mot chiéu xaic dinh. Trong gfin dting bac nhat, séng am 6 xa céc vat can phat ra ti: mét cai loa gan nhu la mot séng phang chay. Khi téi gan mét btic tufmg cfmg, séng am nay khong cbn la séng chay nfra do hien tucjng phén xa hay cbn goi la Sl. _I Vang doi hay tie-'ng vang (11.7). Hinh 7b. Trlrring hqp sréng dm lcluing 2.2.3. SL_r truyén khéng bié'n dang cua séng phéng chz_ty PM M mug dw’ Gié. Sf! s(z, I) la m()t tin hieu truyén dQC theo chiéu duong cfia true 2 véti van 2 we khong d6i u. Thbi gian dé séng truyén tinh tir diém z = 0 la 1(2) = —- va u do dc’): s(z, I) = s(0, I — r(z)), hay s(z, I) = 5E0, t — (h.8). : (z. I) théi diém I 1 Tin hiéu nay duqc biéu dién bang ham mét bién sau: thfli diém 1+ 1 s(z, I) = f(u) Véi u = I - i va f(u) = s(0,u). 1/ 2.2.4. Tru'<‘mg hqp séng chgy, phing, dan séc Séng s(M, I) duqc goi la dan sa‘c né'u s(M, I) la mét ham sin dcfmg theo thbi v1 213" I61 mQi diém C6 dinh M - Hinh 8. SIrII'14yé)I kluing biéh dz_1ng.
  12. 12. Do dc’), séng chay, phang don sac truyén khéng bie'n dang theo chiéu duong cita true 2 sé cc’) dang: s(M, t) = s, ,, cos[o)I — 0&2 + (901 6 day s, ,, la bién dc) caa séng, to la mach s6, v = 2°°— la tan s6 séng va (p0 la Tl. ’ pha caa séng tai g6c toa dc‘) (xem H-Prépa, Séng, ndm Ilui‘/ mi). Buéc séng A la chu ki trong khong gian cfia h: ?1m_s(z, I). Dich chuyén mot khoang 7» theo phuong (Oz) tuong ang véti mc_‘>t st; bie'n déi pha being 21: , hay A_£_21IU v a)- -Bat/ <=9=.2_. u Khi dc’) s(z, I) = S", cos(wt — kz + (p0). ° Chang ta cfing c6 the biéu dién séng nay bang énh phL’rc cita ham sin: s(M, I) = .fle(£) vdi § = 50 exp[i[m; — va go = s, ,, exp(i<p0). s duqc goi la bién dé phfrc cfia séng. ° Chang ta c6 thé khéng can sit dang m¢t he quy chié'u gain véri mtf>t he toa do bang cach dua vao vecto séng I? = ZTHEE va vectd vi tn’ F = W . Khi dc’): g = .g0exp| :i(a)t — kz)] = ;0exp[i(cot — ° Cac_mat dang pha (hay mat séng) la nhfmg mat phang trt_Ic giao vdi vecto séng k (h.9). M()t tin hié; u truyén vdti van t6c khéng d6i v d(_)c theo chiéu duorng cita truc (Oz) sé tao thanh mtf)t séng chay, dan sac véri tan s6 v = ;’—n né'u nhu‘ n6 C6 dang: s(M, I) = s, ,, cositnt -%z H90). Butétc séng 7. trong moi trufmg la chu ki trong khong gian cfia séng tai thbri aiém t c6 dinh, nghia ta 2. = 3 = ——2;: ” . Tcing quat hon, séng dan sac 1:‘: phfing né'u nhu céc mat dang pha la nhfmg mat phfmg trtrc giao vai phuang truyén ct’) vecto dan vi :7 khong déi. Néfu I} = 2T"12' la vecto sang thi séng chay, don sac c6 biéu thfrc phac la: g =50 exp[i(o3t—kr)]. ° T/ mgit ngt7 “dan stir” dzrqc lci'y Ithrong Quang hoa. Trong / niéin séng tinh sting khd kién, mo"z' Iain s0"Iu'o'ng fmg vo"i m_o‘I mtiu. ' M43! so’ng / zodn Iodn don scic phdi Ian Iruyén vo‘ hc_m trong khéng gian vd Irqng Ihéi gian. Ccic séng IIn_rc Ie"déi( co’ k/161' ddu va‘ kéi Ihtic nén ch: C6 Ihe’Id gain dan sdc. M_o‘I so'ng bait kt‘ Iuo‘/1 luo‘n co’ the’ dzrqc xem Id Iéhg ctia nhz'é}z xéng don séc. Cluing Ia se" dé cap déh no’ If phdn cua”? gzia clurang. Tfnh c/ ui'I ndy minh Chang cho v_i In’ ml Iién ctia ccic sting dan sdc. ° So’ng dan scic cfing co’ I/ ‘l€fldl[(_7C bién dién being ham pluic sau: 5 = ~St>°XP[ i£3}: [—z - WM V5” £0 = £m°"P(‘i<P0)- Z Hinh 9. Srirzg C/1(1)’, plztilzg, dan sa‘c. Tin lu'éusc(5 pha nhtrnlum Igti M1, M2 vd M3 .
  13. 13. R0" rang rang phcin thI_t'c ctia g la niurnhan trong Cd hai each bie"u dién Cac cimyén gia ve”‘Quang hpc Ihtrang hay dfmg caciz vie‘? tin? hai. ve‘ pitan minh, citting Ia se”dt‘mg each vie‘? giéng nhtr trong Di_e‘n hoe hoac C (7 hgc, nghfa Id: s= s0exp i(wI-212) . ' ' A Khi doc saciz hoac dan de” bai Ioan, nhat Ihiét phdi tim hiéit xem trong d6 ngtrai ta dd st? dnng each vie‘? nao. 2.3. Séng phat ra tt‘I met ngufin gan nhu’ ngu6n dit‘= .°m 2.3.1. Séng cau Me hinh truyén séng khong bié'n dang kheng the ap dang dttqc met cach lien nghiem cho song phat ra tit met nguen gan nhu nguon diem trong pham vi met hinh nén (h. 10). Néi Chung, ngay_6 cach nguen met khoang 1c’rn'hon vai buétc séng, séng don sac duqc biéu dién trong tea de cau vdi bién de phac: wttwnt r Cac mat dang pha la nhfmg mat cau, v‘1 vay, séng c6 ten gei la séng cau. Ciui y’: 1 Sn’ gia'm bién dé dao dang Ilzeo ham — C6 ! i’l€JdI({7C chfmg minh bang Slf bdo toan ndng itrang. r Céng sud? do séng bftc xa If it‘ vai dién tich séng truye‘n qua S va vat’ biniz piutang bién dé dao déng. C dng sud’! do ngmfn pita! ra trong géc dcjc Q dtrac Ian iIfQ1 gzii qua cac phdn m_a'I can cé di_én lich ta S(r) = Qt‘ va do dd (h. l1): -_V= £o s,2"(r)S(r)= cIe hay s, ,,(r)r= cte. 2.3.2. Gan tiang séng chgy, phang, ddn sac (3 xa ngufin hay chinh xac hon la né'u 2' >> A. thi nhfmg bié'n thién vé pha r6 ret hon nhiéu so vdi bién thién caa 1 . Né'u r bié'n thién met vai buéc séng thi bién , . do 3 hau nhu khong do°i, trong khi do Coscp nhan mei gia tri gifta -1 va +1. I Do dé, trong met mién khong gian hfiu han, Chang ta sé sit dang biéu thac séng gain dang sau: g = ._v0 exp[i(u)I — A 3 Ban chat dien ta’ cfia énh sang 3.1. Séng dien tit chay, phang, don sac Séng dien tit chay_, phang la st; Ian truyén deng thdi met truong dien E(M, I) va met trubng tit B(M, t) vdi tee de c trong Chan kheng. Cac truong E va E la cac truong ngang tac la vuong géc véi phuong truyén cé vector don vi 17 . Chang dao deng deng pha va cac vector 17 , if va E théa man hethac 73 = 1.2 / E (11.12). C Hinh 10. Sang ctfn piuit m It? mg)! nguén diéht. Ngmfn nay pita! yang trong mét ilillil nén. h) Géc kh6i Dqi ittg/ ng géc khai dfmg tle’ do pittfn kitting gian ciu'ru trong mg)! iu‘niI nan Itim 0. N éit S Ia dién Iicit pittfn ma! cu'u trim 0, ban kinh R (IlI‘_0C "cit ra" bdi itinit min nay tin‘ géc i. 'It(3'i Q la Q = % . DE dang ciuhtg minh rang Q (lac lap vai R. Djnit ngIn'a so cap nay grin giéng niur I113? vai go’c pitting. Hat" nfra dtrétzg Iitcing pita’! xmft It? 0 se' "ccft ra" mét cung c6 (16 zldi L trén tltrang trim tam 0, bén kinh R. Géc pining 0. gifra imi ufra dating tiuing do’ Ia L (1=R. Hinh 1111 via b. Ninfitg kitai niérn so‘ cap vei géc icit(3'i ( S = QR2 ).
  14. 14. He thac nay duqc rat ra tit Cac phucmg trinh cc ban caa tmfmg dien tit, Cac phuctng trtnh MAXWELL, da duqc hec trong giao trinh Dien tit hec. N6 chi hoan toan dang d6i véi nsng pitting nhung cfing ta met gin dang rat tet dai véi met seng bat ki khi 6 kha xa nguen. Vao the ky XIX, sau Cac ceng trinh lt’ thuyet caa MAXWELL, ngufxi ta da hieu rang Cac séng anh sang thtrc ra la nhfmg séng dien tit C6 tan s6 vao khoang 10' 4 Hz. va gia tri c tien doan tit‘ It’ thuyet dien rt: dang bang van tec ann sang do duqc It: the ky xv111. 3.2. Van te'c va chié't sua't Van tec C cita Cac séng dien tit trong Chan kheng la met hang S6 vat If co ban, kheng pha thuec vao Cac dieu kien Ihl_IC nghiem va vao he quy chieu duqc ditng de do n6. Tri s6 cita n6 xa'p xi bang 100.108 ms'l va thuémg duec goi la van Io”'c anh yang trong Chan khéng. Trong met mei tntémg trong suet (kheng khi, nuétc. thity tinh. ..), van te'c vcaa tin hieu sang luen nhe hon C. Chiet sua't n cita mei trueng duqc dinh nghia la n = 5 . D61 vo"i Cac vat lieu trong suet, n nam trong khoang ti: 1 den 2,5 U (it. l3). 3.3. St; nhan biét mau sac Mau sac la met cam giac thi giac C6 duqc khi nao be phan tich Cac tin hieu sang do veng mac thu nhan. Tuong (mg vo’ti mei tan se trong vitng kha kien la met mau nhung dieu nguetc lai thi kheng dang. De hieu khai niem mau sac, can phai C6 met vai kien thac so luqc ve SL_I nhin mau. Veng mac cita mat nguei C6 Cac te bao nhay sang goi 1aIé'bao que va Cac te' bao cho phép nhan biet mau sac gei la té'bao nén. Ngu"0i ta Chi C6 the phan biet Cac mau sac neu cuetng de anh sang dit manh. Ducti anh trang, ngubi ta chi nhin thay den va trang. De kiem Chang dieu nay, ta chi can lam thit nghiem “mit” nhu sau: neu ai dc’) dua cho ta xem met vat ma ta chua tirng thay thi ta khong the nhan biet duqc mau sac cita vat d6 (dieu Cha yeu dei vcti thir nghiem nay la phai hoan toan chua biet vat d6 vi hinh anh trong 6C kheng nhfmg pha thuec vao Cac tin hieu do veng mac truyen to’ri ma Cen vao tn’ nhét nfta). 'Iht_Ic ra. Cac te bao no’n gem ba loai C6 Ct_Ic dai cita de nhay nam 6 vitng de, vitng xanh la Cay va vitng xanh lam (it. l4). Cam giac ve mau sac C6 duqc la do nao phan tt’ch Cac tin hieu truyen tdi tit ba loaj te bao nén nay. Vt’ dtt nhu neu tebao “db” va te' bao “xanh la Cay” bi kt’Ch tht’Ch nhu nhau, trong khi dc’) te bao “xanh lam” bi kich thich yeu hon thi nao sé giai thich nhfmg tin hieu nay nhu duqc gay ra do mau vang. Nhu vay, nao C6 the phan tich duec Cac bac xa don sac kha kien. Nhtrng nguqc lai. neu anh sang tdti mat la met hen hep d6, xanh la Cay, xanh lam vdi nhfmg ti le thfch dang thi nao cfing se phan tfch anh sang a'y nhu C6 mau vang. Khi ca ba loai te bao bi kfch thich gan nhu nhau, mau sac nhan biet duqc sé la mau trang. He mat - nao la met be phan tich tan se kha the thien. Tuy nhien, “nhuqc diem” nay lai I6 ra C6 lei, n6 cho phép tai hien de dang Cac mau sac. Vt’ da nhu C6 the tai tao tat ca Cac Cam giac mau sac tit 3 tin hieu mau phat ra tit nhfmg hat phat quang d6, xanh la Cay, xanh lam tren man hinh video. 43 ml. huéng truyén Hinh 12. Séttg diet: It? Cil(_ly. pining. Hinit biéit dtett mgit tang dién It‘! dan Mic lai Z kitting dai. Chiet suat thity tinh quang hoc nuéc (6! the léng) vao khoang 1,5 1,33 Flourine CaF2 1,43 kim cuong 2.42 kheng khi I 0003 trong khi quyen ' Hinh 13. Bzing mgit JO’ citiét snzit trrtng vftng kitzi kiéit. 0.4 0.5 0,6 0.7 mm) Hinh 14. D0 rtfing ctiu aic Ié'b<i0 nit42_v mau trong mat ngtrt‘/ t'.
  15. 15. Tuy Vafly, khong nén quen ring nou mziy quay video ghi 12_1i mot méiu Vang don séc thi hon hop do - xanh lei city - xanh lam tzin xa. tir mén hinh 121 hoém to2‘). n khzic theo quan diém song sinh séng. Céc hon hop cha't mau sir dung trong hoi hoa do tzii tao tot czi céc métu séc cfiug dua trén nguyén li tuong tI_r nhung khéc o‘ czich pha tron czic méu so cop ’1c‘§C h: _It mau khong phat ra einh szing mi) lai hop thu loc lua énh séng. u'c_1[ mau xanh lam hop thu manh mau do V51 mau xanh lzi céy con hat mau véuig l2_)i hop thu mau xanh lam va do; hon hqp hai loai hat nay so hzip thu chfi you mau do V51 do do zinh szing phén xa co sfic xanh lé cay. 3.4. Tinh lién tuc cfia pho song dién tcr Thong thuong. nguoi ta phan lozgi céc song dién tit theo nguon phét song hozic theo [on so cua chfing. ° Ceic song Vo Iuyen (song Hertz) duqc tao ra bori nhfmg dong dien trong céc mach dao dong. Song dién tir “nhan tao” déiu tién hay song Hertz duoe Heinrich HERTZ tao ra va thu nhau V510 ham 1888. ° / nh sang (theo nghia rong cua IL‘: néty, bao gom cé hong ngoai, tit ngoai, tia X) duqc phét ra tir czic nguyén ti’: Vii phén tit. ° Mot céch tuong tL_r, st; chuyén doi gifra 2 trang théi néng luqng khéc nhau cua hat nhan nguyén tit cfing phat ra nhfmg bL’Ic xa dién tir nhung co [fin so lo‘n hon nhiéu. Do 151 nhfrng tia y. Hin/ I 15 nhéc lai nhfmg mién [fin so chu you cfia song dien tit. Céc song énh saing khai kion co buoc song niim trong khoéng ttr O, -4pm (tim) don 0,8 pm (do). Mién hong ngoai xa phfr len mién tin so vo tuyé'n siéu cao. Do vay nguoi ta cc’) thé kiom chtmg being thL_rc nghiem su dong nhéit hinh thL’rc gifra song Hertz V51 song énh szing. ' Céc song dién tir truyén trong chén khong voi vzfm toc c xfip xi bftng 3,00.l08 m. s'] . Trong czic song dién tir do co céc song sinh séng khfi kié'n (mg voi céc tfin so niim trong khofmg gifra 4.1014 Hz V51 8.1014 Hz, nghia la‘) (mg voi czic bu'oc song trong chain khong nfim trong khozing gifra 0,4|. Lm (tim) V2‘: 0,8um (do). Sir phét xa 2’tnh séng khzi kiéh lién quan don céc chuyén doi électron trong czic nguyén tI"r hozftc phim tir. ° Trong moi truong trong suot co chié't suot n, v2_‘In toc truyén cita {inh sénglé v= fi—. 4 Nguon séng 4.1. SL_r phét xe_I cua nguyén ti} 4.1.1. Céc mL'rc néng Iuqng V2‘: ta? in so Chung ta bié’t riing néng Iuqng cua nguyén tir bi/1rg'ngni’/ Ida (xem H— prépa, Hoé hoc, nam thfr nha't)_. diéu do co nghia 1:‘) no chi co tho nhan mot so gizi tri hoim toén xéc dinh goi la caic mfrc ndng lzrgmg. MI’rc ca ba’/ I 151 mt’Ic co néng luqng thfip nhfit con céc mL'rc khéc duqc goi 121 czic mL’rc kic/ I Ihich. 7:14 [in so (Hz) tia hong ngoai lien lac bilng vé tinh radar télévision HVI song ngzin song trung song din" CAC SONG HERTZ Hinh 15. PII:3'. '(iIIg dién Ifl.
  16. 16. (3 nhiét do thfip, da so cac nguyén tir ném or mtic néng Iuong cuc tiéu. Nou - nhiét do tang lén hoac né'u moi truong bi nhfrng ta’c dong bén ngoai nhu sI_r phong dién chang han thi céc mfrc nang luong cao hon sé din dan bi lap day. Nhtmg mot nguyén tit bi kich thfch luon co xu huong hoi phuc nghia la chuyén vé mL’Ic co bén. Mot trong nhfmg céch hoi phI_Ic kha di la phat xa ra mot photon, nghia lit mot “hat” nang luong dion tit. Song kém theo photon nay co tin so 151 V duqc xfic dinh bang hieu nang luong A5 gifra 2 trang théi (/1.16): A? ’ = /w van /1 = 6,63.1o‘3‘*J. s Ia hang so‘ PLANCK. Nhu Vay trong Vfing kha kion, Aif vao khoéng 1eV. 4.1.2. Doén song Mot song pheing don sac truyén theo (02) so co biéu thL’rc nhu sau: E = Em c0s[u) (I — + <p]c7,, + Eym C0s[u) [I — +y]Ey voi I ham trong khoéng tir —ao don +00 Va voi moi 2. Mot nguyén tit co lap chi phat xa trong mot khoéng thoi gian hfru han T0 thuong vao co 10-1 I 5. Mac du rot ngén so Voi nhfmg phép do thoi gian thong thuong nhung khoéng thoi gian phét xa nay lai rot lon so voi chu kl bI’rc xa Va Vi Vay chting ta co tho xem song do nguyén tit phat ra Ia song géin don sac. Gié tri trung binh ciia 1 0 phu thuoc Vao nhiéu you to. va dac biot la nhiot do. (3 nhiet do cao, so lain Va cham gifra czic nguyén tir so rat lon, lam gian doan qua trinh phat xa V51 do do lam giém :0. 1 Chang ta cc’) tho biéu dién. dién truong tai M, EA(M, I) cua song do nguyén tit nam (3 diom A phat ra theo phuong (02) being mot doan song (11.17). mién biou thI'rc cfia E t—£"_ E[I1;I1 +10] E/ t(: ,I)= Em, cos[(I) (I—%)+<pA]EX +Eymcos| :u) (/ —%)+i1,, ]El, . ": ,¢[’I1’t+T<)] EA(M. /)=6 ‘ Hinh 17. C110 cladn 5611 g gzin 11:») mir. Tai mot diém cho truoc, thoi gian ghi nhan doan song 12‘) 1:“. Tai mot thoi diém xéc dinh, do dai cfia doan song 151 I0 = cro (l1.l8). Song zinh sang toi M 151 tong cfia caic doan song phzit ra tit rat nhiéu nguyén tfr. Cou trtic cfia no phu thuoc vao bén chit cfia nguon: nguon sang co dién (tu nhién) hay laser. 4.2. Cé'u trI'Ic thoi gian cfia énh séng phét ra ti‘: nguon co dién 4.2.1. Sl_I phét xa khong ké't hop Do lam vi dti Vé mot nguon co dién gfin don sac, ta co’ tho ké don dén hoi thily ngén, hay den hoi natri co lép them loc sang chi cho zinh sang cua 1 “vach pho” di qua. Trong mot nguon co dién cfing con duoc goi la nguon khong kéi l1_op, cac nguyén tfr phat xa mot czich hon loan nhfmg doan song co thoi gian kéo dai T0 voi pha ban dau my )7. Hinh 16. C126 mIi'c / Icing Iirmtg Va clluyéii am" bI'rcxt_1. E, ‘ 1 <———-——— i I r+ ———> Hinh 18a. Dadn . '(ing: E X(I) lz_1i 1 dt'éi71 Lviidilzlz. T0 E, 3. -D 7 -. I Hinh 18b. D0011 . v(’mg: E/ ,(z) Iqi I Ihfri diéin xzfc dinlt.
  17. 17. Song phat ra tit nguon la tong cua cac doan song noi tron so co dang gan sin nhung cac pha gifra hai thoi diom cach nhau mot khoang thoi gian Ion hon ‘[0 la hoan toan doc lap nhau. Do don gian. chting ta co the: xem rang song phat ra ti: mot nguon khong kot hop la sir ko tiop lion tuc cfia cac doan song co thoi gian kéo dai xap xi bang T0. Cac doan song nay la khong kot hop nghia la khong co tuong quan pha Voi nhau. ° Bdn rhdn cdc bién do song cling thdng g1'dngv0'1' khodng rlI0‘i gian doc fI‘lfI1g ‘E0 . Trong tlzzfc téf cluing ra khong tin/1 déiz II/ u7'ng I/ Icing gid/ zg bién do my vi no’ quci II/ Ian/1, khong I/1637])/1(1)‘ Izién dirgrc bong n/ Ifmg dd}! I/ zu thong dung (xem bdi rgip 7). 4.2.2. Thoi gian kot hop va do dai kot hop Chting ta thira nhan mo hinh ko tiop lion tuc cac doan song khong kot hop. ' Thoi gian kot hop ‘EL. bang thoi gian kéo dai trung hinh cua cac doan song tai mot diom cho truoc. Doi Voi nguon co dion, ‘II C trung Voi khoang thoi gian phat xa ‘E0 ctia nguyon tit. ° Do dai kot hop / L. = crt. la do dai trung binh cua cac doan song (no con duoc goi la do dai kot hop thoi gian). ° Doi Voi cac don hoi natri hay don hoi thiiy ngan thuong dfing trong cac ball that tap, rt. Vao khoang 101113 Va 16 co Vai milimet. ° T/ u_rc té'rIu‘p/ u'rc tap / Ion, C0’ Ic7se'clu’nI1 xdc /1012 néit mo‘ rd song phdt ra II? /zgztolz khong kéi / toy) n/ urm.0‘I song grin don soc co’ pha biéii déii chqinz ( so Voi chu ki cua song). Klzi (16. TL. biéil diéii kliodltg 1/1571" gian doc Irimg ma‘: song can gi17'ngu_Vén p/ Ia ciia mz‘/1/1. 4.3. Cou trL'Ic thoi gian cfia énh sang phét ra ti‘! laser Bfrc xa laser khong ton tai trong IL_l' nhion. Thiot bi laser xuat hion vao khoang nam 1960 phat ra anh sang co cau trtic khac han Voi anh sang to nhién. 4.3.1. Mo té so luoc laser (Thiot bi khuoch dai anh sang bang bfrc xa cam (mg) Y tuong chit you 131 bat buoc cac nguyén tit kich thich phai phat xa tai cilng mot thoi diom. Voi mot pha xac dinh, chL’I khong do cho chiing hoi phuc mot cach ngau nhion. Muon Vay. nguoi ta sir dung qua trinh bfrc xa aim {mg do E1NS1'E1N phat hion ra. Xét hai mac nang ltrong E1 Va E2 . Khi nguyén tit bi kich thich chiu tac dong boi mot song dion tit co tan so V sao cho E, — E2 = /N , xac sua't do no hoi phoc Va phat xa mot photon so tang lén rat lon. Hon nfra, song do nguyén tL'I phat ra khi do lai co ciing tan so Va ciing pha Voi song toi. Mot laser khi. nhu laser He—Ne thuong dfmg trong cac bai thL_rc tap, gom co mot ong chfra khi dat gifra hai guong. Mot trong hai guong (duoc goi la gtrong loi ra) cho di qua mot phan nho nang luong tori no (11.19). .15. Hinh 19. Laser khi
  18. 18. Chat khi’ duoc kich thich bang phong dion so khong con can bang nhiot nfra Va so nguyon tir nam or trang thai hang luong kich thich E2 lon hon so nguyon ti: nam o trang thai E1 (h.20). Nguoi ta noi rang da co duoc sI_r nghjch ddo m_a‘t do‘. Khi do, ong chtia khi co tac dung nhu mot bo khuoch dai anh sang doi Voi tan so tuong ting Voi chuyon doi E2 — E1 : nou song or loi Vao ciia ong co tan so nay thi trong ong so co nhiou photon bI’rc xa cam (mg hon photon bi hap thu Va 6 loi ra so co mot song anh sang bion do lon hon nhiou. Khi ho so khuoch dai nang luong sau moi Ian khi’: hoi ciia chfim tia bI‘I trtr duoc nhfmg hao phi (gay ra do nhiou nguyon nhan kt’ sinh Va do phan nang luong thoat ra ngoai qua guong loi ra), bfrc xa laser bat dau duoe hinh thanh. Tan so phat laser con phu thuoc Vao khoang cach gifia hai guong. Cac song chong chat lén nhau sau moi Ian khi’: hoi can phai dong pha do khong triot tiou Ian nhau. 4.3.2. Cac tinh chat cfia song phat ra ti‘: laser Cac nguyén tfr phat xa mot cach trail to‘ Voi pha ban dau gan nhu‘ bang nhau. Song tong hop so co dang: E_. (z, t) = Em cos[co [I — ij + <p(t)] C Ey(z, t) = Eym cos[u) [r _ 3] + ti; c ° Cac bién do E_, Va E y khong doi theo thoi gian Va khong bi thang giang nhanh nhu trong nguon khong kot hop. 0 Cac ham <p(r) Va W (t) bion thién rat cham theo thoi gian. Trong khi chu ki song Vao co 10'” s thi khoang thoi gian dac trung cho sI_t bion thion vé pha 6' cac laser thong dL_1ng chi Vao co’ 10-75 . tuong ting Voi mot do dai kot hop co hang chuc mét. Nguoi ta co tho cho tao duoc nhfmg laser on dinh dong lam chuan do do thoi gian. Pha cfia nhfrng btic xa laser nay hau nhu on dinh trong khoang thoi gian gain 1 giay. ° Tiot dion chtun laser chi mo rong ra rat chain (nho hon 1 m o khoang cach 1km): cac tia sang gan nhu‘ song song. Do do, chiim sang phat ra tit laser co nhfmg tinh chat rat gan Voi mot song phang don sac. Buoc song ctia laser He-Ne thuong diing la 632,8nm. Ngoai ra con co nhiou loai laser nfra. khac nhau Vo cong suat Va Vé do don sac. Cac diot laser rat thong dung Va ré tién nhung co do dai kot hop kha nho. chi Vao khoang Vai mm. Song phat ra tir nguon sang co the; dtroc xem nhu la mot chuoi lion tiop cac doan song gan don sac co thoi gian kéo dai trung binh 1.’ C (con goi la thoi gian kot hop) rat Ion so Voi chu ki cita song. -11 ° tr dién hinh vao khozing 10 5 doi Voi nguon co dion (hay nguon khong kot hop) gan don sac. ' 1:0 dion hinh vao khoang 10'7s doi Voi laser (hay nguon két hop) thong diing. Nhiou khi chting ta co tho xem song phat ra tit laser la mot song phang don sac. 17f 2-OHsong nang luong E. hap thu] ‘ phat xa 51 E. Hinh 20. S1/pluit laser gay N: do clmyéit am‘ gifla céc m1’rcIIdIzg1It(_mg E, M E2 .
  19. 19. 5 SL_r phén c| _xc cfia séng énh séng 5.1. sq phén cL_rc théng MOI so’ng sinh szing 151 sting pladn c1_rc t/1&7/zg né'u nhu phuong cfia dién Lruimg E(7‘, t) 151 khéng déi. khong phu thuéc V510 F V511. 5.2. Phén tich Vectd dién truésng Xét mél séng dién It‘: truyén theo true (Oz). Vécto E vuong géc V61 (02) V21 duqc phim tfch trong hcf: ca 56 (EX, 5). ) thimhz EH(z, t) = EV. (z, r)E'. + E/ V(z, r)E). . Nhu vz‘_1y, séng véclo E(z. t) 151 ké't qué chéng chfit cfia hai séng phan Cl_IC thing theo czic phuong éx V51 éy . T&'I nhién 151 sq phan lich trén khong phzii la duy nhéit, hé C0 56 (EX, E/ V) C6 thé quay xung quanh (Oz). Sl_I phan tich toain hoc nay duqc thL_rc hien vé mat vat 11’ bzing caich dung czic kinh loc dzfic biél C6 tén goi I21 kinh p/ zén c: _rc. Kinh phan cuc Lrong su6t d6i véi séng phan cue théng theo mot phuong nao dc’) V51 hoim toén duc d6i vdi séng phan cuc thing theo phuong vuéng géc véi phuong (16 (11.21). 5.3. Anh séng tL_r nhién kh6ng phén cL_rc Néu chflng ta tién hémh mét thi nghiém nhu trén hinh 22 thi sé théiy ring anh sang truyén qua kinh phan cue khong phu thuéc vino st; dinh huéng cfia kinh. Séng ti: dén phét ra 121 két qué chéng chat cfia rzit nhiéu doan séng phzit ra tit czic nguyén tit day 16c dén. _DoéLn séng néo cfing IE1 phan cuc nhung theo czich my )7: do dd phuong cfla E sé 1‘a bit ki V51 thay déi mét ceich ngéu nhién vdi khoéng thdi gian dao trung ‘C C. . Nhu'ng czic déiu thu (mét, I6 béo quang dién. ..) khong the‘? theo kjp nhiing sI, r bién d6i nhanh nhu vay. Chfing thuc hien phép la'y trung binh theo mét s6 rift lén céc doim séng. Do do’, vé m2'_1t th1_Ic nghiém, tat cé czic phucmg phan cuc la tuong ducmg. Trong trufmg hqp nay, einh sang tt_I nhién 151 kl1o‘ng pIza‘n ct_rc. kinh phan cac quay Hinh 22. S0’d(5 p/ Iain lich dull sting do rm)! dén p/ nil ra. C/ Mi y’: ' Klzdi niém phtin czfc / ién quan déiz clcfu thu dzrzjc xfrdtmg. Néia n/ zzrcluing ta cé mét dd}: tlm C6 the’ theo (16a' k_ip n/ zfmg biéiz rhién séng véi nlzjp diéu 10} 1 Hz thi cluing ta se"/161' rzing (inh sdng / a‘ plain CI_l'C vd C6 p/ urong 1)/ zcin ctfc biéh d0”i. V0'“i nlzfmg dd}: I/ m tlufc re‘: cluing ta / gzi néi rdng clzinlz (in/2 séng (16 Id khéng p/1a'n cI_rC. ' C/ urmzg 9 cfia tap séch nay duqc démh cho viefc nghién cliu Sl. _l' phan Cl_IC cfia zinh séng. . 18;: Hinh 21. S1_r (‘/1011 loc llzdnlu plzcin E X cfia di_e‘n Ir1rr>'ngulzr‘7 kinh plain cqrc. E [(2 dién Irm‘rng lqi /67 win kin/ I plain cI_rc. E Id dién 1rm>'ng Iqi I0? ra kinh pluin cm:
  20. 20. 6 Ctrong do séng 6.1. Céc dé'u thu énh séng Co rat nhiéu loai déu thu ainh séng: mét, may quay vidéo, phim chup sinh, photodiot vét cé nhfmg dung cu thi nghiém nhay séng hon nhiéu nhu czic nhétn quang dién (h.23). Trong mién song tinh saing, tat cé céc dfiu thu déu nhay vtii cong sua't btic xa cita song dién tt‘I. 'Il1eo nht'mg diéu di hoc trong giaio trinh Dion rt‘: hoc, cong suéft nay ti lé vcii binh phuong cuotng do dien tru<‘mg vét Voi di¢n tfch bé mat htiu ich cua déu thu. Ceic ddu thu co mot khoétng thoi gian dép ting T R nito do. Trong khoétng thoi gian n£1y, cht2ng rich phdn gié tr_i czia E2 . ° Thoi gian dzip ting TR cita mét nguoi vao khoéng 1/20 giay: su “cham chap” niiy duqc sir dung trong dién tinh dé tao ra éo giaic hinh énh dong khi chié'u lén métn 24 hinh énh tinh trong 1 giay. ° Céc to’ bao quang dién c6 thoti gian dép ting T R ngén ttii 10-6 s . ' Céc diu thu trong phong thi nghiem c6 thé co thoti gian dép Ling ngén tcii 10-105 nhung vén con rat dai so vcii chu ki song tinh sting khé kién. Do do, tat cé czic délu thu déu do giai tri trung binh cita cong sua't nhan duqc trong rat nhiéu chu kl dao dong sting. 6.2. Dinh nghia cua ctrbng do séng Mot dfiu thu co dién tich nhay sing ht'ru ich S sé cho mot tin hieu ti ltf: Voi S (E2) , né'u nhu (E2) 151 gié tri trung binh cita E2 tinh trong thoi gian dép Ling cua déiu thu. Chting ta dinh nghia ctrdng do sting I la cong suit trung binh >, Kla‘théso'tiltf: . cita btic xi; lén bé mat nhan séng, ttic 121 I = K<E C ht? )2.‘ Li thuyéi‘ di_én It‘! cho thciy trong chdn khong, cong sud’! Itic I/1:37" ctia btic xq lén bé‘ mzjr hi —’i‘’- E2 . c D0 dé. chting ta C6 thé7bie’u diein rt/ (‘mg minh hé sé'K, nhtmg rrén rlttrc re‘; ta chi rim cdch xdc dinh do ttrangphdn chfrklténg pha’i céc gid trj tuyér déi ctia ct(c‘mg do‘ sdng. Vi wjy, no’z' Chung Ia khong cdn phdi biéit diein mang minh hé s6'K. 6.3. Ctrong do séng vé st_r phén ct_rc Chting ta hiy phan tich mot song thétnh hai song phétn cuc theo hai phuong vuong goc vcii nhau: E = ENE). + Eyéy . Cuotng do cua song dé cho st‘: 151: 1 = K(E2> = K(E§ + E§> = 1<(E§)+ K(E§). Né’u kt’ hiéu cuong do cua caic song phan cuc thanh phéln 15. Ix vét Iy thi ta duqc: I = Ix +Iy. Cuong do cua mot song bat k‘1 béng tong cuorng do cua hai song phan cuc thing theo hai phuorng vuong goc Voi nhau mé khi tong hqp lai sé cho ta song ban déu. Taic dong cua photon lén am cut: C lam bat ra mot electron (hieu ting quang dién). Electron néy duqc gia to'c boi hiéu dién tho‘ gifra C vét dién cuc D1. tcii dtfap Vito D, vcii mot dong nang dit lfm dé létm bat ra mot so dien tit khéc. Dén luqt minh, ctic dién tti néy l2_ti dtrqc gia to'c bfxi hiéu dién the’ gitia D1 via D2 , vét moi diefin tit lai litm baftt ra rt‘: D2 nhiéu dién tir moi. Being czich ting thém mot so dién cuc trung gian. ta co me’ nhan duqc tai duong cuc A mot tin hl¢u tuong ting v6i hang triéu dién tit trén mot photon téi. Ctic dung cu néty cho phép do ctic l quang thong rat yé'u. Chting co thbi gian dzip ting rift ngfin, chi vac khoéng 10'”) giéy. Hinh 23. 0/ng nhdu quang dt'_én.
  21. 21. 6.4. Tru'c‘$ng hqp song don séc 6.4.1. Biéu thtirc ctia cuang do Xét mot song don sac, phan cuc thang: E = // i.’e(E) vat E = E, ,, cos(u)t + cp(M)), hay viotduoidang phtic E = Ell(M)exp(1'w1). Nou gia tri trung birth (E2) = E3, <C0S2(0J 1)) duoe tinh trong rat nhiéu chu kl, hay noi chinh xéc hon la trong mot khoéng thori gian rat lcin so vcii chu kl, thi ta so co: <cos2(cot)> = 2 va do as 1 = %KE3,. Nou chting ta ditng bién 11¢ phtic E3, = |E2l = E. E" ( E, ‘ la kt’ hieu lién hop phtic cita E ) thi biéu thtic cuorng do sé la: 1 = %KE. E‘. dung 1 I-Iién ttrorng phéch 0' tidy. chting Ia gid s1°rra°ng song dnh sting phdt ra t1‘rIaser Id s0’ng dan sdc. Mot dtiu tlm n/ tgin a’nh sting n‘r hai lase1'gié11g hé! nhau. Hai song Io"i C6 ctrdng do I l , I2 vd phdn ct_rc theo cfmg mot phtmng. Cdc bmic song cfia clning rd? gain '0'i 632,8nm vd do chénh Idn sci’ Id Av = 1 MHz. Hdy xdc dlin/1 c1ro‘71g do do dtrqc bring hai ddu thu C6 Ihdi gian (kip 1'mgIdn Itrqr Id. ‘ TR] = lOns Va 1R2 : 100115. Ta chon vécto don vi E2. theo phuong phan cuc Chung cita ca hai song. Daftt E1 = ElER vori El = El0cos(colr + cpl) V5. E = Ezéx E2 = E20 COS((02I + (P2). Cac pha cpl va cp2 (la hang so nou cac song la hoan toan don sac) phu thuoc vao vi tri cita dau tltu va cita cac laser. Cong sua't ttic thoi ma dfiu thu nhtftn duoe la: ml = 1<(E, + E2)2. V1 1 R rat lcin so vori chu ki song nén: 1 1 , 1 11 = 1<(E,2) = §KEl2ll va 12 = K<E22> = §KE§l, . 2 20. Cufmg do do duoc trén déiu thu khi do sé la: 1: 1<(E,2) + 1<(E§) + 2K(ElE2) = 1, + 12 +2 1l12 (cos(mlr + cpl)cos(w2t + cp2)) , hay 1 = ll +12 +/ E<cos[(u)l +oo2)t +cpl +cp2]) + 1l12 (cos[(tnl — 1112)! + cpl — cp2]). (cos[(col + m2)! + cpl + 1112]) luon luon bang 0 vi chu kt cita ham hinh sin nay rat nho so vol 1.’ R . Trai lai, hiéu col — co2 tucrng ting Voi tan so Av = 1MHz vi chu ki 1115 V21 do do gié. tri trung binh ttrong ting sé tt‘ty thuoc vao loai dau thu. 0 Diiu thu dap ting nhanh: Ham cos[(tnl — (02)! + cpl —q>2] gan nhu khong thay doi trong khoéng thori gian ‘t Rl . Gia tri trung blnh cita ham nay tinh trong khoéng thoi gian r R, sé gfin bang gia tri ttic thori cua no. Cuong do do dLIC_)'C sé thang giang vcii téin so Av (hién tuqng phéch): I = 1l+ 12 + 1l12 cos(21tAvt +cp). ' Déiu thu dép ting cham: ham cos[(o)l — co2)t + cpl — cp2] . bion thién duorc rat nhiéu chu ki trong khoéng thoi gian ‘E R2. Gia tri trung binh cita no tinh trong thori gian nay sé bang 0, ctrong do do duqc sé khong doi vét bang: 1=1l+12.
  22. 22. . .3 . -x . . , 7 Bteu dten vo hudng 7 r r p cua song anh sang ________ Nhfmg tinh toan vo quang hoc song noi chung la xac d'1nh cuong do tong hop do su chong chat cita nhiou song. Chting ta so chting to rang do tinh toan cuong do nhiéu khi co tho khong doy don tinh chat véctor cita dion trttong song anh sang. 7.1. Song phan ctrc phang Song phan cttc thang theo phtrong (Ox) duoe mo ta bang mot ham vo huong s(M, I) thoa man: E E(M, 1) = .s(M. t)E_l. va 1 = K(s2> Tiop theo ta so xét don su chong chat hai song. 0 Truoc hot, ta khac sat trtrong hop hai song phan cuc theo citng mot phu‘O’ng 9). , vuong go’c vol ca hai phuong truyon song (1124). E1 = sl(M. r)Ey va E2 = s2(M, t)Ey. Ighi do’ ta co tho gan duoc vao ham vo hucing s(M ,1) tuong ting vcii tong E = E1 + E2: E = s(M, t)'e’y vat s(M, t) = sl(M, r) + 1-2(M,1). Nhu vay, biou dién vo hucing cita song anh sang la dit do tinh ctrong do sang I = K <s2> . Chting ta co’ tho “khong biot” don phtrong phan cuc va viot: I = K<(sl +s2)2>. Trong nhfmg truong hop khac, biou dién vo hucing nhu tron chi la gan dting. Chting ta so lam ro diou nay qua mot vai vt’ du. ' Xét hai song phan cu‘c trong mat phang duoc xac dinh bang cac phuong truyon_ song. Voi nhfmg kt’ hiou trénl1i11h25, ta co: E(M,1) = sl(M, t)17l + s2(M,1)172 = [sl(M, t) + s2(M, r)]cosaa(. + [sl(M, t) — s2(M, I)]sin0tE2. Nou on dit nho thi mot cach gan dting ta duoe: E E1 2 sl(M, t)E2l. va E2 2 s2(M, r)EA. Con E : s(M, t)Ex Voi s(M, I) z sl(M, I) + s2(M, r) Va I z K<s2> : K<(sl + s2)2> Su mo ta thuan ttiy vo httotng cac song sang la dfi do tinh cuong do l(M) vcii mtic do gan dting cao. Trai lai. khi goc 01 ion. biou dion gan dting vo htrong so khong con thoa dang nfra 1 :2 K((sl + s2)2). ° Bay gio hai song lai co phtrong phan cuc vuong goc vol nhau. Voi nhfmg kt hiou tron hinh 26, ta co tho viot: E(M, z) = sl(M, t)17l + s2(M, I)172 va (E2) = + #5 <(sl +s2)2> Ijhtr vay, trogg truong hop nay, khong tho coi su chong chat hai song E1 (M. t) va E2(M, t) nhu mot phép cong cac song vo huong. Tom lai, do xac dinh cuong do tong hop do su chong chat hai song dion tit, ta co tho coi moi song dion ttr nhu mot song vo hucing s(M, t) nou nhu cac phuong phan cL_tc gan trttng nhau. Nou diou kion nay khong duoc thoa man thi can phai gift nguyon biou dion vécto cL’1a trttong dion tit‘. 21 Hinh 24. Ccic £lié1tt1'1r(‘n1g E1 vd E2 66 cfmg plnrm 1g. Hinh 25. Hai song (6 ctic p/ tzrmtg pltdn ctrc gcin nltau néh géc 01 Id 11/111’. Hinh 26. Hai plurmtg phtin c1_rc vuong gzic wii It/ tau.
  23. 23. 7.2. Anh séng ta; nhién khong phén Cl_. |'C Trong phén nay, chfing ta sé khéo seit truotng hqp duqc minh hoa trén hinh 27. Moi song 151 mol song énh sang n_t nlzién, gén don séc bao gom nhiéu doin song phan cL_rc, V51 co pha tily )7. Né'u céc phuong truyén song gén trfmg nhau (oz nho) thi ta co thé coi céc vécto don vi 171 V51 :72 trfing voti E, E z (Ex, + Ex2)a_, . + (Ey, + 15,2 )2, Tiép theo, ta tinh giai tr: trung binh cfia (E2) trong thoi gian daip (mg 1R cfia dfiu thu duqc gié thiét 1:31 ra't Ion so Voi thoi gian ké't hqp: (E2) = <(Ex1 + 1:32)? ) + ((15,. + Ey2)2>. V1 St} phan cue cfia tfmg song bién thién mot caich ngfiu nhién theo thoi gian nén hai phuotng lit tuong duong nhau vé mat thong ké vi do do : ((5 +5 Z)-( 2 (2)-2E E 2 x1 'x2) ‘ (Eyl + Ey2) hay E ‘ ( yl + y2) ' Chting ta co thé xem moi song nay nhu‘ mot song vo huong. s1(M, t) = 5Ey1(M, t) va s2(M, t) = x5Ey2(M, t), vadagu 1 = K<E2> = K<s2) voi s= s1+s2. Song vo huong tuong duong voi truotng E1 (M, t) sé co dang : 51 = sl, ,,(t)cos[cot — E} +(p1(I): |. Chling ta thfra nhan ring c6 lhé khong céin phéi dé y déh nhfrng thing giaing cfia bién do vi xem slm IE1 mot hing so. Trong rift nhiéu trufmg hqp, cufmg do séng gay ra do st; chong chéit cfia nhiéu song dién ti! c6 tho duqc tinh toén nho mot mo hinh don gién hoa. Trong mo hinh néy, dién truong dutyc xem I2‘: tuong [mg v6'i mot dai luqng vo huong. Phép géin dfing néy ép dung duqc : ° trong trufmg hqp rift hay gap 1:‘: céc song khong phim c1_xc co phuotng truyén gafin trimg nhau ° doi Voi céc song phim cue mé ta bié't ring céc phuorng phim cuc cfia chting gfin trilng nhau. 7.3. Tin hiéu séng — Trong khuon kho cfia phép gén dfmg vo huotng, thong tin hfru ich cho viec tinh toén cuotng do sting duqc chtia trong hém vo huéng s(M, t) mi ta sé goi 121 tin hiéu sdng. Né'u song zinh séng la don séc thi ta co thé viét : s(M, t) = s, ,,(M)cos(u)t + cpA_, M + cpo) = s, ,,(M)cos(q>(M, t)), Voi A la mot diém co’ dmh néo do duqc dimg lém go'c toa do. cpA_, M = cp(M, t) — q>(A, t) 151 hiéu pha gifra 2 diém A V2‘: M tai cfing mot thoi diém. Nhu chfing ta sé tha'y, <pA_, M phu thuoc V5.0 vi tri cfia céc diém A vi M cfing nhu vao moi truimg gifra hai diém a’y. Chfing ta biéu dién hieu so pha néy mot céch tong quait thong qua bién do phftc cfia t1’n hieu sang : g = .g0(M)exp(icp) vol cp(M, .*) = cot + (pA_, M. Hinh 27. SI_( chéug cita"! uia hai . '(5ng dull xring ll_f ulzién. Hai séug C6 dé pluin czfc my 51.
  24. 24. Ung Voi moi song tinh sang d0'n sfic, mach so 03, ta c6 mot song vo huong duoc goi la tin hiéu sang : s(M, t) = sm(M)cos(cot +(pA_, M +cp0), hay duoti dang phfrc: §(M, t) = §0(M)exp(i(a)t +(pA_, M 7.4. Curling do cfia song ddn site 5 ti lo voi bién do phtic cua cac thanh phan cua dion trufmg E nén cuong do cua song tuong [mg sé ti lo voi I 5 I2: 5; * . Noi chung, trong Quang hoc, ké't qua co )7 nghia khong phai la cong sua't cua buc xa lén mot don vi diéjn tfch cua mat nhan sang ma la so do tucmg ting cua dfiu thu. Vi vay, chung ta co tho gop tat cé cac he‘; so Ii 16: trong ham dap (mg cua dau thu va vié't mot cach don gian la I = _s_. § *. Cuimg do séng la mot dai luotng ti lo Voi gié tri trung binh cua binh phtrorng tin hiéu szing. Doi vori song anh sting dom sac, ta co thé vié't : I= s,2,, hay I= §.§*. Czic dfiu thu anh sang déu nhay voi cuimg do sang. 8 Pha cua song énh séng Ta bo qua nhfmg {hang giang vé bién do dao dong cfia song anh sang don sac va gia sf! rang cac diéu kién cua phép géin dung vo huotng déu duoe thoa man. Do xac dinh hoan with song don sac do. ta chi can bié't cuong do va pha cua no tai moi diém trong khong gian. 8.1. Song vé tia séng Cac tia scing la nhfmg duorng truyén sang, tié'p xuc tai moi diém voi phuotng truyén song anh sang. Doi voi song phéng, cac tia sang la nhfmg duong thing song song vc’xi nhau. Doi voi song cau, chting la nhfmg nfta duorng thing phat xuat tit diém nguon. Chung ta thira nhan rang nhfmg tia sang nay dong nhat Voi nhfmg tia sang cua Quang hinh hoc. Cac tia sang cua Quang hinh hoc tié'p xtic tai moi diém voti phmmg truyén song. 8.2. Hiéu pha gifra hai diém cung ném trén mot tia séng 8.2.1. St; truyén song trong moi trudng trong su6't, dong chit Xét mot tia sang thing trong mot moi truotng dong chat co chiét sua't rt, di qua mot diém 0 nao do va co vécto don vi H. M la mot diém ném trén tia sang. r = 17.0714 la quang duong truyén cua anh sang gifra Ova M, duoc xem la mang déiu duong né'u theo chiéu truyén sang. Pha cua song tai M duoe viét nhu sau: 27w ¢(M, f) = 0)’ — kl’ +([)() = 0)’ — fl‘ +(. [)(), 23
  25. 25. hay ¢(M, !) = cot — MW r +oo = 0)! — 22:". + tp0,né'u A0 Iibuétc song 0 ) trong chin khong. Tai moi thoi diém, hieu pha gifra hai diém 0 viM Ii: ¢0_, M = —2Tmv r = —2—nnr = —2—nnfi.5M = v6'i E = rz2—7[a'4'. C M M 7%) 8.2.2. Tinh Iién tuc cita pha Tai mil phin cich gifra hai moi truong trong suot, cic tia sing bi khtic xi vi phin xi Néu nhu kich thuoc ngang cfia chum sing rat Ion so voi buoc song thi cic tia sé bi loch theo cic dinh Iuit SNELL-DESCARTES. Trong truong hop nguoc Iii, chung ta quan sit duoe hion tuong nlu'e"u xq inh sing sé duoc nghién ctiu 6 cic phin sau. Ta ki’ hieu n, Ii chié't suit cfia moi tmorng trong do song truyén toi vi n2 Ii chié't suit cfia moi truong ex phia bén kia cfia mit Iuong chat (h.28). Chung ta thira nhin ring tai moi diém cfia Iuotng chit: ° pha cfia song khtic xi bing pha cfia song toi. - ne'u n, > n2 thi pha cita song phin xa bing pha cua song roi. ° né'u n, < n2 thi pha cita song phin xi bing pha cua song tori cong them mot Iuong bing TL Chung ta cling thiza nhin ring: ' su phin xi trén kim Ioii lim cho pha cfia song bi giin doin mot Iuong bing 1t. ° khi song di qua diém hoi tu (h.29), cin phii cong them 1: vio hieu pha duo'c tinh toin theo khoing cich. Cic két qui niy co thé thu duoc tfr cic dinh luit cua Dion ti: hoc. Pha cfia song inh sing Ii lién tuc khi: ° khtic xi; ° phin xi trén mot luong chit tai do song tori truyén vio trong moi truotng co chié't suit Ion hon; Pha cfia song inh sing bi giin doan mot luong bing 1: khi: ° phin xi trén mot Iuong chit tai do song tori truyén vio trong moi tru‘o'ng co chié't suit nh6 hon ; 0 phén xi trén bé mat kim loai ; 0 di qua diém hoi tu. Trong bat tép 5 ta so trinh biy su chL’mg minh cic dinh luit Snell-Descartes tt‘I mo hinh song inh sing. 8.2.3. Su‘ truyé'n séng qua mot | o:_it céc moi truong trong suot dong chit ké'tié'p nhau Biy gio, ta sé khio sit mot song truyén qua mot Ioit cic moi truorng trong suot, dong chit, co chiét suit Iin Iuot Ii n1,n2 , Mot tia sing phit xui't ti‘: diém A trong moi truotng thu nhi't sé bi khtic xi trén cic luotng chat tii cic diém I1 , I2 (h.30a) vi di qua diém B trong moi truong co chié't suit up. Theo tinh chit lien tuc ctia pha, cpA_, B = (pA_, ,l +(p, l_, ,2 +cp,2_, ,3 +. ..+(p, ,H_, B, 211 hay tpA_, B = —— + 1:21:21]? + + r1,-1_t, -.. I,-_1I, - + + n, ,@. Ip_1B . M Hinh 28. Pluiu xq Irén mat Itluing klu’~IluIy tinh. Dr) Iéclz plm gdy ra do pluin xa. ‘ (pA_, ,, = n1AI + I11/B+1t Hinh 29. Pha cua sting khi (Ii qua mg)! tliéin hot‘ in : q, A_m = M8 +11: Hinh 30a. Sir Iruyé‘/1 cua tia sting qua Iiliiéic moi lrtrting kluic nhau.
  26. 26. Ta goi quang l_o‘ (AB) 121 téng céc so’ hang Er trong dfiu ngoac don: (AB) = Z111,-17,-.2,‘ , né'u Z; 151 dufmg di cfia tia sfing trong moi trufmg déng cha't, c6 chiét suai n, - . Cain chfi 3? ring quang IQ nay dling being khoéng caich ma séng truyén duqc trong chin khéng trong Cflng m(f)t khoéng Ihbri gian ho€_1C (16 C6 cilng mtjt dtfa léch pha. Hiéu pha khi dc’) duqc viét nhu sau: <pA_, B = —2En(AB). Téng quét hon, né'u séng bj gién dogn vé pha thi ta co’ Ihé via: 2 (pA—>B = _'}%(-AB) + ‘psup- (psup cc’) duqc khi séng bi phén xa vi di qua nhfmg diém h<f)i tl_J. Néi chung, (psup IE1 mot bcf>i s6 cita 1:. 8.2.4. Quang lc} vé pha Trong trufmg hqp t6ng quait, chiét suit co’ thé biéh thién mcfn céch lién tuc vz‘1 tia szing sé bi u6n cong di. Chfing ta sé suy rong dinh nghia cfia quang 10 Va biéu thtic dc) léch pha. Theo dinh nghia, quang 10 (AB) giira hai diém A V51 B cfia m()t tia séng (h.30) 12‘): B (AB): j’m2.di, A 6 day I: I2‘: chiét suiit (phu thuoc véo diém khéo sét) V51 17 I51 vécto don vi tié'p tuyén véri tia séng. D6i véi séng d0‘n slic c6 mach S6 0) via bucic séng trong chén khéng 1.0, hieu pha gifra hai diém A V2‘: B tai moi thin’ diém 151: 211: ‘PA—>B = "K(AB)+(Psup = '%(AB)'HPsup' S6 hang (psup thufmg 12‘: min béi s6 cfia 7t, ct’) duqc ti: nhimg gién doan vé pha khi séng bi phim xa hoac di qua m()t diém h()i tu. 8.2.5. Sl_I tn? lai nguqc chiéu cfia énh séng Né'u énh saing truyén It‘: A dén B doc theo m(‘_’>t tia szing thi n6 cfing C6 thé truyén nguqc lai ti: B vé A cfing theo duémg dc’). That vay, céc dinh luat phén xa vi khac xa khong phu thucfac V510 chiéu truyén zinh sang. Céc quang 16) (AB) theo mcf>t chiéu vii (BA) theo chiéu nguqc lai déu béng nhau. Né'u déo lai chiéu truyén énh séng thi céc tia séng vim khong thay dfii. 8.3. Djnh Ii MALUS 8.3.1. Mét séng Xét mC)t séng ainh séng phét xufit It‘: nguén diém A (11.31). Mat séng I2‘) mat duqc xéc dinh béi tap hqp nhfmg diém céch ngu6n diém cimg mcfn quang It}. Né'u séng phét ra ti: nguén diém I3 don séc thi czic mat séng sé trimg V61’ céc mat ding pha. Vi du nhu né'u moi trufmg IE1 déng chit thi mat so’ng 1a cic mat célu cé tam tai A. Chting ta c6 thé nhan tha'y ring céc mat séng true giao véi czic tia séng. Dinh li MALUS sé téng quzit héa tinh chit niiy. Hinh 30b. Quang lg) (AB) bdngs H (AB): _[n(M)fi. dM A H = _[n(M)4M A Hinh 31. El, 22 V12 23 Id céc rm}! Ming: (AM)= (AP)= (AQ).
  27. 27. 8.3.2. Phét biéu dinh Ii MALUS Céc mat s6ng tr1_rc giao V6i céc tia séng Mot czich chfmg minh don gién djnh 11’ quang hinh hoc nay duqc dua ra trong bdi Iép 6. 8.3.3. Mat phéng ding pha cfla chum séng ddn séc song song Ta dial mét nguén diém don séc tai tiéu dién vat Cfia mét tha'u kinh hoi u_1 (11.32). Céc tia séng [6 1a khéi tha'u kinh déu song song V6i nhau V2‘: C6 Vécto don vg la 17. Theo dinh l1'MALUS, CéC ma: ding pha la nhfmg ma: phéng vuong g6c V6i Caic tia saing V51 do d6 vuong g6C V6i phuong truyén szing. S6ng tuong (mg 151 s6ng phéng, don séc C6 dang: . g0€Xp| :i((1.)t— k. r)] van k = 2—"m7. M C111? 2: ° Thzfc ra, mgir nguén sting th1_(c khéng bao gz'o"1a‘ mét ng1m‘)1 dié'm vd cfing khéng bao gid‘ It} don szfc. Do d6, so’/1g nh_a‘n d! (_UC C111’ gdn citing la‘ so’ng phéng dan sic. S11’ gin dxing I6? nhd? C6 dtrgrc do‘? va"i c111‘m1 tia laser. 74;: dL_mg 2 Tinh toén quang 16 C110 mér rhzfu kinh héi n_1 méng dd! trong k11o‘ng khi dttac Ch1é1l sting bing mét nguén diém /15m trén riéu dién vdr nhtmg 0' ngodi riéu diébz chfnh ctia Ihzfu kinh (daft PM = a) . Hziy tinh ca’c hiéu quang 16. 1) trén hinh 33 8) (AQ) ‘ (AP) I 2) trén hinh 34 3) (QA) — (PA) I b) (AM) - (AP) 5 b) (MA) ~ (PA); chin sang 16 tron Hinh 32. C6611 I40 mg)! cluim Iia xung song. Cluin Ming [6 twin mim I1’ Iiéu ¢Iie’m ctia I1z¢Tu kinh bl . Hinh 34. Cluim lid song song hgfii I1; trén liéu dién (inh C1111 (ltd): kinh. #- “cl 1) a) Ta sir dung dinh I1’ MALUS n6i ring Céc tia Hinh 33. Cluim Iia xucfl pluil Ifrngmfn dié'm nfim trén Iiéu di_én v¢_2I clia (India kinh Id mg? ! cluim song song. séng vuong g6C V6i czic mat s6ng. Mat séng biéu dién mét tap hqp nhfmg diém ma caic quang lo tinh [Er ngu6n diém de'n chfing la nhu nhau. Diéu d6 cho phép ta khéng dinh ring (AQ) = (AP) vi PQ vuong g6C V6i Caic tia séng, nghia lit: (AQ) - (AP) = 0-
  28. 28. b) Ta C6 thé V161: C1112 y’: (AM)-(A1=) = (AQ) + (QM) _ (AP) = (QM) Cdc kéi qua’ c6 rI1é'd1ing . . 1 1 ~ , I1gz_1cn11ie'n111zm1g k110‘ng theo ket qua 0 "em dlfgt‘ quén jfing 50’ . ... ... ... ... ... ... ... .. . . Nhung (QM) = QM = PM Sim = asina , suy GAUss v1‘(a rrinlz bay dd ra (AM) — (AP) = asina . k110‘ng 111111 déh 1111111 dang c1z1’n11 xcic ctia r/1a"uk1’n11. T/ ufc réfi d_o‘ dzfy (quang /1_oc) c11a I/ ufu kinh C6 2) Theo 51; H6 1231 nguqc chiéu cfia énh sang, mcfn cach Wong “.1 ta 55 (159793 Hinh 35. D6 (lay q11a11g11g1c a) A _ PA = 0 ; - 1 1 . » cI1am{51I11z111ki11l1((iz1z2ylc) (Q ) ( ) ‘ nlymg anh hlmng "ha, 11l(11111'1Il1l 11(_31'11_1)1c11(3I1g pluii b) (MA) — (PA) = aslnot . d. m/1 (12.35). ,); ,,, (;, ,, ,;, ,g, ,,', 3.3.4. Tinh ché'tcC1a céc cép diém Iién hqp Gié sir diém vé_1tA V51 énh A’ C1'1a n6 qua mcfat quang he gfim Céc guong V5. théiu kinh (11.36). Ta xél hai tia séng bat ki di 111 A den A’, cit mac séng 2 ' 1:11 P V2‘: Q. ° Theo d1nhliMALUS: (AP) = (AQ). ° Theo dinh luat trér lai nguoc chiéu, A’P V2‘: A'Q cfing Iii nhfmg tia séng vi (AP) = (A'Q) hay (PA) = (QA) Ta C6 Ihé kél luan (AP) + (PA') = (AQ) + (QA') . Quang 16 gifla hai diém lién hcyp qua m<‘_)t quang hé tuang diém kh6ng Hinh 36-A W3 A’/61 ¢'é5IItWm1iéII/ I<7IJ- )3 phu thu6c V510 tia séng n61 hai diém : ?iy. vd 2' (611011/Itillrruilccftt)/1? 2 "I47! J'!5I'K~ I Hé thtic lién hqp 1) Tinh quang 16 (FM) vci 11‘: (16 my ra 51; ph1_1 Ng1ro"1' ta klzdo sdt 30 dd ve"rrén 1111111 37. T1zd'11k1'n/1 (111155 5'10 ‘((5 dd)’ 011“ (M11 “"11 W30 1‘- héi 111 L C6 riéu 1:1] f ', dmjc Izim bzing 1111133 111111 2) Tim 1411' 11_é thfrc lién 111771 51151’ viii czic 110cir111 dé chiéi sud? /1 vd dé day 1611 111161 c11a no’ la eo. XA vd xA- c11a/1a1'dié'm11é11h_op. N “ ’ dr d'r'r" 1"’ F ' rh"k’I. ,, , . , , gll0I1SL111g 1_0'C U 1811 (16117 cua au [/11 Gla Su H chléu cua M trén quang truc‘ Theo d1nh 11’ MALUS, H V51 M néim trén cimg mcf)t m€1ts6ng. Do d6, (FM) = (FH). Nhur1g(FH)= rzkk(d — e0)+11e0 = d + (11 — l)e0. T1‘1'd6 suy ra (FM) = d + (11 — 1)e0. L1’ Iugan Iuong 11;, trong diéu kien GAUSS, t1’1‘c 121 doi V61 nhfmg tia nghiéng V61 quang tr1_1c mét géc nhéz (FM) = F1 + 1M + (n — l)e(r) 2 = f'[1+ ’ j+d-f'+(11—1)e(r). 2f.2 Hinh 37. A Va A’ Iién 11z_)p vé‘i nhau qua L.
  29. 29. Déng nha't hai biéu thfrc cua (FM) ta ducjc: r2 r2 r2 (AA‘)= (—xA) 1+—2 +. rA- 1+ 2 g([') : go — -M _ 2.X'A 2XA' 2(11 — l)f 2 2) A V5. A’ 121 hai diém lién hqp qua L nén quang 16 (AA’) khéng phu thucfJC V510 diém 1. Trong diéu kién GAUSS: (AA) khong phu thu(_>C V510 rnéu nhu ——l +—l = —1'. (AA’) = A1 +1A’ + (n — l)e(1') x,1 x,1- f SCI dung Czic ke't qué 6 phén trén: He mac nay Chfnh 11 he mac lién hqp DESCARTES. P D5 luyén taflp : xem béi téjp 3. Dubng cong ph6 cfia mcfzt doén séng gén don séc__ 9 (3 1161 §3. chting ta dai m6 tai s6ng é. nh saing phzit ra til min ngu6n nhu mcfnt Chuc31 lién 116p ceic doan s6ng géin don sic C6 nhfmg dc) léch pha my )7. Trong phein n‘ay, ta sé nghién CL'ru mét Czich m6 hinh h6a tuong duorng khéc. 9.1. Vi dL_I vé dubng cong ph6 dang Lorentz Thay Cho v1¢C khfio sat m6t s6ng hinh sin. mach 56 (no , C6 th61 gian kéo dai hfru h2_1.n, ta sé mo 151 séng phét ra tir mcjt nguyén tflr nhu‘ 121 két qué Chfing Cha't cfia V6 sf)’ s6ng hoan tofan don szic C6 tin 56 Ian can V61 mo . (Oz) 15 phuong truyén s6ng, (mg V61 m61 giéi ph6 nguyén 16 da) C6 mét bién dc) phL’rC: C ds(M, t) = f((u )exp[1'm [1 — ifldaa . Bién dc) phL'rc t6ng Ccfmg C6 duqc do su Chfing chfit cua Caic giéi ph6 sé 151: . _s(M, t)= 01 f(co)exp[ico[t—-Z-Mdo). c on = —oo f ((1) ) l2‘1 duémg Cong ph6 bién d6 cua ngu6n. T51 nhién, as chi C6 thé 151 duong Cbn f(co) chi C6 nhfmg gié I11 dang ké trong mt_)t khoéng tén 56' nhé quanh (130 . T1’Ch phan ttr —oo déh +oo Chi 151 mc‘_)l thu phép toén hoe khong énh hufmg g‘1dé'n két quzi. Dé lam vi du, ta xétflw) 121 dLrc‘mg Cong ph6 dang Lorentz (11.38): f(w)= —%7- 1 + 4‘’’: —’ °"’ A01 2 Khéo sét d6 th1h51mf(w)Cho lhéfy bién dc) Chi nhan nhfmg gié tr‘; ding ké 661 V61 nhfmg tin s6 ném trong mcfn giéj h¢p quanh (1)0. Hinh 38. Dming cong dang L0re11!: : A0) 111 (I6 rging 111111 cl1ié11 cao (1155 171111 rging). 28 A
  30. 30. Détinh s(t), ta d6i bié'n u = co — (no va 1/ = [I — 5) . Khi d6, ta sé duqc: C 00 . ;(M, t) = Sexp(iw0v) I d14 , ““°°l + 4 u 2 A0) Q) ® . ;(M, r) = Sexp(ia)()v) I C050”? du + i I smowg du . u= —ool + 4 " u= —ool + 41; A012 A002 Tfch phan thL’r hai bang 0 (vi ham dudi da'u tfch phan 1:1 ham lé) cbn gié trj cfia tfch phan thfr nhfit cé Ihé tim duqc trong cac seich tra cfi’u. Quay vé caic bién ban diiu. ta duqc: z Au)t—— 2 S . g(M, I) = ?: m—exp':1(n0(r——: —Mexp ———2—-—-C— , Biéu thtic trén m6 té m<'; >t ham h‘mh sin, mach s6 030 . c6 bién do A b; gidi han theo thbi gian béi ham mfi. Chfing ta tim lai duqc doén séng tucmg tu nhu nhfrng doém séng di mo té truéc day, chi khfic 15 bao hinh cita né C6 dang ham mfi chL’I khong phéi la dang chfr nhat 0139). DC) r<_5ng -c C (vii do dc’) ca dc) dai ké't hop Ihbi gian)cf1a doan séng nay 12‘: my lhuéc vao dc) rang phé Au) : khoéng thfri gian trong d6 bién dc’) A 1é1“lén” (ta quy uéc Ajax < A < Am )ph2'1i Lhéa msnhe Ihfrc Au) = 2 hay Acne = 4. Néu v 151 Ian s6 thi céc dc) rfgng Av va At lien hé vdi nhau bang he thfrc: AVIC = E z 1 7: 9.2. T<"§ng quét héa Mot dang dufmg cong ph6 khéc (xem {mg dung 4) cfing cho ta ke't qué tuong IL; mc‘_)t céch dinh tinh: AVTc = 1 . Thuc ra, dc’) la hai cach m6 1:’: tuong duong vé cimg mat hién tuqng séngz cach mé ta I1; nhién trong mién Ihbi gian s(t) va cach mo tai trong mién tfin s6flu)) sao cho: §(t) = I f(<n )exp(icot)da3 (tai z = 0). u) = —oo C6 thé chfmg minh rang dubng cong phé bién déflm) duqc tinh tit §(t) bang cong thL’rc: f(u)) = 3 J‘s(t)exp(—i(nr)dt. TI —oo Nhu vay, vi flm) va 5(t) c6 thé tinh duqc qua nhau nén : f(co) vd §(r) déu mang rd’! cd tlzéng tin Iién quan déh tin hiéu sting. S6ng géin don séc cf) the‘? duqc biéu dién mat cach tuong du'o'ng hoac bang m(f)t chu6i lién tié'p céc doan séng hinh sin, déc lap nhau, c6 thfri gian kéo dai trung binh ‘cc , hoac bang s| _r ch6ng chfit cfia nhiéu séng don sic trong mét giéi ph6 c6 dc) rcfmg Av lén can téin s6 trung tam V0 . 1: C va Av lién hé V6i nhau bang he thfrc Avrc as 1 . 3(1) Hinh 39. Dodn Ming C6 bao hinh luim mfi.
  31. 31. C /112 y’: Hé pr/ n’rc trfn C6 tl1é"dzr_dc hiéit mér cdch d_inlz tinh nlnr sau: céc séng / tinh sin cI10‘ng chzit lén n/ tan C6 cling pha tai trim dodn‘so’ng. Sau do’, do chu kt‘ cua c/ uinag hm kluic nhau cho nén cluing léch pha ddn kin’ di ra xa. Cdc/ z tdm mo‘! khoang ndo dé, p/ Ia czia cdc s0’ng In my )3 vd séng r0‘ng hop Se" bcing 0. 74p dong 4 Duimg cong phfi dang chfr nhat s(t) rc') rang la met tin hieu hinh sin co’ mach sf)’ Hziy xdc dinh dgmg viz ddn/1 gid rho‘) gian kéo ddi (D0 , bien dc} hm» Va bi bjén djeu theo bao hinh; Tc ctia cdc dodn so’ng néit nlm dztdng cong plté’ A czia so’ng én/1 sdng dzr<_7'c c/ to n/ m'sau. ' 51111] A , 0) f(u)) = 11 ne'u 0) 6 mo — iAu); o)0 + iAu) gm _ Ao) — _ smC[Tf)' 2 2 ——f 1 1 2 flm) = Om-gum g [mo _ §Au); (1)0 + END] Sau nay, chung ta sé cc‘)n nhieu léin gap lai ham 1 1 sinc(u) = Sm". D6 thi cua g(r) duoc vé tren Ta cc’) the doén nhan ngay la 1, »- __. II ‘ AV / zinlt 40. Tich phan duoc gum han trong mlént Bién do song rat nhé khi c’) xa dinh trung tam vi [mo _ LAO) ; (D0 + 1&0] _ chung ta xem thoi gian phat xa cc la do rong cua 2 2 dinh trung tam nay hay 17 ~ 4i - L a)0+—A23 C An) Av ' §(r) = h I exp(z'u)t)dt °’<)‘%P‘ 1(1) /1 . .Ao) A0) = _—exp(to)0t)[exp(1—i—rj — exp(—1Tt): |. Chuyén sang ham sin, ta duoc: . Au) Sll'1(Tlj hA()) ——-j 2 ’ Hinh 40. Darin sring cr5 dining cong pIu5’z1guzg r. :In7‘nIuj! . £0) = I» Be’ luyen tép: béi tép 4. 9.3. Anh bién déi FOURIER Su chuyén ti: duémg cong ph6 f(u))sang 30) 151 vi’ du zip dung cua mot phép toén goi 1a phép bien doi FOURIER ma cac tinh chat cua no duoc trinh bay trong phfin phu 1l. _lC. Xua’t phat tfr cac tinh chat cua énh bie’n d6i FOURIER, chung ta cc’) the tim lai duoc céc he thtic gifia mo hinh doian song vi) mc‘) hinh do rong pho. 0 Sai khéc mot he so’ hing so‘, bién dc) ; (t) 151 énh bié’n ddi Fourier nguoc cua duong cong ph6 f(a)). Do d6 duong cong phci cfing chinh 151 sinh bien doi Fourier cua 5(1), sai khac mot he so hang sc‘). 0 Ne’u fix) 12) met ham chin “dang chuong” cc’) dcf) rcf)ng dac tnmg la Ax thi F (u) cling 151 ham “dang chuc‘)ng” c6 do rong Au sao cho: , AxAu z 27! Ap dung cho truong hop song, he thtic trén trc') thanh r£Av -~ 1 voi ‘E; 12‘) thoi gian kéo dai cua doan song cbn Av 15 do rcf)ng pho cua vach khéo sat. : 364))
  32. 32. .. ‘. Q’ *%. DI€U CA7) CHI NHO’ u DAI cuone vé‘ SONG eon sic - Mot tin hieu truyén voi van to'c khong doi v doc theo chiéu duong cita truc (Oz) sé la mot song chay phang, don sac co tan so v = 3 neu nhu no cc’) dang: 21: s(M, t) = sm cos(c1)t —%z +cp0). Buoc song 9» la chu ki khong gian trong moi truong khao sat tai mot thoi diam txac dinh, nghia lit : = y_ = 21w v a) ' Duoi dang phtic, song cc’) biéiu thc’Ic la 5 = so exp[i(a) t — it -F voi it = zxlii 1:‘) vécto song. ° 6 xa nguon, mo hinh song phang noi chung 12‘) met gan dting rat tot. in soNG AN: -I SANG - Song dien tit truyen trong chan khong vc’)i van tc‘)’c c xap xi bang 3.108m. s’1 . Cac song anh sang kha kien la nhimg song dien tit co tan so’ nam trong khoang gifra 4.10" Hz vs‘) 8.10” Hz , nghia la co buoc song trong chan khong A0 nam trong khoang gifra 0,4p. m (tim) Va 0,8pm (do). So phat xa anh sang kha kié'n lien quan den cac chuyen doi electron trong cac nguyén tit‘ hoac phan ti)’. - Trong moi truong trong suot duoc dac trtmg hoi chiét suat n, van toc truyén anh sang la v= £. ll ° Song phat ra tit nguon sang co the duoc xem nhu 12‘) met chuoi lién tiep cac doan song gan don sac co thoi gian kéo dai trung binh 1: C (thoi gian ké't hop) rat Ion so voi chu ki cua song. Dai luong I6 = etc bieu thi do dai kéft hop thc‘)i gian. Tc diéin hinh vao khoang 10"" s doi Voi nguon sang co dien (nguon khong ket hop) giin don sac. at THANG BAC THC‘): GIAN Trong Quang hoc, chcing ta gap ba thang bzftc ve khoang thoi gian: - Chu ki song anh sang: T at 10*” s . - Thoi gian ké’t hop: - nguon sang co dien: cc tv 10‘” s; - nguon laser: ‘cc =4 10'7s . ° Thoi gian dap (mg cita dan thu: - cac dau thu thong dung: Ion hon 10'6s ; %s. ' Song gan don sac co the duoc bieu dien mot cach tu'ong duong hoac bang mot chuoi lien tiep cac doan song hinh sin, dc‘_)c lap nhau co thcri gian kéo dai trung binh 1:‘) ‘cc , hoac bang so chong chat cita nhieu song don sac trong mot giai pho co do rong Av Ian can tan so trung tam V0. 1, vi) Av lien he voi nhau bang he thtic Avrc 4: 1 . - mat ngucri:
  33. 33. I G/ ‘iN DUNG vo HUONG Trong rat nhiéu truimg hop, dap {mg cfia dau thu co the duoc xac dinh bang mot mo hinh don gian hoa. Trong mo hinh nay, dien truong duoc mo ta bang mot dai luong vo huong. Phép gan dting nay ap dung duoc trong truong hop rat hay gap la cac song khong phan cc_rc cc’) phucmg truyén gain trimg nhau. ' Ung Voi moi song anh sang don sac mach so (0 , ta cc’) mot song vo huong duoc goi la tin hieu sang: s(M, t) = s, ,, (M)c0s (cot + cpA_, M + cpo) , hay duoi dang phtic: s(M, t) = §0(M)exp(i(a)t +¢A_, M )). ° Cuong do sang la mot dai luong ti le Voi gia tri trung binh cita birth phuong tin hieu sang. Doi voi song anh sang don sac, ta co : I= s,2,, hay I= s§'. Cac dau thu anh sang déu nhay voi cuong do sang la dai luong ti Ie voi cong sua’t bt’Ic xa cita song lén be mat nhan sang. n QUANG Lo ' Cac tia sang cfia Quang hinh hoc, tiep xlic tai moi diem Voi phuong truyén song. ° Pha cfia song anh sang la lien tuc khi khtic xa hoac phan xa trén luong chat tai do song tori truyén vao trong moi truong co chié’t sua’t Ion hon. - Pha cfta song bi_ gian doan mot luong 7: khi phan xa trén luong chat tai do song toi truyen vao trong moi truc‘)tng co chiet suat nho hon, khi phan xa trén be mat kim loai va khi di qua mot diém hoi ta. - Theo dinh nghia, quang lo (AB) gifta hai diem A va B cfia mot tia sang la: B (AB): fmzdi, A (1 day, 11 la chiét suat (phu thuoc vao diem khao sat) va 17 la vécto don vi tiéfp tuyén voi tia sang. Doi voi mot song don sac co mach so 0) va buoc song trong chan khong lo, hieu pha gifra hai diem A va B tai moi thc‘)ti diem la: (P. /t—>B = _2K1f(AB)+‘Psup = _%), ‘(AB)+(Psup ' ‘ So hang cpsup thuong la mot boi so cita 1: co duoc tit nhfmg gian doan vé pha khi song bi phan xa hoac di qua mot diém hoi tu. ° Neu dao lai chiéu truyén anh sang thi cac tia sang van khong thay doi. ° Mat song la mot mat duoc xac dinh boi tap hop nhfmg diem cach nguon diem mot quang lo. Né’u song phat ra tit nguon diém la don sac thi cac mat song dé trimg voi cac mat dang pha. I D! NH Li MALUS Cac mat song trc_Ic giao Voi cac tia sang. Quang Io gifra hai diem lién hop qua mot quang he tucmg diém khong phu thuoc vao tia sang noi hai diom ay. . r32°p .
  34. 34. 3-QHs<')ng AP DUNG TRUC TIEP BAI GIANG 1 Bié'n dieu bang cach xoay kinh phan cttc Mot chitm anh sang to nhién song song, khong phan cttc co ctrong do 10 truyén qua mot kinh phan Cl_IC co’ dinh Va sau do qua mot kinh phan cL_tc tht’r hai quay quanh quang truc Voi Van toc goc (D. Gia sit rang cac kinh phan ct_Ic la 11’ tuong, hay tinh cuong do sang 1’ di ra khoi kinh phan ct_IC thtr hai. 2 cuang do va dong photon Mot chitm laser duoc xem la mot song don sac co buoc song 632,8nm Va cong suat lmW. Tiet dien chfim tia la 3mm2 . Nguoi ta xem rang cuong do trong chitm la deu. l) Xac dinh ltru luong D cita dong photon. 2) Cong suat bfrc xa la 3}’ cita mot den phat anh sang dang huotng phat la bao nhieu do cuong do sang a cach den lm bang cuong do cita chttm laser nay. 3 Mau sac cfia mot mang nttoc xa phong Mot bong bong nuoc xa phong co do day e Va chiet suat n = 1,3 duoc chiou sang thang goc. Mang co he so phan xa nhc) nétt cuottg do cac song co duoc sau hai hay nhieu Ian phan xa la khong dang ké. 1) Hieu pha gifra hai song phan xa tit hai mat cita mang la bao nhieu? 2) Voi dieu kien nao thi anh sang co buoc song trong Chan khong A0 sé phan xa Voi cuong do cL_tc dai? 3) Tai sao bot xa phong duoc chie’u bang anh sang trang lai 1a’p lanh nhieu mau sac khi no rat mong? Hay cho biet co do day cita bot xa phong co nhieu mau sac. 4 Dttong con pho dang Gauss Hay xac dinh dang doan song Va co do lon [hoi gian ket hop cita mot song anh sang gain don sac co duong cong pho bien do duoc biéu dien bot cong thtic: 2 f(co) = Aexp[—[2(DA:0) Bietrang: +Texp| :—[2i)2:'exp(1'nx)dtt= A‘‘‘/ ;expi—[ ’‘ Ti 2 LEE] VAN DUNG voN KIEN THUC 5 cac dinh luat DESCARTES va ma hinh song Mot luong chat phang phan cach hai moi tntotng trong suot co chiét suat nl Va n2 . Mot song phang, don sac, co véctc) song its truyen trong moi truong chiét suat n, , bi phan xa v‘a truyen qua (hay khtic xa) trén luong chat. (0, Ex, 2,) ta mat phimg ltrottg chat, (0, 2,22) 151 mat phang tot. M la mot diém cita luong chat Va F = 0’M . Nguoi ta kt’ hieu It; , hr Va ht la cac véctd song cita cac song phang toi, song phang phan xa Va song phang truyen qua. 1) Hay biéu dien pha tai M qua pha tai 0, /2 va F doi Voi ca ba song. 2) Nguoc lai, cac dinh luat SNELL-DESCARTES bang cach sit dong tinh lien tuc (hoac tinh gian doan mot luong 1:) Vé pha cita mot song phang (xem H-Prépa. Song, ndm thi? hat). 6 Binh It MALUS if i 33
  35. 35. Mot tia sang phat ra tit diém A co’ dinh, di qua mot loat cac lufrng chat, theo lo trinh: (AI1I2.. .I, ,_1M) . K1’ hieu quang lo (AM) la L(M). 1) Hay biéu clén lfl) qua cac vécto don vi :7, , L72 va cac vécto A11 , I1l2 , v.v. .. 2) Xét tia Ian can (AI'1 ['2 . ..I', ,_, M’) duoe suy ra ti! tia ban gau banganhfmg cgch chuyén tinh tiéh vo cung be’ dll, dI2,. .., dIp_1, dM. a) Djnh luat SNELL-DESCARTES vé khuc xa suy ra he thfrc gifra 17,-, .7”, via d-I)‘. b) Tinh hiéu quang lo dL gifxa hai tia nay. 3) Tu‘ nhfmg ké't qua trén suy ra dinh 11‘ MALUS. 7 Céc thang giéng cubng do v6i dfiu thu dép (mg nhanh Dé mo ta anh sang gan don sac phat ra tit mot nguon co dién, nguoi ta thfra nhan mo hinh sau: ° chi can ap dung phép gan dung vo hudng la du. ' bién do dao dong va tan so’ blfrc xa la nhu nhau doi Voi Ia’! ca cac nguyén tit. - tai moi thoi diém, 6 M ed chong chat cac doan song phat ra ti: N nguyén tir, co cung thoi gian kéo dai ‘tc va co bién do phfrc: ; p(M, r) = §0exp[i(oot +q: p(r))] ; ' cac pha cpl, khong co M lién quan gi voi nhau. Chung git”! nguyén khong d6i trong khoéng {hoi gian z 1. 1a nhu nhau doi vat ta‘: ca cac doan song, sau do, chung bién thién mot 0 “ cach tuy y. Nguoi ta cfing thtra nhan mot két qua thfing ké nhu sau: né’u mot diém di dong M djch chuyén tir vj tri 0 trong mat phang theo mot duong gap khuc gom N doan co cung do dai a nhung dinh huong tiny y, thi gia tr; trung binh cua khoang cach OM sé la ax/ N . Mo hinh nay co tén goi la “hanh trinh ngau nhién” (xem H-Prépa. Nhiér d_o‘ng lugc, ndm rh1’rnhd’r, bdi nip 5, chzrcmg 4). 1) Hay viét biéu thfrc bién do phfrc t1’Ic thori §(M ,1) . 2) Hay vié't biéu thfrc cuong do sang Va so sanh cuong do quan sat duoe trong hai truong hop thori gian dap (mg cua dau thu la: °1énho'n sovéi ‘Cc; °nh6honsov6i TC. Ban co suy nghi gi vé tinh kha thi cua thi nghiém thfr hai ? 8 Dc} rE_>ng DOPPLER A. Hieu {mg DOPPLER MOI tin hiéu phat tit mot nguon chuyén dong M tai thoi diém I, duqc thu nhan 6 mot diém C6 djnh P tai thoi diém r’. Gia sfr r(! ) = PM via do do r(r) la khoéng cach PM lai thoi diém r, 27 la véctovan to'c cua_ M, a la goc gifra 17 Va 0M . 1) Hay biéu dién I’ qua I, van t6c c Va 1(! ). 2) Nguon phat ra cac tin hicftu tuan hoan co chu ki T va co tan 50' sao cho ta co thé b6 qua nhfmg bié'n thién cua uva on trong mot chu ki. a) Hay vie’! biéu thtic cua hiéu r(r + T) — r(r) b) Tit do, suy ra chu kiT' cua tin hieu thu nhan duoe tai P. f. c) Hay viét biéu thfrc cua ti s6 cua cac Ian 56 — , giéi han 6 bac nha't cua 3 . c 3) Cho mot vi du vé hiéu (mg DOPPLER trong mién song am. B. Song sinh sang phat ra ti: hoi don nguyén [fr Chung ta gia sir rang cac ké't qua truéc day déu ap dung duoe cho cac song dién ttr. Trong dam hoi don nguyén ti: co khdi luong mol M. nhiét do T, van to'c cua cac nguyén tfr duqr: phan bo' theo dgnh Iuat MAXWELL-BOLTZMAN: ne‘u N la téng so’ nguyén tL'r thi so nguyén tfr co thanh phau van to'c vx namtrong khoéng tir ux dé'n ux + dvx sé la: 2 dN= N M exp[—MU"'jdux 27': RT ZRT Cac nguyén tfr bi kich thfch do phong dien sé phat xa anh sang. Anh sang do ta co thé xem la hoan toan don sac, né'u nhu chung dfrng yén thi co buoc song trong Chan khong la A0. Dau thu duoc dat a du xa nguon dé chi ghi nhan nhfmg song‘ (phang) C6 phuong truyén song song véi (Ox). 1) Goi dl la cu'<‘mg do sang ma dau thu nhan duoc trong giai phd (A, A + d}. ), chfmg minh rang: 2 I1 = 5% = Kexp[—(}”A; ‘°]
  36. 36. Hay biéu dién hang s6 AX qua cua M, R, A0 , c va T. 2) Hay vé phac d6 thj ham 110») Va giai thfch so qua y ngh'1'a cua Al . 3) D0’i voi vach xanh cua thfiy ngan, R = 8,3 lJ. K-1 , M=2lO g, T= 1000 K. Hay tinh AT)‘. 4) Bang thuc nghiém, nguoi ta do duqc do dai két hop la vao khoéng lcm. Liefu hiéu (mg DOPPLER C6 phai la nguyén nhan chinh gay ra do tong ph6 nay hay khong? 9 Sl_I Iéch pha gifra hai séng ké't hqp Mot song phang duqc xem la don sac di qua mot thau kinh hoi tu méng C6 ban kinh R va tiéu cL_r anh f ’. Mot man anh duqc dat 6 cach thau kinh mot khoang la 3f’. Hay xac dinh phan man anh duqc roi sang béti hai song sang Va tinh do léch pha cua chung taj mot diém trong phan man do. Thau kinh duqc lam bang thuy tinh chiét suat /1 Va do day cua no 6 vi tri quang truc la e. L01 GIAI 1 Gm’ . 'z? (02) Id pllmmg rruyé'n Mug, (Ex, 2.. . El) lai ln_é m yd gain w’n' kinh p/ uin (yr (/11? rzluii rd (6,, E; ) Id 11;‘ 1'0 . w' gcin wil’ kinh Ilu'(/ lai. Cdr giti ! r_i trung bin]: d1((/ r (inh trong Ilzdi gian drip mtg ula chiu Ilm dm_Ir' gia’ Illiéi Id rd? lén . '0 win‘ Ilu‘n' gian kéi / uyp aid duh xzing nlumg ru? nlm" so wii (‘Im ki may kinh p/1u‘nr1A(('. 0 Trmir kin/1 phain ('{(('IIu?11Iui't. ' K(E(2)X) = K(E0_, ,)2 = 12L ' Gifru / mi kinh p/ vdu ({(r'. ' 75 = EOJEX = E0X[: cos(0!E', +sincoIE'y]. ' R11 kim’! kinh phdn ('l_f(' IIu'rI1ui. ' E: E0, coscotzfix viz K<E2) = I‘ = %l0<: os2cot. Czrfmg Jr} xtillg b; 'b1'é?1dLéIA W’/ i III(_l(‘, I X0’ 2(1) . 21) D = , (I() (16 D = 3.2.10” pII(iI(3/1/3'. 2) .1’ = arfmg dz} x dién ! i('/ a. T(u' kluuilzg air/1 lm, diéu Iirl: d: ((Ir' déu rlliéit Ming [(2 47: m2 . Hit’ J’ = lmW, la ('6 4“ 3 l0“' mg)! Hing szufi rd? I671. 3 Ta ddn/ I . 'ri'. 'riI1g Mi Id 367), air sting plrdn . '(_1 trén hai Itrélzg (lid? /(1 Ari’) vd 2. 1) Séng I b_i pluin xq trén lzrfing rl1u"'! kl: r3ng klu’ - m((‘rc (l_e‘rh phu Ihém mg}! Im_mg 1:). Song 2 n'uyé}1 Ifrlc/1(3ng khi Jung Inlflr, hi pluin xq rrén lm7ng (ltd? Iuair — klufiug khi vd . ‘au (16 truyéh n‘r Iurdr xung I. -/«mg khi. (p1(M)= (p0(A)+2XT: AM+n ; (p2(M)= (p0(A)+2E1T(2I: e+AM) __ 47tne _ n‘(zI(fi. -uyra: cp = <p, —(p2 — M TE 2) Ctrimg {Ir} cin/1 sting pha): X4 .517 (‘lf(' dai uéiz It/ u( / mi xézxg 1 vi! 2 dfing pha v{/2' n/ mu. 4ne _L+_l_ I -L- . 2p+l ' M} 11) Zne 4ne (p = p27: (wii puguyén), Imy A0 = 1., " W ' 3) Séng p/ uin Xt_l {('/ Wig r/ ui'! ('13a / lai Ming 1 W2 2). vé('6II1dz¢. v¢i('rrirélnéit nIu( dgi ddy (Ila mzing xzfp xi" Mlzg drj day Ind nrang zhzg w’/ i mi (hi ((3 rm}! (1_((‘ dqi du_yul1u"! trung vfmg Hui kiéh, Ifrr Ir}: 1 1 1 —: =T—— hay e= =0,3pm. 2,": )"lI'm )’d(') Mdu stir (‘Lia sélzg pluiu xgl phu I/ m(_3(‘ vdo dqi ddy (tia mang mair M2 phong. K / Iodug rdrlt giiru hai a_((' zkzi Iién riép I/ kia ma"): /: _é I/ uir: A I 4Bié: z (I6 pIu'(r rzia x«31zgn'u: xg giu'iplu1' do) Id: .1. = A. xpH2‘°A'a‘: ’0flexp[-no (, -§)]d. o . I)é'xzir' rljnh {(1) , ta quy vi Iir/ I phzbz dd (‘Ila lacing (‘l1(‘/1(1(3’I'/71?}! u :0) —(n0 : -.2 . g(z. t)= AA°"/ Eexp —[! —;J exp[ia)0(I—%)] . 2 4A0) L Tu dm/ (' rm)! (loan Ming gdu dmz . s'd}', Inga‘/1 36' (no , (11 bar) lu‘uh dgmg G/ wss. T/11): ‘ gian kéo dcii ("flu ciodn mtg My dmjr xéc cljn/1 n? (‘cic gid nji 0.) mtg wil" It/117713 bién alt) xriug bring bién dgi c1_(cdq1i (‘Ilia (‘/ )0 e vd MI1g. ' = .3. " A0) ‘ Tulqil/ utdmjrI1éII11?r'n‘uIIgb(}iI1(2(‘. ' 1: (Av z 1 . ‘C 51) q>; (M)= <p. -(0)+Ea. I" . ¢, (M) = q>, (0) +E, J ya (pi(M) = (p. (0) +/1.; . 2) (pi(M)= cp, (M) wi do do (ii —I: i). F=O I(liII1()1d[é; l1M(‘l1U Iufing (Mi. Suym, It’; — Z1 vuénggrir t'(iiI1r(7I1_g'r‘I1zfI, Iruy IT’; =0t? , +1». . ' in mim vonglmjlpllcz’/ zgIr}i. 0 I112, = I: *;. c7, rdi = —k—‘ July It, sin9, = I12 sine: . n2 n1 Mr)! air]: nrmzg n_r, Ia I/ m tllf(_I(‘ air d_inI1 lug}! pluin . ’(_l duh xélzg (xem H- Frépu, .S‘r3IIf1. mim IIu'r 2). = 4,21.-w. my Ia _
  37. 37. 61) L<M)= n,n, ./T/ ,.+ u2n2.fi/ ‘Z +. ..+ u, ,n, ,.I, ,_. M. 2) :1) Then din/ I Iugil xin. n, - — I1, +111,-+1 vmfiug grit wfi Ind! Iming (‘/ M17. T1? (16 my ra: dI1.(n, -F, — n, -,1u, ~+, ) = 0. b) dif-IQ = 0 , vri1'»1(u'ib(i} ki. Tm}; vgiy, .7, It1'é(Irrdrnz'[. dfi vuéug gér vr}'i I16 vdzladé wring gér wii M’ I , -I , - +1 . dL = nlu, .zII| + 112112 . (dI2 _—_dl, ):. .. + rlBu, ,.(dM —dI, ,_, ). Nllfmg Iu_1I£(‘r5 (Iqng ulur dll . (n| u| — M2112) zliu being 0 vii rIri'('r)I1 Igli dL = npu, ,.dM. J) Néit M 117 M' déll IIIIIII trén rfmg rm)! Ingil . '(5ug lhi dL=0. = O :10? vr'II'Ir1g: idj('II rImyé7xI1gnyén I13’ d-IL-4‘ IréuIm_iIxr3I1g. D0 1113, up ruling gér roi / mjl sting. D6 r'Iu'uIl Id mji dung djnll If MALUS trong mrzing I: r_Ipnz1_'. N m 71) . _v(M, /)= Z§p(M. I) = .'0exp(ia)I)zexp(—i(p, ,). p= l p= l 2) I= (§*) wfi N N aux‘ = 33 exp(i<4>, ,) exp(—i<v. ,)]~ p= l q: ! K/ mi rriéh ('(I(‘ . 'ri'I1guzg rrrmg ngru_i(' dan. Ia dm/ ('. ' ; ._; "‘ = .'%[N +2 Zcosupp -(pq)j. P q= r> ' Tnténg I: Cdr (p P git? ugnyén k/ Ming Iltuy dd? lrong klmdng Ihrii gian ‘tr . Mn (16 biéiz Ihién nu)! aid: my )3. Gid Ir] Irung hinh (tia air X0’ lugng cos((p p —(pq) tinh trong nu)! klmdng Ihrii gian rd? [611 . Y() wfi Tr déu b¢7ng(). Tughi Irlvgirzdlrgrrlrzgilzw‘/ ng dgikllérzg do? I = N; -5 . - Tmomg luyp 2: Tu Hi tI: e'gia' . x1’( Hing air‘ (p I, kluing [hay dd? trong klwdng Ihr‘/ i gian ddp mg, - rfia dzfu Ilm. Trong mrfmg [um néy. lgzi M1137 ! I1()'i dié}n. ' I = Q * . Z c0s((p , , —(pq) ((5 Ilréj dug/ r‘ 4*! ’ xem 1111:! Id hinh rlniéil trén lTI_l(‘ (Ox) (‘flu vécru king rrjng (1241 mg}! "luinlt Iriuh ngu'u ulziéu" (15 N — I hm’/ (' ('6 4142 ddi mg)! zlrm vi rhea air’ lutfnzg niy 3?. Néi: N dd I611 III! ‘ 2 cos(q), , —q; q) 2: x/ Ncoswp , wh’ qr’, /(2 mg)! tI= =r: gér mio dd, Jr)? rtfi nlubxg p kluir nhau. Czi dgi I611 (tia Z cosw , , dug)? n xrfir dinh mqil rdrlz Immg !1_t: Z COSWF : / XFC0S(| ) . P q) Ia) mg}! gér ruin J6, biéh thién theo Ihili gian véi kllodlzg ! I:(‘n' gian (I{7r mmg T‘. . C mi? (ting. Ia (11101-. ' Z cos(q), , —(p, ,) z x/ /Vzcusw P m N m I = N. fi(l + comp). «*0 r Nlur niy, mmg inking /1972 my (': (01:g dgi I bi thang gidng mgmh J/ ll(lIlIl gid Irgi N 3'3 . Tlu’ ngIIi_ém ndy klzéng ! I:é'rIu, ((' hién dug/ (' wfi ! é'bz2o quang clién (bring Ilutfmg nhung c(iJIué’IIu)nl1 (ring v(h'n1(3IdJu flux ddp mtg nhanh vd : m_iIugu17u Mug ('6 (Mi gian ké? Il(_Ip 411? 8A.1): '=: +i). c - -_ d7 . , dL7 , , , . - . 2) a) U= :ij—"e, +;-FL, '—. It —d’L vuong "ac vm a, new : —C= D.§, =ucosc1. Néia v vao: kI1éngdu"iIIn‘: r(I + T)— r(I) = vcosaT . b)T‘= (/+T+—j"('+T)j—(r+fl): T(l+”°°‘a). C C C c)§: (1_z/ ccgsa). 3) Am phzil ra I1? élri nghe (‘an Ium khi mi I[éI1 Igti grin wi ng/1e IIZIIH hm: khi mi (Ii ra xa. 15.1) I. ’/Ilg wfi vgin tr)? u, ,! u ('(5II1(§! I)u‘/ K‘ xrilzg I. = A0 [I — . Curing dgi dl !1'I_é véi (IN: _ M _MU% . dl—AN 2nm_exp[ 2R, rj| dLx| . Thay | dU, | = L)d7» . vd Ia €IIl'(/ (‘ I , _ cri dqng d12ngnIu(r'a'n pluii rlubzg 2R1‘ MC2 I 2) Ta Ilm dugrr mrjl d1(r‘mg mug dgng Gauxs dinh Itim Igi 9.0. AA it} do rging ruin r'l: I'éh cao (‘tia dmhtg mug My. 3) AT’)*=9,4.10-7. 4) Al= cr, -m"t(Af= l. T1? :16 my ru: M Af~5.1o-5. minh véi A7. = M 0 0.4 0,8 1,2 1.6 ; :,_, NIu(w_1y, Iu'¢‘u mtg D! )/’I’u; 'R kluing pI1a'i déng vai In) ('Iu'nIr. C air va r'Iu_1m nguyéu (1? him gidm Ilufi gian kéo ddi (‘tia cal" dodrz sring Imii Id nguyén nluin rhinlr gziy / zén Jr} rrjng vqrl: ph(3'Iu)y. 9 Mr]! difnz M trén rmin (Mr xdr djnll bring klmdng ('(I(‘Il r n‘(die7n dd zléh quang tr1_¢r. Séng bf Iérh I cltiéia sting phzfn mdn (3 bén trong a’m)ng trén rd bén kinh R. Sring kluing b_i Iérlr 2 rllléir sting phdu man (3 bén ngoai (lumzg min ((3 bén kinh R. Dr: dd, plufn mriu (IW_/ (‘ rd hai xzing rlxiéit sdzzg du‘1,r djn/ I hing R < r < 2R . S(5rxgIt}ir(5[1I1a (p0 nlurn/1uu! gu' H0, H1 wk H2 . 2_7‘ X . TIl€()(I_l‘I1IlIINI/ ILUSI (HlM) = (HlF')+ (I"M) = (H0F')+ (F'M) . So wfi lgi rrinh dr/ r theo quang Irqw Hi (‘ting (Ir) ddi hinh Iugr 1} trong kluiug kIu'. rI1é11 kinhdmxIhémvziamélquanglép/11¢. ‘ Me — e = (I! — l)e . Tfrzlé xuyru: <p. (M) =4.p(, —k[f'+ (u— l)e + F'M]+7t «psup =1t). '()rl{rIér'I1pI: u.' (p = k[f'+(n—1)e+ F‘M— 3f']+1t . 'ivz_2y. q)2(M)= q)0 ~k3f‘ wfi 1: = Khi dfmg lai (fair . '0'I: qIzg Ixjc hai (flu , Ia cé II: é'vie‘i. ‘ F ' M 2 2 f '+ . Cmfir'1)ng Ia dug/ r: (p = kl: (u — l)e + +7: . I361; .53 '05“;
  38. 38. ]/ c§ am Ca’: hién tugmg giao thoa la‘ hé qua’ cu'a bdn chzft séng cfia anh sang. Mét sé'hz'_én twang giao thoa co’ thé'quan sci! duqc trong dai s0"ng hang ngay, vi dy nhu‘: ° Cac mau scfc la}; lanh, sinh déng trén nhfing mang bong béng xd phang, nhfing vé? dcfu loang trén mat dd? hay mat kinh. ° Cac mau scic nhin thay trén mail dfa laser hay dfa CD-Rom. ° SL1 pha'n chiéia nhiéu mau sac trén kinh chzfn gio’ cfia été. .. Trong chztong nay, chung ta Se” t1'é'p can lcfn dciu tién véi hién twang giao thoa trong khuo‘n khé’ mé hinh séng dan gian hoa czia anh sang vd de”y déh nhfing dat: die"m cda cac nguén sang cfing nhu cfia cdc dcfu thu quang hoc. Muc TIEU I Djnh nghia hien tuqng giao thoa. I Céc diéu kién dé cé giao thoa trong quang hoc. I Céc khzii niém vé tinh ké'I hop thb‘i gian V51 khong gian cho phép quan sét duqc hien tuqng giao thoa. DIEU cA‘N BIE'T 'rRUc’1c I Céc khéi niem vé doén séng, Sl, I phan cue v‘a énh séng tu nhién. I Quang 10. I Cufmg d0 séng. 5 M6 hinh énh séng tunhien. E Thb‘i gian ké't hqp TC.
  39. 39. Giao thoa hai, s6ng phat ra ttr hai ngu6n diém c6 cung tan st‘); 1.1. Dinh nghia Khi cufmg déqtfing ccfmg gay ra do ch6ng chat cita hai hay nhiéu séng khong bang téng cac cufmg d<f) timg séng d6, chfing ta néi rang da cé hi_én tuqrng giao thoa hay cac séng dé da giao thoa véi nhau. 1.2. B6 léch pha Ta xét hai ngu6n sang diém nam tai hai vi tn’ S1 va S2 (h.1a). Cac nguén nay phat ra nhfmg doan séng duqc gia thiét la c6 cung tan so’ v. Né'u thira nhan mo hinh vb hudng (h.1a) thi cac tin hieu phat ra c6 thé duqc vié't nhu sau: ° d6i véi S1 : s1(S1,t) = A1 COS(2‘ltVt +(p1) vdi A1 > 0 trong khoéng thiri gnan r1. ' d6ivéri S2: s2 (S2,! ) 2 A2 cos(21rvt + (p2) véri A2 > 0 trong khoéng thbi gian ‘:2 . _ D6i véri méi doén séng méi, (p1 va (p2 lai nhan mot gia tr; my )7, méi. Vi co ché phat xa trong hai ngudn la nhu nhau nen ta c6 thé xem rang thbi gian ké't hqp 1: C cc’) cung mot tr; s6 d6i vdi hai nguén d6. Cac tin hiéu phat ra ti: S1 va S2 déh mf_)t diém M sé c6 biéu thfrc: SM (16 )j+‘Plsup +(P1:| ; (S2M) C °t1’nhiéu phat til‘ S1 : s1(M, t) = s1m COS[27tV (I — ° tin hieu phat tir S2 : s2(M, t) = s2,, , COS[27tV (I — ]+ <p2§up + cp1:| . (S1M) Va (S2M) la cac quang It} cbn (015111, va (p2Sup la cac do lech pha phu c6 thé c6 do phan xa hoac do di qua mot diém hoi tu. D0 léch pha tai M cua séng phat ti: S2 so véri séng phat t1‘: S1 la: (11 M1,) = [M [(S2M) _ (SIM) C C ° <p(M, t) biéh thien theo thai gian vi cac so’ hang <p1 Va (p2 bién d5i tuy )7 ddi véri m6i doan séng méi. A 0 Cac so’ hang khac déu khong d6i via my thutfac vao dufmg di cua tin hieu sang ti: ngu6n déh diém M. 1.3. Hiéu duémg di Dé biéu dién phan khong phu thuoc vao thc‘Ji gian cua dc) lech pha, ta dua vao cac dinh nghia sau: 0 hieu dufmg di hinh h(_)c Ia 5,, ,,(M) = (S2M) - (S1M); j+(P1sup +(p1“P2sup"‘P2:I’ - hieu duémg di b6 xung 1a 51,1 = §'7(<p, s.,1, — cpmp) ; ° hieu quang 10 la 5(M) = 6,, ,,(M) + SP1, ; Khi dc’), d0 léch pha duqc biéu dién qua 5 (M) nhu‘ sau: 2 2 <P(M»') = 1[TV5hIz(M) +<P1sup ‘<P2sup +‘P1—<P2 = LC‘/ ’5(M) “P1 ‘<P2» 2 hay ~ <p(M. r)= —1§6(M)+<m -«>2 ne’u sir dung bucic séng trong chan khong lo. $1 $2 Hinh la. Ca'c tin Iu'_éu pluit ra 112' S1 Va 5 2 Iruyéh 161' M. Hinh lb. D67 vo'i nufi ngudn. cac doa‘n séng ke"u'e‘p nhau c6 pluz my )3.
  40. 40. 1.4. Cu'<‘1ng dc} Hai séng chéng chat lén nhau (dimg quén rang thtrc ra 1a cac dién trufmg gay ra béi hai nguén chéng chat lén nhau) nén tin hieu sang tai M sé la: s(M, t) = s1(M, I) + s2(M, t). Cac dfiu thu déu nhay v6‘i cubng dc‘) sang I ti lé véi gia txj trung binh cua s tinh trong thai gian dap (mg ‘I: cfia dau thu: 1 = K((s, + 52)? ‘ = Ins? ) + {mg} + 2K(s1s2). 1 . , ' K(s12) = 3Ks12,, , = [1 la cucmg d<f) cua séng phat ra tu‘ nguon 1. 2 ' K (5%) = %Ks%, ,, = 12 la cufmg dtf) cua séng phat ra t1‘I ngu6n 2. ' 2KS1mS2m = 4,II1I2 , dOd6I 2KS1s2 = 4 I112 cos[27rv [1 — (Slim) + ¢P1sup + <91] C ><c0s[21rv [I — (S2M)) + <P2sup + <02] C (S1M) _ (S2M) C C = 2 11/2 cos[27rv [2t— )+<p1suP +(p1 +(p2sup +<p2 <s1M> _ (S2M) C C +2 I1l2 cos[27rv [2t— )+(p1sup +(p1 +(p2Sup +(p2]. Trong Quang hoc, thai gian dap (mg cua dau thu luon luon lén hon nhiéu so vdi chu ki séng. S6 hang dau tién cita tdng trén la mot ham hinh sin, tan so’ 2v c6 gia trj trung binh cua nc’) luon luén being 0. Va khi dua vao hiéu quang lo 5(M), ta duqc: 2 1 =11+ 12 + 2./11/2 <cos[—315(M)+(p1 41,2» C hay biéu dién qua do léch pha (p(M, t) : 1 = 11+12 + 2(fl1§(coscp(M, :)). Gia tr; trung binh nay duqc tinh tai mét diém M C6 dinh, trong thbi gian dap (mg TR cua dau thu. Chti y’: Néit dciu thu cé thai gian dap {mg ‘E R rd? nho' hon ‘E C (Iho"i gian kéi / lap cfia nguén) thi y (M , t) se"ha1¢nh1rkl1ang doli trong khodng 1.‘ R . Sau khi tinh roan, ta s€dwc_J'c. ' » Zn I = 11+ 12 + 2 1,12 cos[T5(M)+¢1—m2j. 0 Ngwai ta da‘ lam thi nglziém véi hai laser ca thai gian kéi hop rat Ian (cc? 10-6 s ) phat cfmg mét ta‘): sé'va cac dd}: thu dap1'mgra'tnhanh. Kéi qua cho thay dting Ia C6 hién twang giao thoa (I at /1 + 12) nhwng né chi 632 dinh trong mét khocing thai gian rz/10' hon lus. 1.5. S6ng khéng ké't hqp Thuc ra, dau thu quang hoe luén C6 thbi gian dap ting TR rat ldn so v6'i Tc. Tai m(‘_)t diém M cho truérc, dan thu ghi nhan gia trj trung binh cua cos[2fi5 (M) + (p1 — <p2j trong mét 56 ra't16‘n cac doan séng ké'tié'p nhau. r I

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