Dispersiya svitla zalezhnist pokaznika zalomlennya abo dielektrichnoyi proniknosti seredovisha vid chastoti svitla Vnaslidok zmini pokaznika zalomlennya zminyuyetsya takozh dovzhina hvili Zavdyaki dispersiyi bile svitlo mozhna rozklasti v spektr za dopomogoyu prizmi k w 2 p l w n w w c displaystyle k omega frac 2 pi lambda omega n omega frac omega c de k w displaystyle k omega hvilove chislo l w displaystyle lambda omega dovzhina hvili n w displaystyle n omega pokaznik zalomlennya w displaystyle omega kutova chastota c shvidkist svitla Vidnoshennya v p h w k c n displaystyle v ph frac omega k frac c n nazivayut fazovoyu shvidkistyu Zmist 1 Normalna j anomalna dispersiyi 2 Fizichna priroda yavisha 3 Vlastivosti ta proyavi 4 Uzagalnene formulyuvannya visokih poryadkiv dispersiyi optika Laha Lagerra 5 Div takozh 6 Literatura 7 PosilannyaNormalna j anomalna dispersiyi RedaguvatiZdebilshogo pokaznik zalomlennya zrostaye zi zbilshennyam chastoti Take zrostannya nazivayut normalnoyu dispersiyeyu Pri normalnij dispersiyi chervone svitlo zalomlyuyetsya slabshe nizh blakitne Anomalna dispersiya zmenshennya pokaznika zalomlennya zi zbilshennyam chastoti sposterigayetsya na chastotah sho blizki do smug intensivnogo poglinannya Fizichna priroda yavisha RedaguvatiSeredovishe reaguye na zminu zovnishnogo elektrichnogo polya zminoyu navedenoyi v nomu polyarizaciyi Polyarizaciya vinikaye zavdyaki zmishennyu zv yazanih zaryadiv napriklad zmishennyu elektroniv vidnosno yader atomiv Procesi zmishennya ne vidbuvayutsya mittyevo a vimagayut pevnogo chasu Krim togo zmishennya mozhut buti riznimi za velichinoyu j stavati osoblivo znachnimi todi koli chastota zmini zovnishnogo polya potraplyaye v rezonans iz kolivannyami harakternimi dlya sistemi Koli elektrichne pole svitlovoyi hvili yaka rozpovsyudzhuyetsya v seredovishi zminyuyetsya povilno seredovishe vstigaye povnistyu vidreaguvati na zminu polya Yaksho zh elektrichne pole zminyuyetsya duzhe shvidko elektroni ne vstigayut vidslidkovuvati jogo zmini Cim poyasnyuyutsya rizni znachennya pokaznika zalomlennya pri riznih chastotah elektromagnitnih hvil Vlastivosti ta proyavi RedaguvatiOdnim z naochnih proyaviv dispersiyi ye rozkladannya bilogo svitla pri prohodzhenni jogo kriz prizmu doslid Nyutona Riznicya fazovih shvidkostej dlya promeniv iz riznoyu dovzhinoyu hvili pri poshirenni v prozoromu optichnomu seredovishi zumovlyuye dispersiyu u vakuumi shvidkist svitla zavzhdi odnakova nezalezhno vid dovzhini hvili viprominyuvannya Dispersiya svitla dozvolila vpershe vpevneno dovesti toj fakt sho bile svitlo skladayetsya z svitla inshih dovzhin hvil Yavishe dispersiyi mozhna sposterigati pri zalomlenni sonyachnogo svitla u kraplyah vodi yaki utvoryuyutsya v atmosferi Vono suprovodzhuyetsya rozkladom na kolorovi promeni Cim poyasnyuyetsya utvorennya veselki Dispersiyeyu svitla poyasnyuyetsya i hromatichna aberaciya nedolik linzi pov yazanij z tim sho zobrazhennya predmeta maye kolorovi krayi Ce poyasnyuyetsya tim sho fokusna vidstan linzi dlya promeniv riznih koloriv ye riznoyu Uzagalnene formulyuvannya visokih poryadkiv dispersiyi optika Laha Lagerra RedaguvatiOpis hromatichnoyi dispersiyi za dopomogoyu perturbativnogo pidhodu cherez koeficiyenti Tejlora pidhodit dlya optimizaciyi zadach de neobhidno zbalansuvati dispersiyu vid dekilkoh riznih sistem Napriklad u lazernih pidsilyuvachah impulsi spochatku roztyaguyutsya v chasi shob uniknuti optichnogo poshkodzhennya kristaliv Potim u procesi posilennya energiyi impulsi nakopichuyut neminuchu linijnu ta nelinijnu fazu prohodyachi cherez rizni materiali Nareshti impulsi stiskayutsya u riznih tipah kompresoriv Shob skinuti bud yaki zalishkovi vishi poryadki v nakopichenoyi fazi okremi poryadki dispersiyi zazvichaj vimiryuyutsya i balansuyutsya Dlya odnoridnih sistem takij perturbativnij opis chasto ne potribnij napriklad poshirennya impulsu v hvilevodah chi optichnih voloknah Dispersijni poryadki zvodyatsya do analitichnih rivnyan yaki analogichni uzagalnenim peretvorennyam Laha Lagera 1 2 Poryadki dispersiyi viznachayutsya rozkladannyam fazi Tejlora abo hvilovogo vektora f w f w 0 f w w 0 w w 0 1 2 2 f w 2 w 0 w w 0 2 1 p p f w p w 0 w w 0 p displaystyle begin array c varphi mathrm omega mathrm varphi left right omega 0 left frac partial varphi partial omega right omega 0 left omega omega 0 right frac 1 2 left frac partial 2 varphi partial omega 2 right omega 0 left omega omega 0 right 2 ldots frac 1 p left frac partial p varphi partial omega p right omega 0 left omega omega 0 right p ldots end array nbsp k w k w 0 k w w 0 w w 0 1 2 2 k w 2 w 0 w w 0 2 1 p p k w p w 0 w w 0 p displaystyle begin array c k mathrm omega mathrm k left right omega 0 left frac partial k partial omega right omega 0 left omega omega 0 right frac 1 2 left frac partial 2 k partial omega 2 right omega 0 left omega omega 0 right 2 ldots frac 1 p left frac partial p k partial omega p right omega 0 left omega omega 0 right p ldots end array nbsp Virobnichi dispersiyi dlya hvilovogo vektora k w w c n w displaystyle k mathrm omega mathrm frac omega c n mathrm omega mathrm nbsp i fazi f w w c O P w displaystyle varphi mathrm omega mathrm frac omega c it OP mathrm omega mathrm nbsp mozhe buti virazhayetsya yak p w p k w 1 c p p 1 w p 1 n w w p w p n w displaystyle begin array c frac partial p partial omega p k mathrm omega mathrm frac 1 c left p frac partial p 1 partial omega p 1 n mathrm omega mathrm omega frac partial p partial omega p n mathrm omega mathrm right end array nbsp p w p f w 1 c p p 1 w p 1 O P w w p w p O P w 1 displaystyle begin array c frac partial p partial omega p varphi mathrm omega mathrm frac 1 c left p frac partial p 1 partial omega p 1 it OP mathrm omega mathrm omega frac partial p partial omega p it OP mathrm omega mathrm right end array 1 nbsp Pohidni bud yakoyi funkciyi sho diferenciyuyetsya f w l displaystyle f mathrm omega mathrm lambda mathrm nbsp u prostori dovzhin hvil abo chastot viznachayutsya cherez peretvorennya Laha yak p w p f w 1 p l 2 p c p m 0 p A p m l m m l m f l displaystyle begin array l frac partial p partial omega p f mathrm omega mathrm left mathrm mathrm 1 right p left frac lambda mathrm 2 pi c right p sum limits m 0 p mathcal A mathrm p m mathrm lambda m frac partial m partial lambda m f mathrm lambda mathrm end array nbsp displaystyle nbsp p l p f l 1 p w 2 p c p m 0 p A p m w m m w m f w 2 displaystyle begin array c frac partial p partial lambda p f mathrm lambda mathrm left mathrm mathrm 1 right p left frac omega mathrm 2 pi c right p sum limits m 0 p mathcal A mathrm p m mathrm omega m frac partial m partial omega m f mathrm omega mathrm end array 2 nbsp Matrichni elementi peretvorennya ye koeficiyentami Laha A p m p p m m p 1 m 1 displaystyle mathcal A mathrm p m mathrm frac p mathrm left p mathrm m right mathrm m mathrm frac mathrm p mathrm mathrm 1 mathrm m mathrm mathrm 1 nbsp Zapisane dlya dispersiyi grupovoyi shvidkosti GDD navedene vishe viraz stverdzhuye sho postijna dovzhina hvili GGD matime nulovi vishi poryadki Vishimi poryadkami otrimanimi z GDD ye p w p G D D w 1 p l 2 p c p m 0 p A p m l m m l m G D D l displaystyle begin array c frac partial p partial omega p GDD mathrm omega mathrm left mathrm mathrm 1 right p left frac lambda mathrm 2 pi c right p sum limits m 0 p mathcal A mathrm p m mathrm lambda m frac partial m partial lambda m GDD mathrm lambda mathrm end array nbsp Pidstanovka rivnyannya 2 virazhenogo dlya pokaznika zalomlennya n displaystyle n nbsp abo optichnogo shlyahu O P displaystyle OP nbsp rivnyannya 1 prizvodit do analitichnih viraziv dlya poryadkiv dispersiyi Zagalom dispersiya p t h displaystyle p th nbsp poryadku POD ye peretvorennyam tipu Lagerra negativnogo drugogo poryadku P O D d p f w d w p 1 p l 2 p c p 1 m 0 p B p m l m d m O P l d l m displaystyle POD frac d p varphi omega d omega p 1 p frac lambda 2 pi c p 1 sum m 0 p mathcal B p m lambda m frac d m OP lambda d lambda m nbsp displaystyle nbsp P O D d p k w d w p 1 p l 2 p c p 1 m 0 p B p m l m d m n l d l m displaystyle POD frac d p k omega d omega p 1 p frac lambda 2 pi c p 1 sum m 0 p mathcal B p m lambda m frac d m n lambda d lambda m nbsp Matrichni elementi peretvoren ye bezznakovimi koeficiyentami Lagerra poryadku minus 2 i mayut viglyad B p m p p m m p 2 m 2 displaystyle mathcal B mathrm p m mathrm frac p mathrm left p mathrm m right mathrm m mathrm frac mathrm p mathrm mathrm 2 mathrm m mathrm mathrm 2 nbsp Pershi desyat poryadkiv dispersiyi zapisani yavno dlya hvilovogo vektora G D w k w 1 c n w w n w w 1 c n l l n l l v g r 1 displaystyle begin array l boldsymbol it GD frac partial partial omega k mathrm omega mathrm frac mathrm 1 c left n mathrm omega mathrm omega frac partial n mathrm omega mathrm partial omega right frac mathrm 1 c left n mathrm lambda mathrm lambda frac partial n mathrm lambda mathrm partial lambda right v gr mathrm mathrm 1 end array nbsp Grupovij pokaznik zalomlennya n g displaystyle n g nbsp viznachayetsya yak n g c v g r 1 displaystyle n g cv gr mathrm mathrm 1 nbsp G D D 2 w 2 k w 1 c 2 n w w w 2 n w w 2 1 c l 2 p c l 2 2 n l l 2 displaystyle begin array l boldsymbol it GDD frac partial 2 partial omega mathrm 2 k mathrm omega mathrm frac mathrm 1 c left mathrm 2 frac partial n mathrm omega mathrm partial omega omega frac partial 2 n mathrm omega mathrm partial omega mathrm 2 right frac mathrm 1 c left frac lambda mathrm 2 pi c right left lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 right end array nbsp T O D 3 w 3 k w 1 c 3 2 n w w 2 w 3 n w w 3 1 c l 2 p c 2 3 l 2 2 n l l 2 l 3 3 n l l 3 displaystyle begin array l boldsymbol it TOD frac partial 3 partial omega mathrm 3 k mathrm omega mathrm frac mathrm 1 c left mathrm 3 frac partial 2 n mathrm omega mathrm partial omega mathrm 2 omega frac partial 3 n mathrm omega mathrm partial omega mathrm 3 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 2 Bigl mathrm 3 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 Bigr end array nbsp F O D 4 w 4 k w 1 c 4 3 n w w 3 w 4 n w w 4 1 c l 2 p c 3 12 l 2 2 n l l 2 8 l 3 3 n l l 3 l 4 4 n l l 4 displaystyle begin array l boldsymbol it FOD frac partial 4 partial omega mathrm 4 k mathrm omega mathrm frac mathrm 1 c left mathrm 4 frac partial 3 n mathrm omega mathrm partial omega mathrm 3 omega frac partial 4 n mathrm omega mathrm partial omega mathrm 4 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 3 Bigl mathrm 12 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 8 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 Bigr end array nbsp F i O D 5 w 5 k w 1 c 5 4 n w w 4 w 5 n w w 5 1 c l 2 p c 4 60 l 2 2 n l l 2 60 l 3 3 n l l 3 15 l 4 4 n l l 4 l 5 5 n l l 5 displaystyle begin array l boldsymbol it FiOD frac partial 5 partial omega mathrm 5 k mathrm omega mathrm frac mathrm 1 c left mathrm 5 frac partial 4 n mathrm omega mathrm partial omega mathrm 4 omega frac partial 5 n mathrm omega mathrm partial omega mathrm 5 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 4 Bigl mathrm 60 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 60 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 15 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 Bigr end array nbsp S i O D 6 w 6 k w 1 c 6 5 n w w 5 w 6 n w w 6 1 c l 2 p c 5 360 l 2 2 n l l 2 480 l 3 3 n l l 3 180 l 4 4 n l l 4 24 l 5 5 n l l 5 l 6 6 n l l 6 displaystyle begin array l boldsymbol it SiOD frac partial 6 partial omega mathrm 6 k mathrm omega mathrm frac mathrm 1 c left mathrm 6 frac partial 5 n mathrm omega mathrm partial omega mathrm 5 omega frac partial 6 n mathrm omega mathrm partial omega mathrm 6 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 5 Bigl mathrm 360 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 480 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 180 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 mathrm 24 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 lambda mathrm 6 frac partial 6 n mathrm lambda mathrm partial lambda mathrm 6 Bigr end array nbsp S e O D 7 w 7 k w 1 c 7 6 n w w 6 w 7 n w w 7 1 c l 2 p c 6 2520 l 2 2 n l l 2 4200 l 3 3 n l l 3 2100 l 4 4 n l l 4 420 l 5 5 n l l 5 35 l 6 6 n l l 6 l 7 7 n l l 7 displaystyle begin array l boldsymbol it SeOD frac partial 7 partial omega mathrm 7 k mathrm omega mathrm frac mathrm 1 c left mathrm 7 frac partial 6 n mathrm omega mathrm partial omega mathrm 6 omega frac partial 7 n mathrm omega mathrm partial omega mathrm 7 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 6 Bigl mathrm 2520 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 4200 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 2100 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 mathrm 420 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 mathrm 35 lambda mathrm 6 frac partial 6 n mathrm lambda mathrm partial lambda mathrm 6 lambda mathrm 7 frac partial 7 n mathrm lambda mathrm partial lambda mathrm 7 Bigr end array nbsp E O D 8 w 8 k w 1 c 8 7 n w w 7 w 8 n w w 8 1 c l 2 p c 7 20160 l 2 2 n l l 2 40320 l 3 3 n l l 3 25200 l 4 4 n l l 4 6720 l 5 5 n l l 5 840 l 6 6 n l l 6 48 l 7 7 n l l 7 l 8 8 n l l 8 displaystyle begin array l boldsymbol it EOD frac partial 8 partial omega mathrm 8 k mathrm omega mathrm frac mathrm 1 c left mathrm 8 frac partial 7 n mathrm omega mathrm partial omega mathrm 7 omega frac partial 8 n mathrm omega mathrm partial omega mathrm 8 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 7 Bigl mathrm 20160 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 40320 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 25200 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 mathrm 6720 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 mathrm 840 lambda mathrm 6 frac partial 6 n mathrm lambda mathrm partial lambda mathrm 6 mathrm 48 lambda mathrm 7 frac partial 7 n mathrm lambda mathrm partial lambda mathrm 7 lambda mathrm 8 frac partial 8 n mathrm lambda mathrm partial lambda mathrm 8 Bigr end array nbsp N O D 9 w 9 k w 1 c 9 8 n w w 8 w 9 n w w 9 1 c l 2 p c 8 181440 l 2 2 n l l 2 423360 l 3 3 n l l 3 317520 l 4 4 n l l 4 105840 l 5 5 n l l 5 17640 l 6 6 n l l 6 1512 l 7 7 n l l 7 63 l 8 8 n l l 8 l 9 9 n l l 9 displaystyle begin array l boldsymbol it NOD frac partial 9 partial omega mathrm 9 k mathrm omega mathrm frac mathrm 1 c left mathrm 9 frac partial 8 n mathrm omega mathrm partial omega mathrm 8 omega frac partial 9 n mathrm omega mathrm partial omega mathrm 9 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 8 Bigl mathrm 181440 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 423360 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 317520 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 mathrm 105840 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 mathrm 17640 lambda mathrm 6 frac partial 6 n mathrm lambda mathrm partial lambda mathrm 6 mathrm 1512 lambda mathrm 7 frac partial 7 n mathrm lambda mathrm partial lambda mathrm 7 mathrm 63 lambda mathrm 8 frac partial 8 n mathrm lambda mathrm partial lambda mathrm 8 lambda mathrm 9 frac partial 9 n mathrm lambda mathrm partial lambda mathrm 9 Bigr end array nbsp T e O D 10 w 10 k w 1 c 10 9 n w w 9 w 10 n w w 10 1 c l 2 p c 9 1814400 l 2 2 n l l 2 4838400 l 3 3 n l l 3 4233600 l 4 4 n l l 4 1693440 l 5 5 n l l 5 352800 l 6 6 n l l 6 40320 l 7 7 n l l 7 2520 l 8 8 n l l 8 80 l 9 9 n l l 9 l 10 10 n l l 10 displaystyle begin array l boldsymbol it TeOD frac partial 10 partial omega mathrm 10 k mathrm omega mathrm frac mathrm 1 c left mathrm 10 frac partial 9 n mathrm omega mathrm partial omega mathrm 9 omega frac partial 10 n mathrm omega mathrm partial omega mathrm 10 right frac mathrm 1 c left frac lambda mathrm 2 pi c right mathrm 9 Bigl mathrm 1814400 lambda mathrm 2 frac partial 2 n mathrm lambda mathrm partial lambda mathrm 2 mathrm 4838400 lambda mathrm 3 frac partial 3 n mathrm lambda mathrm partial lambda mathrm 3 mathrm 4233600 lambda mathrm 4 frac partial 4 n mathrm lambda mathrm partial lambda mathrm 4 1693440 lambda mathrm 5 frac partial 5 n mathrm lambda mathrm partial lambda mathrm 5 mathrm 352800 lambda mathrm 6 frac partial 6 n mathrm lambda mathrm partial lambda mathrm 6 mathrm 40320 lambda mathrm 7 frac partial 7 n mathrm lambda mathrm partial lambda mathrm 7 mathrm 2520 lambda mathrm 8 frac partial 8 n mathrm lambda mathrm partial lambda mathrm 8 mathrm 80 lambda mathrm 9 frac partial 9 n mathrm lambda mathrm partial lambda mathrm 9 lambda mathrm 10 frac partial 10 n mathrm lambda mathrm partial lambda mathrm 10 Bigr end array nbsp U yavnomu viglyadi zapisani dlya fazi f displaystyle varphi nbsp pershi desyat poryadkiv dispersiyi mozhut buti virazheni yak funkciya dovzhini hvili za dopomogoyu peretvorennya Laha rivnyannya 2 u viglyadi p w p f w 1 p l 2 p c p m 0 p A p m l m m l m f l displaystyle begin array l frac partial p partial omega p f mathrm omega mathrm left mathrm mathrm 1 right p left frac lambda mathrm 2 pi c right p sum limits m 0 p mathcal A mathrm p m mathrm lambda m frac partial m partial lambda m f mathrm lambda mathrm end array nbsp displaystyle nbsp p l p f l 1 p w 2 p c p m 0 p A p m w m m w m f w displaystyle begin array c frac partial p partial lambda p f mathrm lambda mathrm left mathrm mathrm 1 right p left frac omega mathrm 2 pi c right p sum limits m 0 p mathcal A mathrm p m mathrm omega m frac partial m partial omega m f mathrm omega mathrm end array nbsp f w w 2 p c w 2 f w l l 2 2 p c f l l displaystyle begin array l frac partial varphi mathrm omega mathrm partial omega left frac mathrm 2 pi c omega mathrm 2 right frac partial varphi mathrm omega mathrm partial lambda left frac lambda mathrm 2 mathrm 2 pi c right frac partial varphi mathrm lambda mathrm partial lambda end array nbsp 2 f w w 2 w f w w l 2 p c 2 2 l f l l l 2 2 f l l 2 displaystyle begin array l frac partial 2 varphi mathrm omega mathrm partial omega mathrm 2 frac partial partial omega left frac partial varphi mathrm omega mathrm partial omega right left frac lambda mathrm 2 pi c right mathrm 2 left mathrm 2 lambda frac partial varphi mathrm lambda mathrm partial lambda lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 right end array nbsp 3 f w w 3 l 2 p c 3 6 l f l l 6 l 2 2 f l l 2 l 3 3 f l l 3 displaystyle begin array l frac partial 3 varphi mathrm omega mathrm partial omega mathrm 3 left frac lambda mathrm 2 pi c right mathrm 3 left mathrm 6 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 6 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 right end array nbsp 4 f w w 4 l 2 p c 4 24 l f l l 36 l 2 2 f l l 2 12 l 3 3 f l l 3 l 4 4 f l l 4 displaystyle begin array l frac partial 4 varphi mathrm omega mathrm partial omega mathrm 4 left frac lambda mathrm 2 pi c right mathrm 4 Bigl mathrm 24 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 36 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 12 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 Bigr end array nbsp 5 f w w 5 l 2 p c 5 120 l f l l 240 l 2 2 f l l 2 120 l 3 3 f l l 3 20 l 4 4 f l l 4 l 5 5 f l l 5 displaystyle begin array l frac partial mathrm 5 varphi mathrm omega mathrm partial omega mathrm 5 left frac lambda mathrm 2 pi c right mathrm 5 Bigl mathrm 120 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 240 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 120 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 20 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 Bigr end array nbsp 6 f w w 6 l 2 p c 6 720 l f l l 1800 l 2 2 f l l 2 1200 l 3 3 f l l 3 300 l 4 4 f l l 4 30 l 5 5 f l l 5 l 6 6 f l l 6 displaystyle begin array l frac partial 6 varphi mathrm omega mathrm partial omega mathrm 6 left frac lambda mathrm 2 pi c right mathrm 6 Bigl mathrm 720 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 1800 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 1200 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 300 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 mathrm 30 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 mathrm lambda mathrm 6 frac partial 6 varphi mathrm lambda mathrm partial lambda mathrm 6 Bigr end array nbsp 7 f w w 7 l 2 p c 7 5040 l f l l 15120 l 2 2 f l l 2 12600 l 3 3 f l l 3 4200 l 4 4 f l l 4 630 l 5 5 f l l 5 42 l 6 6 f l l 6 l 7 7 f l l 7 displaystyle begin array l frac partial 7 varphi mathrm omega mathrm partial omega mathrm 7 left frac lambda mathrm 2 pi c right mathrm 7 Bigl mathrm 5040 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 15120 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 12600 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 4200 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 mathrm 630 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 mathrm 42 lambda mathrm 6 frac partial 6 varphi mathrm lambda mathrm partial lambda mathrm 6 lambda mathrm 7 frac partial 7 varphi mathrm lambda mathrm partial lambda mathrm 7 Bigr end array nbsp 8 f w w 8 l 2 p c 8 40320 l f l l 141120 l 2 2 f l l 2 141120 l 3 3 f l l 3 58800 l 4 4 f l l 4 11760 l 5 5 f l l 5 1176 l 6 6 f l l 6 56 l 7 7 f l l 7 l 8 8 f l l 8 displaystyle begin array l frac partial 8 varphi mathrm omega mathrm partial omega mathrm 8 left frac lambda mathrm 2 pi c right mathrm 8 Bigl mathrm 40320 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 141120 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 141120 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 58800 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 mathrm 11760 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 mathrm 1176 lambda mathrm 6 frac partial 6 varphi mathrm lambda mathrm partial lambda mathrm 6 mathrm 56 lambda mathrm 7 frac partial 7 varphi mathrm lambda mathrm partial lambda mathrm 7 lambda mathrm 8 frac partial 8 varphi mathrm lambda mathrm partial lambda mathrm 8 Bigr end array nbsp 9 f w w 9 l 2 p c 9 362880 l f l l 1451520 l 2 2 f l l 2 1693440 l 3 3 f l l 3 846720 l 4 4 f l l 4 211680 l 5 5 f l l 5 28224 l 6 6 f l l 6 2016 l 7 7 f l l 7 72 l 8 8 f l l 8 l 9 9 f l l 9 displaystyle begin array l frac partial 9 varphi mathrm omega mathrm partial omega mathrm 9 left frac lambda mathrm 2 pi c right mathrm 9 Bigl mathrm 362880 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 1451520 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 1693440 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 846720 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 mathrm 211680 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 mathrm 28224 lambda mathrm 6 frac partial 6 varphi mathrm lambda mathrm partial lambda mathrm 6 mathrm 2016 lambda mathrm 7 frac partial 7 varphi mathrm lambda mathrm partial lambda mathrm 7 mathrm 72 lambda mathrm 8 frac partial 8 varphi mathrm lambda mathrm partial lambda mathrm 8 lambda mathrm 9 frac partial mathrm 9 varphi mathrm lambda mathrm partial lambda mathrm 9 Bigr end array nbsp 10 f w w 10 l 2 p c 10 3628800 l f l l 16329600 l 2 2 f l l 2 21772800 l 3 3 f l l 3 12700800 l 4 4 f l l 4 3810240 l 5 5 f l l 5 635040 l 6 6 f l l 6 60480 l 7 7 f l l 7 3240 l 8 8 f l l 8 90 l 9 9 f l l 9 l 10 10 f l l 10 displaystyle begin array l frac partial 10 varphi mathrm omega mathrm partial omega mathrm 10 left frac lambda mathrm 2 pi c right mathrm 10 Bigl mathrm 3628800 lambda frac partial varphi mathrm lambda mathrm partial lambda mathrm 16329600 lambda mathrm 2 frac partial 2 varphi mathrm lambda mathrm partial lambda mathrm 2 mathrm 21772800 lambda mathrm 3 frac partial 3 varphi mathrm lambda mathrm partial lambda mathrm 3 mathrm 12700800 lambda mathrm 4 frac partial 4 varphi mathrm lambda mathrm partial lambda mathrm 4 mathrm 3810240 lambda mathrm 5 frac partial 5 varphi mathrm lambda mathrm partial lambda mathrm 5 mathrm 635040 lambda mathrm 6 frac partial 6 varphi mathrm lambda mathrm partial lambda mathrm 6 mathrm 60480 lambda mathrm 7 frac partial 7 varphi mathrm lambda mathrm partial lambda mathrm 7 mathrm 3240 lambda mathrm 8 frac partial 8 varphi mathrm lambda mathrm partial lambda mathrm 8 mathrm 90 lambda mathrm 9 frac partial 9 varphi mathrm lambda mathrm partial lambda mathrm 9 lambda mathrm 10 frac partial 10 varphi mathrm lambda mathrm partial lambda mathrm 10 Bigr end array nbsp Div takozh RedaguvatiDispersiya hviliLiteratura RedaguvatiRomanyuk M O Krochuk A S Pashuk I P Optika L LNU im Ivana Franka 2012 564 s Elektronna polyarizovnist feroyikiv monografiya V J Stadnik M O Romanyuk R S Brezvin Lviv nac un t im I Franka Lviv LNU im I Franka 2014 305 c Bibliogr s 287 305 V Levin V Goldshtejn Prosta fizika Vid atomnogo yadra do mezhi Vsesvitu K Nash format 2020 296 s Popmintchev Dimitar Wang Siyang Xiaoshi Zhang Stoev Ventzislav Popmintchev Tenio 24 zhovtnya 2022 Analytical Lah Laguerre optical formalism for perturbative chromatic dispersion Optics Express EN 30 22 40779 40808 Bibcode 2022OExpr 3040779P doi 10 1364 OE 457139 Popmintchev Dimitar Wang Siyang Xiaoshi Zhang Stoev Ventzislav Popmintchev Tenio 30 serpnya 2020 Theory of the Chromatic Dispersion Revisited arXiv EN Bibcode 2020arXiv201100066P doi 10 48550 ARXIV 2011 00066 Posilannya RedaguvatiDispersiya svitla Universalnij slovnik enciklopediya 4 te vid K Teka 2006 nbsp Ce nezavershena stattya z fiziki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Otrimano z https uk wikipedia org w index php title Dispersiya svitla amp oldid 39235019
