Ответы (1115944), страница 5
Текст из файла (страница 5)
BaiZjZee_evghklbemq_clj_m]hevihemqbfqlh==OA2 OB OA1A1 A2 OA1C N CCOC1; ke_^h\Zl_evgh lj_m]hevgbdbgbdb K1K2N b A1A2M ih^h[gu ihwlhfm 1 = 1 2 =A1M A1 A2 OA1OC1N b OA1M ih^h[gu ih ^\mf klhjhgZf b m]emf_`^mgbfblh_klvm]euNOC1 bMOA1 jZ\guZwlhhagZqZ_l qlh ijyfu_ OM b ON kh\iZ^Zxl LZdbfh[jZahfbgl_jn_j_gpbhggZy dZjlbgZ jZkiheZ]Z_lky\ iehkdhklb ijhoh^ys_c q_j_a j_[jh debgZ ?kebk\_l iZ^Z_l gZ ihehkdm i_j_f_gghc lhesbgu lhhq_\b^gh bgl_jn_j_gpbhggZy dZjlbgZ g_ [m^_liehkdhc h^gZdh hgZ \kz jZ\gh g_ fh`_l hdZaZlvkyehdZebah\ZgghcgZ[_kdhg_qghklb>jm]hcijbf_jihehkjZ\ghcrbjbgu±dhevpZGvxlhgZ\hagbdZxsb_\hdjm]lhqdbkhijbdhkgh\_gby^\moebgabebebgaubieZklbgdbIjbgZ[ex^_gbbgZhljZ`_gb_emqqZklbqghhljZ`Z_lkyhlih\_joghklb h^ghcba ebga Z qZklbqgh ± ij_ehfey_lky Ij_ehfezgguc emq qZklbqgh hljZ`Z_lky hl ih\_joghklb \lhjhc ebgau b \gh\v ij_ehfey_lky gZi_j\hcebga_?kebijhkljZgkl\hf_`^m\uimdeufbebgaZfbaZiheg_gh\ha^mohflhλϕrr,∆ = n ( h1 + h2 ) + 0 .
ϕ ≈ tg ϕ = ⇒ ψ ≈ ≈22 2 R1R122h1 = r tgψ ≈ 11 λr2r2; ZgZeh]bqgh h2 =⇒ ∆ = = r 2 + + 0 . H[jZah\Zgb_lzfguodhe_p2 R12 R2 R1 R2 2RR1±bgl_jn_j_gpbhggucfbgbfmf ∆ = m + λ0 ⇒ rm = mλ0 1 2 – jZ^bmk m-]h lzfgh]hR1 + R22dhevpZGvxlhgZBgl_jn_j_gpbhggZydZjlbgZehdZebah\ZgZgZ[_kdhg_qghklbIhehkujZ\gh]hgZdehgZ_kebgZiezgdmh^bgZdh\hclhesbguih^jZagufbm]eZfbiZ^Zxl emqb k\_lZ lh h[jZamxlky ihehku jZ\gh]h gZdehgZ ± ^ey jZaguo m]eh\ iZ^_gby lh_klvjZaguo βfh]mlj_Zebah\u\Zlvkymkeh\byfbgbfmfZbebfZdkbfmfZBgl_jn_j_gpbhggZydZjlbgZehdZebah\ZgZgZ[_kdhg_qghklbNhjfmeZ;jw]]Z<mevnZ:Ijb iZ^_gbb emq_c gZ ^\mf_jgmx maeh\mx k_ldm fh^_ev djbklZeebq_kdhc j_rzldbgZ[ex^Z_lky dZjlbgZ ZgZeh]bqgZy bgl_jn_j_gpbbemq_chljZ`zgguohl^\moiZjZee_evguoih\_joghkl_c±\wlhfkemqZ_kj_^Z\_a^_h^gZblZ`_ihwlhfmmkeh\b_fZdkbfmfh\aZibr_lky dZd 2d cos α = mλ , m ∈ ] + . < j_gl]_gh]jZnbb h[uqgh baf_jyxl g_ m]he iZ^_gbyemqZ Z lZd gZau\Z_fuc m]he kdhev`_gbyπθ = − α , ihwlhfm mkeh\b_ fZdkbfmfh\ aZib2r_lky dZd 2d sin θ = mλ ± nhjfmeZ ;jw]]Z<mevnZ hkgh\gh_ khhlghr_gb_ j_gl]_ghkljmdlmjgh]hZgZebaZBgl_jn_j_gpbhggu_dhfiZjZlhjuJ_njZdlhf_ljubki_dljZevgu_ijb[hjuJ_njZdlhj @Zf_gZ Ki_dljZevguc ZiiZjZl NZ[jbI_jh Ijbgpbiu Nmjv_ki_dljhkdhibbIj_^klZ\e_gb_h]heh]jZnbb1) Bgl_jn_j_gpbhggu_f_lh^ubkke_^h\Zgbybgl_jn_j_gpbhggu_dhfiZjZlhju:Bgl_jn_j_gpbhggZydZjlbgZhij_^_ey_lkylj_fyiZjZf_ljZfb λ, nb∆rIhwlhfmagZy^\ZbaljzoiZjZf_ljh\fh`ghhij_^_eblvg_^hklZxsbc±gZwlhfhkgh\Zgubgl_jn_j_gpbhggu_f_lh^ubkke_^h\Zgby.K ihfhsvx bgl_jn_j_gpbhgguo dhfiZjZlhjh\ hij_^_eyxl ebg_cgu_ jZaf_ju lh]hbebbgh]hh[t_dlZijbba\_klguoλbn>eyhij_^_e_gby^ebguh[t_dlZ_]hihf_sZxlf_`^m^\mfyiehkdhiZjZee_evgufbieZklbgdZfbdhlhju_g_iZjZee_evguf_`^mkh[hc^eykha^Zgby ihehk jZ\ghc lhesbgu AZl_f ih k^\b]m bgl_jn_j_gpbhgguo ihehk ih kjZ\g_gbx kimklhch[eZklvxbebh[eZklvxaZgylhcwlZehghfjZkkqblu\Zxl^ebgmh[t_dlZ\khhl\_lkl\mxs_fbaf_j_gbb<dZq_kl\_wlZehgZ[_jmllsZl_evghhlrebnh\Zggu_iehkdhiZjZee_evgu_ ieZklbgdb <hafh`gh lZd`_ bkihevah\Zgb_ bgl_jn_jhf_ljZ FZcd_evkhgZ kf \dZq_kl\_ bgl_jn_j_gpbhggh]h dhfiZjZlhjZ ± h^gh ba [hdh\uo a_jdZe aZdj_iey_lky gZ bkke_^m_fhfh[t_dl_2) J_njZdlhf_lj@Zf_gZ:J_njZdlhf_lj±bgl_jn_j_gpbhggucijb[hjiha\heyxsbcihba\_klguf^ebg_\hegubjZaghklboh^Zemq_chij_^_eblvihdZaZl_evij_ehfe_gbykj_^u<j_njZdlhf_lj_@Zf_gZemqiZ^Z_lgZiehkdhiZjZee_evgmxkl_deyggmxieZklbgdmbjZa^_ey_lkygZ^\ZemqZdhlhju_ijhoh^ylq_j_adx\_lubkjZagufb\_s_kl\ZfbAZl_femqb \gh\v ihiZ^Zxl gZ iehkdhiZjZee_evgmx ieZklbgdm jZkiheh`_ggmx ih^ g_dhlhjufm]ehf d i_j\hc gZdeZ^u\Zxlky b bgl_jn_jbjmxl h[jZamy ihehku jZ\ghc lhesbgu K^\b]23wlboihehkijbaZiheg_gbbh^ghcbadx\_lbkke_^m_fuf \_s_kl\hf iha\hey_l hij_^_eblvihdZaZl_ev ij_ehfe_gby ih mjZ\g_gbx∆ = ( n2 − n1 ) l = ∆m ⋅ λ , ]^_l±^ebgZdx\_lu∆m±qbkehihehkgZdhlhjh_k^\bgmeZkvbgl_jn_j_gpbhggZydZjlbgZHp_gbflhqghklvj_njZdlhf_ljZ@Zf_gZ_keb ^ebgZ dx\_l l kf ^ebgZ \hegu bkihevam_fh]h k\_lZ λ gf Z j_]bkljbjmx-∆m ⋅ λ= 10 −6 ; lhqghklvfh`_l[ulvlih\ur_gZkihfhsvxm^ebg_gbydx\_lbebih\ur_gbyqm\kl\bl_evghklbj_]bkljbjmxs_]hijb[hjZJ_njZdlhf_ljbq_kdb_ bkke_^h\Zgby iha\heyxl hij_^_eylv fhe_dmeyjgmx j_njZdpbxn2 − 1 M; ih nhjfme_ Ehj_gpEhj_gpZ\_s_kl\Z jZkkqblu\Z_fmx ih nhjfme_ RM = 2n +2 ρ4πRM =N Aα , ]^_NA – qbkehiheyjbam_fuoqZklbp\_^bgbp_h[tzfZα±kh^_j`Zgb_dhf3ihg_glZ F ± fheyjgZy fZkkZ LZdbf h[jZahf fhe_dmeyjgZy j_njZdpby ijhihjpbhgZevgZwe_dljhgghciheyjbam_fhklbZihkdhevdm we_dljhggZy iheyjbam_fhklv h[eZ^Z_l k\hckl\hfZ^^blb\ghklblhbfhe_dmeyjgZyj_njZdpbyh[eZ^Z_ll_f`_k\hckl\hfsbcijb[hjnbdkbjm_lk^\b]gZ∆m > 0.1 ihehkulh ∆n =3) Ki_dljZevgucZiiZjZlNZ[jbI_jh:Ki_dljZevguc ZiiZjZl NZ[jbI_jh khklhbl ba^\mo iZjZee_evguo kl_deygguo beb d\Zjp_\uo ieZklbg \gmlj_ggb_ ih\_joghklb dhlhjuo ihdjulu hljZ`Zxsbf keh_f k dhwnnbpb_glhf hljZ`_gby r <oh^ysbc emq [m^_l fgh]hdjZlgh hljZ`Zlvky hl ih\_joghkl_c ieZklbg ihkl_i_ggh l_jyy wg_j]bx baaZ qZklbqgh]h ijhoh`^_gby Ijhoh^ysb_ emqb bgl_jn_jbjmxlh[jZamy bgl_jn_j_gpbhggmx dZjlbgm ehdZebah\ZggmxgZ[_kdhg_qghklbBgl_jn_j_gpbhggu_fZdkbfmfu^ey\heg jZaguo ^ebg [m^ml jZa^_e_gu ijhkljZgkl\_gghijbqzfbaaZ[hevrh]hdhebq_kl\Zemq_cjZaj_rZxsZykihkh[ghklvhdZ`_lky\ukhdhcHp_gbf jZaj_rZxsmx kihkh[ghklv ZiiZjZlZNZ[jbI_jh bkihevamy nhjfmem ^ey ^bnjZdpbhgghcj_rzldbkfR = mN.
<^ZgghfkemqZ_N±qbkehemq_c\ur_^rbobaZiiZjZlZbgl_gIln NI1kb\ghklv N-]h emqZ \ r–2N jZa f_gvr_ i_j\h]h ihwlhfm N =; kqblZy hlghr_gb_ bg2 ln r∆l_gkb\ghkl_cjZ\guf–2Zr ~ 0.8 – 0.9ihemqbfqlhN ~ 10 – 100. m = : jZaghklvoh^Z±λ05wlhm^\h_ggh_jZkklhygb_f_`^mieZklbgZfb~ 10 kfihwlhfmm ~ 10 – 106. LZdbfh[jZahf R ≈ 106 − 108. K\h[h^gmx ki_dljZevgmx h[eZklv fh`gh lZd`_ hp_gblv ih nhjfme_ ^eyλj_rzldb ∆λ = , lh _klv \k_]h 10−5 − 10−6 λ , ihwlhfm ^Zgguc ijb[hj bkihevamxl ^ey bkmke_^h\Zgbylhgdhckljmdlmjuki_dljh\4) Ij_^klZ\e_gb_hNmjv_ki_dljhkdhibb:24Hkgh\ghc qZklvx Nmjv_ki_dljhf_ljZ y\ey_lky bgl_jn_jhf_lj FZcd_evkhgZ emq ihiZ^Z_lgZkl_deyggmxieZklbgdmqZklbqghhljZ`Zxsbck\_lgZa_jdZehZqZklbqghij_ehfeyxsbc _]h gZ a_jdZeh hljZ`zggu_ hl a_jdZe emqb \gh\v ihiZ^Zxl gZ ieZklbgdm hljZ`ZxlkybihiZ^Zxl\j_]bkljbjmxs__mkljhckl\hWlbemqbbf_xljZagu_nZaubbgl_jn_jbjmxlImklvbkoh^gh_fhghojhfZlbq_kdh_baemq_gb_qZklhlu ωjZa^_ey_lkygZ^\_I (ω ).
Lh]^Z j_]bkljbjm_fZy bgl_gkb\ghklv emqZh^bgZdh\u_ ih wg_j]bb khklZ\eyxsb_ 02I (ω ) = I 0 (ω )(1 + cos ∆ϕ ) kf ?keb \ gZqZevgucfhf_gl mklZgh\blva_jdZeZb lZd qlh ∆ϕ = lh ijb ihklmiZl_evghf i_j_f_s_gbb h^gh]h ba∆r (t )a_jdZe kh kdhjhklvx v∆ϕ (t ) = 4π=λ4π2vω t, ]^_V±nZah\Zykdhjhklv\hegufghvt =λV`bl_ev h[mkeh\e_g l_f qlh jZaghklv oh^Z \ ^\ZjZaZ [hevr_ i_j_f_s_gby a_jdZeZ Ihwlhfm j_]bkljbjmxs__ mkljhckl\h aZnbdkbjm_l gZebqb_ i_j_f_gghc khklZ\eyxs_c bgl_gkb\ghklb I (t ) =2vtVIjb ih^Zq_ gZ bgl_jn_jhf_lj \heg g_kdhevdbo qZklhl bo i_j_f_ggu_ khklZ\eyxsb_bgl_gkb\ghklb[m^mlkdeZ^u\Zlvkyihwlhfm^eyg_ij_ju\gh]hki_dljZfh`_l[ulvaZibkZgI 0 (ω ) cos ωτ , ]^_τ =∞kb]gZe F (τ ) = ∫ I (ω ) cos ωτ dω ± h[jZlgh_ ij_h[jZah\Zgb_ Nmjv_ bkoh^gh]h ki_dljZ Ki_d0ljZevguc khklZ\ iZ^Zxs_]h baemq_gby fh`_l [ulv gZc^_g k ihfhsvx ijyfh]h ij_h[jZah+∞\Zgby Nmjv_ I (ω ) = k ∫ F (τ ) cos ωτ dτ .
Hkgh\gh_ ij_bfms_kl\h Nmjv_ki_dljhf_ljh\ ±−∞\hafh`ghklvh^gh\j_f_gghcnbdkZpbb\k_]hki_dljZp_ebdhfZg_hl^_evguoqZkl_cki_dljZdZd\h[uqguoki_dljZevguoijb[hjZo5) Ij_^klZ\e_gb_h]heh]jZnbb:=heh]jZnby ± kihkh[ nbdkZpbb h[tzfgh]h bah[jZ`_gbyij_^f_lZhkgh\ZggucgZy\e_gbbbgl_jn_j_gpbb\heg< wlhf f_lh^_ nbdkbjmxlky dZd Zfieblm^ qZklhlu lZd bjZaghklbnZa\heg jZkk_ygguo ij_^f_lhf Ijb ktzfd_ ]heh]jZffu nbdkbjmxl bgl_jn_j_gpbhggmx dZjlbgm f_`^memqZfbbklhqgbdZhihjghc\heghcbemqZfbjZkk_yggufbij_^f_lhf kb]gZevghc \heghc).
=heh]jZffZ ij_^klZ\ey_lkh[hcieZklbgdmihdjulmxnhlhwfmevkb_cwfmevkbhgguckehc iha\hey_l nbdkbjh\Zlv fbgbfmfu b fZdkbfmfu bgl_jn_j_gpbhgghc dZjlbgu >ey \hkklZgh\e_gby bah[jZ`_gby aZnbdkbjh\Zggh]h gZ ]heh]jZff_ _z h[emqZxl hihjghc \heghc khojZgyy hjb_glZpbx ieZklbgdb ih hlghr_gbxdimqdm<hegu^bnjZ]bjmxlgZaZnbdkbjh\Zgghcbgl_jn_j_gpbhgghc dZjlbg_ h[jZamy ^\Z bah[jZ`_gby ±fgbfh_gZf_kl_h[t_dlZktzfdbb^_ckl\bl_evgh_Hkh[_gghklvx ]heh]jZnbb y\ey_lky khojZg_gb_ ihegh]h bah[jZ`_gby ex[uf mqZkldhf ]heh]jZffu ijb \hkklZgh\e_gbb bah[jZ`_gby ih qZklb bkoh^ghc ]heh]jZffu25mf_gvrZ_lkyjZaj_r_gb_gh\hkijhba\h^blky\_kv kgyluch[t_dl< ]heh]jZnbb ^ey kha^Zgby bgl_jn_j_gpbhgghc dZjlbgulj_[mxlkybklhqgbdbbaemq_gb_dhlhjuobf__l^hklZlhqgh [hevrb_ \j_fy b ^ebgm dh]_j_glghklb Ihwlhfm^ey ihemq_gby ]heh]jZff bkihevamxl eZa_ju h^gZdh \wlhf kemqZ_ bah[jZ`_gb_ ihemqZ_lky h^ghp\_lguf Kms_kl\mxl^\Zimlbihemq_gbyp\_lguo]heh]jZff\hi_j\uobkihevah\Zgb_ eZa_jh\ k baemq_gb_f jZaguo p\_lhf gZijbf_jdjZkgh]hkbg_]hba_ezgh]h<h\lhjuoktzfdZb\hkklZgh\e_gb_]heh]jZffu\[_ehfp\_l_±\wlhfkemqZ_ijbf_gyxl lheklhkehcgu_ nhlhwfmevkbb ihwlhfm bgl_jn_j_gpbhggu_fZdkbfmfujZaguop\_lh\ihiZ^ZxlgZjZagu_ ]em[bgu wfmevkbb H[jZam_lky lZd gZau\Z_fZy ljzof_jgZy]heh]jZffZ\hlebqb_hl^\mf_jguo]heh]jZffihemqZ_fuokihfhsvxeZa_jh\ >bnjZdpby \heg Ijbgpbi =xc]_gkZNj_g_ey F_lh^ ahg Nj_g_ey >bnjZdpby \heg gZ djm]ehf hl\_jklbb b djm]ehc ij_]jZ^_ :fieblm^gZy b nZah\Zy ahggu_ieZklbgdb>bnjZdpbyNjZmg]hn_jZgZs_ebMkeh\byfZdkbfmfh\bfbgbfmfh\^bnjZdpbhgghcdZjlbgu1) F_lh^ahgNj_g_ey:>bnjZdpby \heg ± y\e_gb_ h]b[Zgby \hegZfb ij_iylkl\bc beb \ [he__ rbjhdhfkfuke_ex[h_hldehg_gb_hlaZdhgh\]_hf_ljbq_kdhchilbdbkfIjbgpbi=xc]_gkZNj_g_eyex[ZylhqdZgZ\hegh\hcih\_joghklbfh`_ljZkkfZljb\Zlvky dZd kZfhklhyl_evguc bklhqgbd kn_jbq_kdbo \heg bo gZau\Zxl \lhjbqgufb); 2)Zfieblm^Zdhe_[Zgbc\ex[hclhqd_ijhkljZgkl\Zfh`_l[ulvgZc^_gZdZdj_amevlZlbgl_jn_j_gpbb\lhjbqguo\hegF_lh^ ahg Nj_g_ey khklhbl \ \u^_e_gbb gZ \hegh\hc ih\_joghklb lZdbo h[eZkl_c qlh jZaghklv oh^Z emq_c baemqZ_fuo khk_^gbfb ahgZfb khklZ\ey_l λ/2.JZkkfhljbf kemqZc iZ^_gby iehkdhc \hegu gZ wdjZg Ijh\_^zf hdjm`ghklv jZ^bmkZH:kp_gljhf\lhqd_:; <±lhqdZi_j_k_q_gbywlhchdjm`ghklbbijyfhc:K.
AD± i_ji_g^bdmeyj d ohj^_ BO Lh]^Z m]euOAD b BOC jZ\gu ihwlhfm OC OA )OD BCOC rm≈. OC = rm, OA = l, OD ≈≈ ;OA OC22BC = Z ± jZaghklvoh^Z emq_c ijboh^ysbo \ lhqdm : ba H b K (:< = :H LZdbf h[jZahfr a≈ ⇒ r ≈ 2al ; lhqdZ K ± \g_rgyy ]jZgbpZ m-hc ahgu Nj_g_ey ihwlhfm2l rmλa=⇒ rm = mλl .2>Ze__ jZkkfhljbf kemqZc ^bnjZdpbb gZ lhf `_ wdjZg_ \hegu bkimkdZ_fhc bklhqgbdhfgZoh^ysbfkygZijyfhcH:JZaghklvoh^ZgZ[bjZ_fZyemqZfbijboh^ysbfb\lhqdmr2K^hwdjZgZfh`_l[ulv\uqbke_gZZgZeh]bqghij_^u^ms_fmkemqZx ∆r = m , ]^_L±jZk2L26rm2 1 1 mλlL+ =⇒ rm = mλl * , ]^_l * =2 l L2l+LIehsZ^v mhc ahgu Nj_g_ey Sm = π ( rm2 − rm2−1 ) = πλ l * ± g_ aZ\bkbl hl ghf_jZ ahgu lhklhygb_hlbklhqgbdZ^hwdjZgZLh]^Z_klv\k_ahguNj_g_eybf_xlh^bgZdh\u_iehsZ^bAZf_qZgb_jZ^bmkuahguNj_g_eygZc^_gu[_ahlghkbl_evghdiheh`_gbxhl\_jklbybaZ\bkyllhevdhhliheh`_gbylhqdbgZwdjZg_p_gljahgNj_g_ey\k_]^ZgZoh^blky©gZijhlb\ªlhclhqdb^eydhlhjhcwlbahguihkljh_gukhhl\_lkl\_gghijbi_j_f_s_gbbbah^ghclhqdbwdjZgZ\^jm]mxahguNj_g_eyk^\bgmlky\lhf`_gZijZ\e_gbb2) >bnjZdpby\heggZdjm]ehfhl\_jklbbbdjm]ehcij_]jZ^_:Ijb kha^Zgbb \ wdjZg_ djm]eh]h hl\_jklby ^ey lhq_d jZkiheh`_gguo\^hevhkbhl\_jklby©hldjuluªdZdb_lhahguNj_g_eyBgl_gkb\ghklv k\_lZ \ lZdbo lhqdZo fh`_l [ulv gZc^_gZ k ihfhsvx f_lh^Z \_dlhjguo ^bZ]jZff jZah[tzf dZ`^mx ahgm Nj_g_eygZ fZeu_ dhevpZ lh]^Z \_dlhj ? hl dZ`^h]h ba lZdbo dhe_p [m^_lihkl_i_ggh ih\hjZqb\Zlvky m\_ebqb\Z_lky jZaghklv oh^Z ©ihke_^gbcª\_dlhji_j\hcahguNj_g_ey[m^_lbf_lvjZaghklvnZaπki_j\uf ihwlhfm j_amevlbjmxsZy Zfieblm^Z hl i_j\hc ahgu Nj_g_eykhklZ\bl?]^_?±jZ^bmkhdjm`ghklb.IjbZgZeh]bqghfihkljh_gbb ^ey \lhjhc ahgu Nj_g_ey ©ihke_^gbcª \_dlhj ijb^zl \lhqdm e_`Zsmx qmlv gb`_ gZqZevghc ihkdhevdm bgl_gkb\ghklvihkl_i_ggh mf_gvrZ_lky bgl_gkb\ghklv baemq_gby lhq_qgh]h bk1lhqgbdZ ijhihjpbhgZevgZ 2 ).
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