Ответы (1115944), страница 6

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GZc^zf mjZ\g_gb_bdhe_[Zgbc\hegjZkk_ygguoih^m]ehfϕhlEmqZkldZ s_eb Eϕ = 0 dx cos (ω t − kx sin ϕ ) ,bbEhl \k_c s_eb E = ∫ 0 cos (ω t − kx sin ϕ ) dx =0 b− E0=(sin (ωt − kb sin ϕ ) − sin ωt ) =bk sin ϕ2 E0E0kb sin ϕ π b sin ϕkb sin ϕkb sin ϕ sincos  ω t −.== = = α sin α cos (ω t − α ) , ]^_ α =λ222 kb sin ϕsin 2 α.LZdbfh[jZahfbgl_gkb\ghklvemq_ckh[bjZ_fuoebgahcgZwdjZg I (ϕ ) = I 0α2mλ, m ∈ ]. FZdFbgbfmfu ^hklb]Zxlky ijb sin α = 0 ⇒ α = π m ( m ≠ 0 ) ⇒ sin ϕ min =bπ( 2m + 1) λ . Ijbα = 0kbfmfu^hklb]Zxlkyijb sin α = 1 ⇒ α = + π m (m ≠ −1, 0) ⇒ sin ϕ max =22blh _klv ϕ j_Zebam_lky p_gljZevguc gme_\hc fZdkbfmf \ wlhf kemqZ_EEϕ = 0 cos ω t ⋅ dx ⇒ E = E0 cos ω t , I = I 0 .bAZf_qZgby ijb bkke_^h\Zgbb ^bnjZdpbb NjZmg]hn_jZ bkihevah\Zehkvk\hckl\h lZmlhojhgbafZ ebgau ebgaZ g_\ghkbl^hihegbl_evghcjZaghklboh^Z ^eyijhoh^ysbo q_j_a g_z emq_c ^bnjZdpbhggZy dZjlbgZ hij_^_ey_lky lhevdh m]ehf ϕ ihwlhfm gZ g_z g_ \eby_l iheh`_gb_ebgau DeZkkbnbdZpby \hegh\uo y\e_gbc ^bnjZdpby Nj_g_ey beb NjZmg]hn_jZ]_hf_ljbq_kdZy hilbdZ Jhev ^bnjZdpbb \ nhjfbjh\Zgbb hilbq_kdbo bah[jZ`_gbcMkeh\byjZaj_r_gby[ebadboh[t_dlh\hilbq_kdbfbijb[hjZfb1) DeZkkbnbdZpby\hegh\uoy\e_gbc:JZkkfhljbfijhoh`^_gb_k\_lZq_j_as_evrbjbgub\wdjZg_<lhqdmkdhhj^bgZlhcx +bxx0 ihiZ^Zxl\qZklghklbemqbhldjZz\s_eb tg ϕ1 = 0, tg ϕ 2 = 0 .

?keb^bnjZdpbygZll[ex^Z_lky \ iZjZee_evguo emqZo ^bnjZdpby NjZmg]hn_jZ lh ϕ1 ≈ ϕ 2 , ihwlhfm x0 b.28>Zggh_ mkeh\b_ ^he`gh \uihegylvky ^eyiheh`_gbyi_j\h]hfbgbfmfZλlxmin ≈ l sin ϕ min = , ]^_ l – jZkklhygb_ ^hbwdjZgZ LZdbf h[jZahf g_h[oh^bfuf b^hklZlhqguf mkeh\b_f gZ[ex^_gby ^bnjZdpbb NjZmg]hn_jZ y\ey_lky mkeh\b_λl 1. Ba wlh]h mkeh\by ke_^m_l qlhb2b λ l , lh_klvhldjulZg_[hevrZyqZklvi_j\hcahguNj_g_ey>eygZ[ex^_gby^bnjZdpbb\kdj_sb\ZxsbokyemqZogZau\Z_fhc^bnjZdpb_cNj_g_λl 2ey lj_[m_lky qlh[u ϕ1’ϕ2 lh _klv x0∞b ⇒∞1; \ wlhf kemqZ_ hldjulu g_kdhevdh ahgbλl 2 1  , lhNj_g_ey?keb`_i_j\ucfbgbfmfgZoh^blky\[ebabp_gljZwdjZgZ  x0 b ⇒b^bnjZdpbhggZy dZjlbgZ g_ gZ[ex^Z_lky ± j_Zebam_lky kemqZc ]_hf_ljbq_kdhc hilbdb,ij_^iheZ]Zxs_cijyfhebg_cgh_jZkijhkljZg_gb_k\_lZ±hldjulhhq_gvfgh]hahgNj_g_ey2) JZaj_r_gb_[ebadboh[t_dlh\hilbq_kdbfbijb[hjZfb:Ih aZdhgZf ]_hf_ljbq_kdhc hilbdb ijb ihiZ^Zgbb emq_c gZ h[t_dlb\ \ ijhkl_cr_fkemqZ_hgij_^klZ\ey_lkh[hcs_evbklhysmxaZg_cebgamhilbq_kdh]hijb[hjZ\k_ijhoh^ysb_emqbiZjZee_evgubkh[bjZxlky\lhqdmgZwdjZg_hdmeyj_nhlhiezgd_<j_Zevghklb\k_]^Zijhbkoh^bl^bnjZdpbyemq_cgZs_ebihwlhfmbah[jZ`_gb_fbklhqgbdZy\eyλ_lkyiylghm]eh\hcihemrbjbgu ϕ = , ]^_d±rbjbgZh[t_dlb\ZKe_^h\Zl_evgh^\Zh[td_dlZgZoh^ysb_kygZjZkklhygbbD^jm]hl^jm]ZbLhlijb[hjZ[m^mljZaj_r_gu_kebm]eh\h_ jZkklhygb_ f_`^m gbfb ij_\ukbl m]eh\mx rbjbgm bah[jZ`_gbc h[t_dlh\Dλβ ≈ > ϕ = .

Ihwlhfm mkeh\b_ jZaj_r_gby ^\mo h[t_dlh\ gZoh^ysboky gZ jZkklhygbb LLdλL. >Zggh_mkeh\b_hagZqZ_lihl_jxdh]_j_glghklbemqZfbhl^\moh[t_dhlijb[hjZ D >dλLlh\kf d >= rk , qlhaZdhghf_jghihkdhevdmdh]_j_glgu_emqbhl^\mobklhqgbdh\Dbgl_jn_jbjmxlbg_fh]ml[ulvjZaj_r_guMkeh\b_ i_j\h]h fbgbfmfZ ijb ^bnjZdpbb NjZmg]hn_jZ gZ djm]ehf hl\_jklbbλλLϕ ≈ 1.22 , ihwlhfmmkeh\b_jZaj_r_gbyD > dd >bnjZdpbhggZy j_rzldZ =eZ\gu_ b ^hihegbl_evgu_ fZdkbfmfu bfbgbfmfu ^bnjZdpbhgghc dZjlbgu OZjZdl_jbklbdb ^bnjZdpbhgghc j_rzldb dZdki_dljZevgh]hZiiZjZlZk\h[h^gZyki_dljZevgZyh[eZklvm]eh\Zybebg_cgZy^bki_jkbb jZaj_rZxsZy kihkh[ghklv Djbl_jbc Jwe_y jZaj_r_gby ^\mo [ebadboki_dljZevguoebgbc1) >bnjZdpbyk\_lZgZh^ghf_jghcj_rzld_:29JZkkfhljbf ^bnjZdpbx k\_lZ gZ kbkl_f_ iZjZee_evguo s_e_c jZkklhygby f_`^m dhlhjufb h^bgZdh\u h^ghf_jgZy ^bnjZdpbhggZy j_rzldZ RbjbgZ s_e_c jZ\gZ b Z gZbf_gvrbci_jbh^ih\lhjy_fhklbi_jbh^j_rzldb) – d.

GZj_rzldmghjfZevghiZ^Z_liZjZee_evguc imqhd k\_lZ lh]^Z gZ dZ`^hc s_eb ijhbkoh^bl ^bnjZdpby \ iZjZee_evguo emqZo kf >bnjZdpbhggZydZjlbgZ±j_amevlZlkeh`_gbydhe_[Zgbcijboh^ysbo hl dZ`^hc ba s_e_c jZaghklv oh^Z ^eyemq_c hl khk_^gbo s_e_c dsinϕ). Ihwlhfm aZ^ZqZ k\h^blkydkeh`_gbx N (h[s__qbkehs_e_cdhe_[Zgbckh^bgZdh\ufb Zfieblm^Zfb b jZagufb nZaZfb <hkihevam_fky f_lh^hf \_dlhjguo ^bZ]jZff dhgpu \_dlhjh\ E1, …, EN e_`Zl gZ h^ghc hdjm`ghklb ihwlhfmE1OA = OB =.

α = 2π – N⋅∆ϕ, ihwlhfm∆ϕ2sin2N ∆ϕsin2α2 . Ba E = E sin α , ihE = 2OA sin = E110∆ϕα22sin2π b sin ϕπ Nd sin ϕπ b sin ϕπ Nd sin ϕsinsinsin 2sin 2λλλλwlhfm\blh]_ E = E0; I = I0.2π b sin ϕπ d sin ϕπϕdsin2πϕsinbsinsin λλλλHij_^_ebf iheh`_gby ^bnjZdpbhgguo fZdkbfmfh\ b fbgbfmfh\ ijb \uiheg_gbbmkeh\by fbgbfmfZ ^ey dZ`^hc ba s_e_c \hagbdZxl lZd gZau\Z_fu_ ]eZ\gu_ fbgbfmfu:π b sin ϕmλ= π m ⇒ sin ϕ =, m ∈ ] \ {0}. =eZ\gu_ ^bnjZdpbhggu_ fZdkbfmfu \hagbdZxl \λbnλkemqZ_k^\b]ZnZaπn^eykhk_^gbos_e_c d sin ϕ = nλ ⇒ sin ϕ =, n ∈ ] wlhmkeh\b_khhld\_lkl\m_ljZ\_gkl\mgmexqbkebl_eybagZf_gZl_ey\h\lhjhc^jh[b\ujZ`_gby^eyIij_^_eπ nb Nd sin 2).

QbknmgdpbbI(ϕ)hij_^_ey_lbgl_gkb\ghklv]eZ\guofZdkbfmfh\: I n = I 0 d π nb ehn gZau\Z_lkyihjy^dhf]eZ\gh]hfZdkbfmfZ<p_glj_^bnjZdpbhgghcdZjlbgugZoh^blkyfZdkbfmfgme_\h]hihjy^dZi_j_oh^ydij_^_em\\ujZ`_gbb^eyI, ihemqbfqlhbgl_gkb\ghklv]eZ\gh]hfZdkbfmfZ I = N 2 I 0 .

Hq_\b^ghqlhijbkh\iZ^_gbbiheh`_gbc]eZ\guofbgbfmfh\ b fZdkbfmfh\ wlh \hafh`gh _keb hlghr_gb_ i_jbh^Z j_rzldb b rbjbgu s_eb_klvjZpbhgZevgZy^jh[v\hagbdZ_lfbgbfmfMkeh\b_ fZdkbfmfZ beb fbgbfmfZ ^eyπ Nd sin ϕsin hij_^_ey_l \hagbdgh\_gb_ ^hihegbλl_evguo fbgbfmfh\ b fZdkbfmfh\ fbgbfmfu ijbpλsin ϕ =, p ≠ mN ; m, p ∈ ]; fZdkbfmfuijbNdp+ 1 λ2 .

LZdbf h[jZahf f_`^m khk_^gbfbsin ϕ =Nd]eZ\gufb fZdkbfmfZfb \hagbdZ_l N ± ^hihegbl_evguofbgbfmfh\bN±^hihegbl_evguofZdkbfmfh\Wlhiha\hey_l\uqbkeblvm]eh2()302λ.Nd cos ϕ nGZdehggh_ iZ^_gb_ emq_c gZ ^bnjZdpbhggmx j_rzldm ih^ m]ehf θ fh`gh ij_^klZ\blvdZdghjfZevgh_iZ^_gb_gZgZdehggmx^bnjZdpbhggmxj_rzldmki_jbh^hfdcosθ; ^bnjZdpbhggZydZjlbgZ\wlhfkemqZ_ZgZeh]bqgZdZjlbg_\hagbdZxs_cijbghjfZevghfiZ^_gbbemq_c\mxrbjbgm]eZ\guofZdkbfmfh\: ∆ϕ n ≈2) OZjZdl_jbklbdb^bnjZdpbhgghcj_rzldbdZdki_dljZevgh]hZiiZjZlZ:Iheh`_gby fZdkbfmfh\ ^bnjZdpbhgghc dZjlbgu gZ h^ghf_jghc j_rzld_ aZ\bkyl hl^ebgu\heguihwlhfmijbiZ^_gbbgZj_rzldm[_eh]hk\_lZlhevdhp_gljZevgucfZdkbfmfy\ey_lky [_euf Z \k_ hklZevgu_ hdjZr_gu ± j_rzldZ fh`_l [ulv bkihevah\ZgZ dZd ki_dljZevgucZiiZjZl.K\h[h^gZyki_dljZevgZyh[eZklvki_dljZm-]hihjy^dZ±h[eZklvki_dljZm-]hihjy^dZg_gZdeZ^u\ZxsZykygZki_dlju^jm]boihjy^dh\ImklvgZj_rzldmiZ^Zxl\heguk^ebgZfbhl λ^h λ + ∆λlh]^Zmkeh\b_ ©g_gZeh`_gbyª ki_dljh\m-]h(m – 1)-]hb(m + 1)-]hihλjy^dh\ ( m − 1)( λ + ∆λ ) < mλ ; m ( λ + ∆λ ) < ( m + 1) λ ⇒ ∆λ < , ihwlhfmk\h[h^gZyki_dljZevmλgZyh[eZklvki_dljZm-]hihjy^dZ ∆λc = ; ^eyki_dljZgme_\h]hihjy^dZm = 0) ∆λc = ∞.mM]eh\Zy ^bki_jkby ± m]eh\h_ jZkklhygb_ f_`^m ki_dljZevgufb ebgbyfb ^ebgu \hegdϕ^ey dhlhjuo jZaebqZxlky gZ Å.

Dϕ =. Ijh^bnn_j_gpbjm_f mkeh\b_ \hagbdgh\_gbydλm]eZ\gh]h fZdkbfmfZ m-]h ihjy^dZ d sin ϕ = mλ ⇒ d cos ϕ dϕ = md λ ⇒ Dϕ =. Ijb fZd cos ϕmeuom]eZoϕbkihevamxlijb[eb`zggmxnhjfmem Dϕ ≈ .dEbg_cgZy ^bki_jkby ± ebg_cgh_ jZkklhygb_ f_`^m ki_dljZevgufb ebgbyfb ^ebgudx\heg^eydhlhjuojZaebqZxlkygZÅ.

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