CAPITOLO 2 18
22
0
0
Testo completo
(2) !#"%$&(' ) * $,+-+-"%$,./0"% 2 1 *$3$,' 4 /$ $5 * +-"% 6*$ 17 * $& $, 8:9#;=<=>?A@CBEDGFGH=IJ@CBKLB=M*NOIJDGP=ILFGQR>NS>=QTBEUNS>V=>QW>9=@C>XKJYJB@C@CILDZF\[>=I*QRFZ@C>NOIJFGKJI FG9=IL?AB@CNSBH=I]<=9=IJFG?Z?AI^FGKLI^_]`a>Kb9cB?A@CNOBdDGFG?ABd?AI]@CNOFG@C@CFe[>I]DGNOI^?Z@CFGKJK^IbK^IL;=<cIL[I]9=>=QRFG@CIJDGIfIJK DG<=Ig[ILNS>@C@CBNS>%DGBIJ9=DGIJ[>hDGB9(KLYJFG?A?A>%B@C@CIJDGB_gibFGNOK^>NO>QRBMgIJ9h?A>j<cIL@CBMg[>=IkHcNOIJ9=DGILH=I B@C@CILDGIFGKJKJFdU=FG?A>l[>IQT>@mB=[In[=IoQWIJ?Z<cNOFp[IFG9=DGBNSFGj=jIoFGqrIJQW<=@CFGKJIJMoIJ9NSILsCKJ>=?A?rILB=9=>t> IL9u@CNSFG?AQRIJ?r?ZIJB9=>=Mf<=?AFG@mIfI^9u;=<=>?A@CBpKJFGV=BNOBu[I]@C>?rIJ_ v-wyx. az { |f}~|t~{ f~GLf~|h=op| { yyo~ycf{ f yccyL B9=?AIL[=>NOIJFZQTBl<=9lNOFGjj=ILBQRB9=B=DGNBQRFG@CIJDGBMo[cIoKJ<c9=jP=>q4q4Fp[YJB9=[F λ MDGP=>lIJ9=DGIJ[> 9=BNOQRFGKJQT>=9=@C>(?A<t<=9=FdKJFZQRIL9=FdFG9=IJ?AB@CNSBH=FJGArLGJl[=In?AH=>?A?ABNS>5G_n9lQT>q4q4B ?AI[=ILDZ>5<=9=I^FG?Z?rIJFGKJ>5;=<=FG9c[=B,Bj9cIH=NOB HcNOIJ>@ClB@C@CIJDZFh(?AI^QTQW>@CNSILDZF(H=>NNOB@CFGq4IJB9=> FG@C@CBNO9=BFGKJKLYJFG?A?A>B=@@CIJDGB_- DG>jKJILFGQRB<=9,?ZI^?A@C>QWF%[I FG?r?AI DZFGNS@C>?AIJFG9=I IJ9,DZ<=I <=9=F ?A<=H=>NOsCIJDGIJ>l[>K^KLFuKJFZQTIJ9=F¡?AIJFu9=>KbH=ILFG9=Bt¢~£p>lKJYLFZ?r?A>lB@C@CIJDGBljIJFGDZDGIJFu9=>KHcIJFG9=B(¢ ¤ M DGB9uFG9=jBKJB θ NOIJ?AH=>@C@CBuFGKJKLYJFZ?A?A>¤¥_ φp. x. φa. n. θ0 Onda incidente. y Polarizzatore. P. Per 0<z<d: Cristallo Liquido. z. Analizzatore. ¦A§ ¨ ©ªC« ¬®y¯®°¥± ²o³²O´µ:²:¶·µ:¸¹=ºgµ ¹c»mµ:´ º¹=¼Jº¾½¿¸À:²:³Cµ ¶Á¶r²S¼y²À µ ¹cº®²:³CÂ
(3) º¹c¼Lº
(4) ´®² ù
(5) ¿¸À:²:³Cµ ¶·¶r²S¼L¸³OºaÄ®Åb»O¸¹uÃC¹ ²m¹ ƸÀ:¸ φÇ ³Cµ:È¿=º¥¼L¼L¸WÀSÉ ²OÈ·ÈSºWÊ Ë ±kÉ ¸¹c´ ²mÅ¿¸µ ŵ ¹=»mµy´ ºW¹=¸³CÂ̲:À Â
(6) º¹=¼JºdÈSÃpÃC¹²ÌÀ²mµ ¹=²¡´µÂ²O¼Lº³Cµ²mÀº Í µ ³Cµ ÎL³²:¹®Æcº¹=¼Jº ÃC¹®µ:²SÈSȵ:²mÀº Å ´µ È¿=º ÈSÈ·¸ ³Oº ´Årµ À~»Oõ ²OÈ·ÈSº ¸¥¼L¼ µ:»S¸bÎÁ¸³CÂ
(7) ²gùR²:¹®Æc¸À:¸ ³Cµ:È¿cº¥¼L¼L¸-²mÀ ÀSÉ ²SÈSÈSº ¶r˷и¿¸µ Àrº¶Á¶r¸-½f¿c¸ È·¼L¸-ùW²:¹²:À µ ¶Á¶r²S¼L¸³OºgÑcÅ~»O²:³²O¼L¼Lº³Cµ ¶·¶4²O¼J¸ ´ ²kÃC¹R²:¹ Æ=¸ Ày¸ φÒ Ë θÏ `>K-9=B=?Z@CNSBDGFG?ABMIJK-QWFZ@C>NOIJFGKJ>,FG9=IJ?AB@CNOBHcBhILKDGNSIL?A@CFZKJKLB,KJIL;=<cIL[B,Ó gÔ >5KJYLFG?r?A> B@C@CILDGBDGBIJ9=DGIJ[>DGB9KJF5[=ILNS>q4ILB9c>[>=K [IJNO>@C@CBNS>=_ Õ?A?A<=QRIJFGQRBDGPc>IJK [IJNS>@C@CBNS> CAPITOLO 2. 18. A.
(8) ?AILFB=NOIJ>9=@CFG@CBh<=9=IJsCBNSQT>=QT>9=@C>(9=>KDGFZQRH=ILB=9=>_8:K?A<=B(BNOIJ>9=@CFGQR>9=@CB([>?ADGNOIJ@C@mB [FGK]V=>=NO?ABNO>Ö 9 = (sin θ ,0, cos θ ) ×Ø _ Ù4Ú 8:9cV=ILFGQRB7IJKTsCFG?ADZILB7[=IK^<=DG>7FG@C@CNSFGV=>NS?ZB2<=92H=BKJFGNOIJq4q4FG@CBNO>2iÛDGP=>2KLB2H=BKJFGNOIJqrq®F KLIJ9=>FGNSQT>9c@C>_kÜbYJFG?r?A>,[Iki0sBNSQRFh<=9%FG9jBKJB φÝ NOIJ?AH=>@C@CB,F,¢=_ DGBQRHB 9=IJFGQTB5IJK DGFGQTH=BÞ>KJ>@C@CNOIJDGB2[=>KJKJYLB=9=[=F&IL9=DGI^[>9=@C>ßIL9ß[<=>ÞDGBQRH=B9=>=9=@CI × 9c>K?A>=j<=IL@CB=MHc>N ?A>QTHcKLIJsCILDZFGNS>(KJ>t9=B@CFGq4IJB=9=ILMn>VcIL@C>NS>=QRB([Io>?AH=KJILDZI^@CFGNO>(KJFd[IJH=>9=[=>9=q4Fd?AH=FGqrIJFGKJ>t> @C>QTHcBNOFGKJ>p[>K DGFZQTH=B=Ú¥Ö 0. 0. _Ø Ú × Ø E = E sin φ [BV=>0à ,KJYLFGQRH=IJ>q4qrF5[>KJKJYLB9c[FIJ9=DGI^[>9=@C>_ B=9=?AIL[>=NOIJFZQTB)?A>H=FGNSFG@CFGQT>9c@C>KJ> [<=>pDGBQRH=B9=>9c@CIL_ Ù4Ú E = E cos φ 7KJF7DGBQRH=B9=>9c@C>[>KuDGFGQRH=BáKL<c9=jBKJF7H=NOBIJ>q4ILB9c>[>K [ILNS>@C@CBNS>ß?A<=KWH=IJFG9=Bß[=>=KLKJF0KJFGQWIJ9=FG_Wâ-<c>?A@mF0DGB=QTH=B=9=>9=@C>ß?AIW[=ILDG>2ã®= ä åZGã®åZ= åALæ>=MçFGKJKLY^IL9c@C>=NO9=Bè[>KçQRFG@C>NOIJFZKL>=MçéJV=>[>Yç<=9êIL9c[ILDZ>è[=I NOIJsCNOFGq4ILB=9=> × θ Ú_Wën?A?rFì?AIWH=NOBH=FGj=F0DGB9&<=9=F0V=>KJBDGIJ@C[IWsCFG?A>2írîy × θ ÚM [BV=>íRKLFV=>=KLBDGIJ@Cï[>KJKJFeKJ<cDG>p9=>KfVc<=B@CB_ ÚØ E = E sin φ #KLF#DGBQRH=B9=>9=@C>ð[>KñDGFGQTH=BðH=>NSH=>9=[IJDGBKJFGNO>ðFGKJKLF H=NOBIJ>q4IJB9=>5[=>Kk[ILNS>@C@CBNS>5?A<=KkH=IJFG9=B5[=>KLKJF(KJFZQRIL9cFG_kò FGKJ>%DGB=QTH=B=9=>9=@C>%?ZI [ILDG>ã®=hã®åZ= åALd>,é^V=>[>=Y<=95IJ9=[IJDG>5[=INOIJsCNSFGq4ILB9c>t M[>@C@CB5IL9=[=IJDG> ã®åZ åALãG_fÜbFV=>KJBDGIJ@CW[cI]sCFG?A>uuírîy _ óIL?A@CIJ9=j<=IJFZQTBp[=<=>uDGFZ?AIÖ Ù4Ú φÝôöõ÷ MìÙ®ø õ ÷ ÖdIJK(DGFGQRH=B IJ9=DGIL[>=9=@C> P=FÛ?AB=KLFGQR>9=@C> KJFÛDGB=QTH=B=9=>9=@C> ?A@CNOFGBNO[=IL9=FGNSILFG_5Ü]F*H=BKLFZNSILq4q4FGq®ILB9c>öIL9cDGIL[>=9=@C>ùZM;=<cIL9=[IJM5IL9=@C>=NOFGQR>9=@C> H=FGNOFGKJKL>=KLF,FGKLKJY^FG?A?A>0¢=_aâ-<=FG9=[B)IJK[IJNO>@C@CBNS>)BNOIJ>9=@CFG@CB)<=9=IJsB=NOQR>QR>9=@C> DGBQR>IL9d;=<=>?A@CBDGFZ?ABMKLY^B9=[Fp?AIH=NOB=H=FGjFp9=>KQRFG@C>NOIJFGKL>dDGB9lV=>KJBDGIJ@Ce[cI sCFG?A>úírîy × θ Út>áK^F2?A<cFÞH=BKJFGNOIJq4q4FGqrIJB9=>ç?rI¡QRFG9=@mIJ>9=>çIJ9=FGKJ@C>NOFG@CFZM¡DGBQW> V=>[NS>QTBpIJ9u?r>j<=IJ@CB ×û4Ø _Jü Ú_ Ö)ILK DGFGQWH=BæIL9cDGIL[>=9=@C>þP=Fÿ?ABKJFZQT>9c@C>þKJFÿDGBQRH=B9c>9=@> Ø Ú BφÝ7 NO[IJô 9=FGNS±ILFG_ý Üfõ Fh÷ H=BKJFGNOIJq4q4FZqrIJB9=>5IL9cDGIJ[>9c@C>,(IJ9=@C>N·FGQT>=9=@C>,KJ<=9=jB5KLYJFZ?A?A>£G_ â-<=FG9=[BlIJKb[=ILNS>@C@CBNO>duB=NOIJ>9=@CFG@CBl<=9=IJsCBNSQT>QR>9=@m>MbKJYLB9c[F¡?AIH=NSBH=FGjFu9=>K QTFG@C>NSIJFGKJ>áDGB9áKJF2V=>KJBDGIJ@C&[=IusCFG?A>úírîL >çKLFÞ?A<=F7H=BKJFGNOIJq4q4FGq4IJB9=>á?rI QTFG9=@CIJ>9=>uH=>=NOH=>9=[=ILDGBKJFGNO>pFGKJKJFH=NOBIJ>q4ILB=9=>p[>K [=ILNS>@C@CBNO>=_ ÜbYJIL9c[=ILDG> × θ ÚM(V=IJ?Z@CB [=FGKLKJFúH=BKLFGNSILq4q4FGq®ILB9c>/?A@CNSFGBNO[=IL9=FGNSILFGM(ÛDGB=QTH=NS>?AB/@CNOF KLYJIJ9=[IJDG>Þ > K^YJIL9=[=IJDG>ß _pâ-<=>=?A@CYJ<=KJ@mILQRBç[>@m@CBIJ9=[ILDG>Û ä åZGã®åA åZ^ãç>=[ KLYJIJ9=[IJDG>dVcIJ?A@CBd[FGK^KLFeDGB=QRH=B9c>9=@C>d?A@CNOFGBNS[IJ9=FGNOIJFe9=>KbDGFZ?ABdH=FGNS@CILDGB=KLFGNS>pIL9uDG<=I θ î MDGILBp9c>KoDGFG?ABlIJ9lDZ<=In9djIJFGDG>lH=NSBHNOIJB9=>KH=IJFG9=B[>KJKJFpKJFGQWIJ9=FpKL<=9cjBKJYLFG?A?A> πØ ¢=_¾ÕKÌDGB9=@CNSFGNOIJBM¾?A> θ )q4>NOB=M¾DGIJBì9ì)BNS@CBj B9cFGKL>0FGKJKLF)K^FGQRIJ9=FGMÌ;=<=FGKJ<c9=;=<=> H=BKJFGNOIJqrq4FGq4ILB=9=>ö[>KJKJYLB9c[=F*IL9=DGI^[>9=@C>ù?ZFGNSú?Z>cQTH=NS>öH=>NOH=>9=[IJDGBKJFGNO>öFGKJKJYLFZ?A?A> B@C@CILDGBp>pVc>[NOïKJYLIJ9=[=IJDG>¡BNO[IJ9=FGNOIJBT _ i>Na<=9 θ j>9=>=NOIJDGBM]K^FeNS>KJFGq4ILB9=>uDGPc>pKL>j=FW × θ ÚgFW >R Ù ®Ö E x = E0 cos φ p y. x. 0. p. y. 0. p. 0. p. ⊥. ⊥. ⊥. ⊥. ||. ⊥. ||. CAPITOLO 2. ⊥. 19.
(9)
(10) . 2. . θ0 2. +. . 2. θ0. =. 2. . 1. θ0. ×Ø _Jü Ú. 2. i>NaILK Ó gÔ M]FGU=U=ILFZQRBM]F Ø Ù ÷ M ô Ù4_ nÙ d>T ô Ù®_LÓ Ø ø Ø Á_ v-wyx]wyx ¾{ GpycGyf~|h{ }~| {®Gh d=uy~fL{®{ = |]~|h ~=cG=y| Õ[>?A?ABöDGB9=?AIJ[>NSILFZQRBöIJKDGFG?ABöIJ9ùDG<=I,KLYJB9=[cF*IL9=DGIJ[>9=@C>ù?A<cKLKJF*KJFGQWIJ9=F*?AILF H=BKJFGNOIJqrq4FG@CF¡K^IL9=>FGNSQR>9=@C>pDGB9p<=9pFG9=j=BKLB ;=<cFGKL?rIJFG?AIJ_]8:9u<=?ADZIJ@CFe[FZKLKJFeKJFZQRIJ9=FGMb[cI ?AH=>?A?ABNO>5GMKLYJB9=[Fl?Z@CNSFGBNO[=IL9=FGNSILFl>hKJYLB9c[φÝFBNO[=IL9=FGNSILFlNOIJ?A<=KL@CFG9=B(?AsCFG?AFG@C>([I<=9=F ;=<=FG9=@CIJ@C δ F%DGFG<G?ZFh[=>KJKJ>,V=>KJBDGIJ@C[=I-sCFG?A>5[ILV=>cNO?A>DGB=9,DG<=I?AI-H=NSBH=FGjFc9cB9=>K QT>=qrq4BpU=IJNOIJsCNOFG9=j=>9=@C>oÖ ⊥. ||. ⊥. ×Ø _ Ú. E x ' = E 0 cos φ p E y ' = E 0 sin φ p e. − iδ. ÜbBp?AsCFG?AFZQR>9=@CB δM]sCNSF¡K^YJB=9=[Fe?A@CNOFGBNS[IL9cFGNOIJFe>p;c<c>KLKJFeBNO[=IL9=FGN·ILFGM eH=FGNOI FfÖ Ú _LÓ Ú 2π θ − × Ø × δ= λ >9=>NSFGKLQR>9=@C>MhILKhDGFZQWH=Bñ@CNOFG?AQR>?A?ABñ[FZKLKJF KJFGQRIJ9=F P=F <=9=F H=BKJFGNOIJq4q4FGq4IJB9=> >KLKJIJ@C@mILDGFZ_oi>=N φÝ ô Ó ÷ Mn?AIoV=>NOIJsCI^DGFG9=Bt[<=>lDGFZ?ZII^9=@C>NO>?A?AFG9=@CIÖf;=<=FG9=[B δ ô ý õ ÷ IJK QT>=qrq4Bd?AI]DGBQTHcBNO@CF¡DGBQR>d<=9=F¡KJFGQRIJ9=Fd å ä ãd ã rM]DGILB¡KJF¡H=BKJFGNOIJqrq4FGq4IJB9=> [>KJKLYJB9=[F <c?ADG>=9=@C>ß0[I^V=>9=<=@CF [F0KJIJ9=>FGNO>ßF0DZIJNODGB=KLFGNS"> !Ì;=<=FG9=[B Ù4ø ILK QT>=qrq4B?AI
(11) DGBQRH=BNS@CFDGBQT><=9=FKJFGQTIJ9=FZ$ #T& %Zã®brM
(12) DGIJBKLFH=BKJδFGNOô IJqrqrFGq4õ IJB÷ 9c> [>KJKLYJB9=[F0@CNSFZ?AQT>=?A?AFììFG9=DGBNSF0KLIJ9=>=FGNS>MWQRF0NSI^?A<=KJ@F0Hc>NOH=>9c[ILDGB=KLFGNS>ßNSIJ?AH=>@C@CB FGKLKJFH=BKJFGNOIJqrq4FGq®ILB=9=>p[>KJKJY^B9=[FeIJ9=DGIJ[=>9=@C>_ ⊥. 0. x Asse straordinario n(θ0). A φa. P. φp. z. y Asse ordinario n⊥. A¦ § ¨ ©ªC«
(13) ¬® ¬° 'b²¿ ¿ ³º È·º¹c¼L²m¶Áµ¸¹cºTÈ·»)(cºÂ
(14) ²S¼ µ»O²¾´¥ºÆ®À µ²OÈ·È:µg´¥ºÀ~¿=¸ À²m³Cµ ¶·¶4²S¼L¸ ³OºÌÄlºW´®ºÀ ÀSÉ ²m¹=²mÀ µ ¶·¶r²S¼L¸³º ÑbË+* Àï´µ ³º¥¼J¼y¸³Oº(´¥º Àk¹cºÂ̲·¼ µ»S¸Å¹=¸¹(³²:¿ ¿ ³º È·º¹c¼L²S¼L¸eµ ¹tÎLµ Æ=ó²mÅÆ µ:²O»Sºe¹cº À¿¥µ:²:¹=¸Êr¶hºÀ:²dÈSÃ¥² ¿®³¸µ:º¶·µ:¸¹cº È·ÃÀr¿ µ:²¹¸-´¥ºÀ À:²fÀ:²Âµ ¹=²½ Àù¥Æ¸]Ê~Ë 9ßQRB[B2Hc>N%[>=@C>NOQRIL9cFGNO>Þ?AH=>NSILQR>9=@CFGKJQR>9=@m>ÞKJBÞ?AsCFG?AFGQT>=9=@CB δMTIJ9=@CNOB=[B@C@CB [FGKLKJF7U=ILNSILsCNSFG9=j>9=q4Fç[=>=KLKJFçK^FGQWIL9=FGMp2;=<=>KJKLB[=IpH=BNSKLF7@CNOF7[<=>H=BKLFGNSIJq4q4FG@CBNSI IL9=DGNSBDGIJFG@CIJ_8K?A>DGB9=[B H=BKJFGNOIJqrq4FG@CBNS>ÿ[=>@C@CBæGJJ¤r¤4]ä ã®åA ×&, ILj<cNF Ø _ ÙrÚ_ B9=?AIL[=>NOIJFZQTB5IJKDZFG?ZB%j>9=>=NOFGKJ>,IJ95DG<=IkIJKH=BKJFGNSIJq4qrFG@CB=NO>5i0sCBNOQRI<=95FG9GjBKJB φÝ CAPITOLO 2. 20.
(15) DGB9 KJYJFG?A?Z> ¢ >æKJYJFG9=FZKLIJq4qrFG@CB=NO> Õ#sCBNSQTI <c9 FG9=jB=KLB φ- _ ÜbF , IJj<=NOF Ø _ Ø NOFGH=HNS>?A>9=@CFáKLFáH=B?AIJq4I^B9=>úNO>DGIJH=NSBDGF[>=jKLIdFZ?Z?AId[=>Id[<=>úH=BKJFGNOIJq4q4FG@mBNSIL_dÜbF H=NOBIJ>q4IJB9=>p[>Kf[=ILNS>@C@CBNS>p[>Kf9c>QTFG@mIJDGBu?A<=K]H=I^FG9=Bp[>=KLKJYJIJ9=@C>NSsCFGDGDGIJFeKL<c9cjB¢=_ óBHBÛKLYJFG@C@CNOFGVc>NO?AFGQR>9=@mBÛ[IÕMI^K?A>j9=FGKJ>úNOI^?A<=KL@CFH=BKJFGNOIJq4q4FG@CBÛKJIL9=>cFZNOQR>9=@C> KL<=9cjBpÕ>[pP=FeFGQTHcIL>=q4q®F]Ö E ' = E ' cos φ + E ' sin φ = E (cos φ cos φ + sin φ sin φ e ) ×Ø _ . Ú / NOFGMl;=<=>=KLKJBúDGP=>ÛIJ9=@C>NS>?A?AFááKLY^IJ9=@C>9=?AIL@mÞ[>KJKJYJB9=[Fá@CNOFG?AQR>=?A?AF [BV=> γ <=9 B HH=B=NO@C<9=BúDGB>ssCIJDGIJ>9=@C>_lÕ H=FGNO@CIJNO>ú[FGKJKJF ×Ø _ .~ÚMl[=IB=HγBÛ[EFG'⋅KL(DGE<=')9c]I H=FG?A?AFGjjIJM]NOI^DGFGV=IJFZQTBpKJYJ>=?AH=NO>?A?AIJB9=>pH=>NaKLYJIL9c@C>9c?rIL@C Ö x. a. y. a. 0. p. a. p. a. − iδ. *. I = I 0 cos 2 (φ a − φ p ) − sin 2φ p sin 2φ a sin 2. [BV=>10 KLYJIJ9=@C>9c?AIL@CïQWIL?r<=NSFG@CF¡Hc>N φÝnô φ- ôtõ ÷ _ â-<=FG9=[B I¾[<=> H=BKJFGNOIJq4q4FG@CB=NOI¾?ZB=9=B IL9cDGNOBDGIJFG@CILMÌDGILB= NOIJ?A<=KL@CFfÖ I = I 0 sin 2 (2φ p )sin 2. δ 2. φ-. δ 2. ×Ø _ Ú. ô φÝ − ý õ ÷ M¾KLYJIJ9=@C>9=?AIL@m ×Ø _Lø Ú. A? ?Z>=NOV=IJFGQTBDGP=>20 ô5õ H=>N φÝ-ô,õ÷ M ý õ ÷ MÙ4ø õ ÷ M Ø õ ÷ Mn3ü . õ~÷ _ I 4d?AIJj9=IJsCILDGFdDGP=>=M @CNOFtH=B=KLFGNSILq4q4FG@CBNOIgIJ9=DGNOB=DGILFG@CI^Mg9=B9hFGUU=ILFGQRB%?A>j=9=FGKL>h@CNOFG?AQW>?A?AB%Bj=9=IgV=BKL@FDGP=> KLYJFG?r?A>á[>KeH=B=KLFGNSILq4q4FG@CBNO>çi 2H=FGNSFGKLKJ>=KJBáB[çBNO@CBj=B 9=FGKJ>áFGKJKLFßH=NOBIJ>q4ILB=9=>á[>=K [ILNS>@C@CBNS> ?A<=KïH=IJFG9=B [>=K^KJFìKJFZQRIL9=FZ_¾890FGKL@CNS>0H=FGNOBKJ>M¾?A> KJFH=BKJFGNOIJq4qrFGq®IJB=9=> [>K DGFGQTH=B(IL9cDGIL[>=9=@C>hP=F?ABK^FGQR>9=@C>hKJFlDGBQRH=B9=>=9=@C>h?A@CNOFGB=NO[IJ9=FGNOIJFB(?ZB=KLFGQW>9=@C>(KLF DGBQRH=B9=>9=@C> BNO[IJ9=FGNOIJFGMþKLF ?Z<cF H=BKJFGNOIJqrq®FZq4ILB=9=> 9=B9 DGFGQTUIJF [<=NSFG9=@C> KLYJFG@C@CNOFGV=>=NO?AFZQT>=9=@CB [>KJKJFúKJFGQRIJ9=F > KJFúNOFG[=IJFGq®IJB9=> úIJ9=@C>NOFZQR>9=@C> FZ?r?ABNOU=IL@CF [FGKLKJY^FG9=FGKLIJq®qrFG@CB=NO>Õ_8y9=BKL@CNS>MKLYJIL9c@C>9=?rIL@C ×Ø _Jø Ú*ê9=<=KJKJFêFG9=DGP=>Hc>N <=9=B ?AsCFG?ZFGQW>9=@CB δ H=FGNSIFG[d<=9dQT<cKL@CIJH=KLBdIL9=@C>=NOBl[I3ü . õ÷ _8KDGFG?AB δ ô%õ÷ ?AIHNO>?A>9c@CFGM FG[)>=?Z>=QTH=IJBMa?A>h × θ Ú ô _ I 45?AIaV=>NOIJsCIJDZF,;=<=FG9c[B θ ô0õ÷ × DGsN ×Ø _Lü ÚÚMaDGIJB ;=<=FG9=[BtKLYJFG?A?A>(B@C@CI^DGB(dBNS@CB jB9=FGKJ>(FGKJKLYJIJ9=@C>NOsCFGDGDZIJFl[>=KJKJFdKLFGQWIJ9=FG_nib>NïInDZNOIJ?Z@CFGKJK I KLIJ;=<=IJ[I
(16) 9=>=QTFG@mIJDZI
(17) ?AIÌH=FGNSKJF[IFGKJKJIL9c>FZQT>=9=@CBìBQT>cB@CNOB H=IJDGB × DGsCN û Ù4_ ~Ú_
(18) ò <=@C@CFGV=IJFGM KLYJIJ9=@C>9=?rIL@C?AIFG9=9=<=KJKJFpFG9=DGP=>l;=<=FG9=[B δ p<=9dQT<=KL@CIJH=KLBlIL9=@C>=NOB¡oã JLãp[Io5ü . õ ÷ _ 8:9;=<=>?A@CYJ<=KL@CI^QRB(DGFG?AB(>=9=@CNSFG9=B(IJ9tjIJBDGB(j=KLInIJ9=[I^DGI[=InNSILsCNSFGqrIJB9=>t[>=KJKLFdKJFZQTIJ9=FGMoIJK ?A<=Bt?AH=>?A?ABNO>hp>FG9=DGP=>KLFpKJ<=9=jPc>qrq4Fd[YJB9=[=Fp[>KJKLFpNSFG[IJFGq4IJB9=>IJ9=DGIJ[=>=9=@C>_of>=M FG[0>?A>QRH=ILBMÌFGUU=IJFZQTB δ ô 5ü . õ ÷ IJ90DGBNSNOIJ?ZHcB 9[>9=q4F)[>KJKJFNSFG[=IJFGq4IJB9=>0NSB?A?AFGM ;=<=>?A@CF(?AFGNSdUKLB=DGDGFG@CF([=FGKJKLYJFG9=FZKJILq4q®FG@CBNO>%Õ7>%9B 9hFGV=NO>QRB59=>?A?A<=9=F(NSFG[IJFGq4IJB9=> @CNOFG?AQR>?r?ZFG_ò <c@C@CFGVcILFGMgHc>NRFGKJ@CNO>%KJ<=9=j=P=>q4qr>h[YJB=9=[FGM δ FG?r?A<=QR>=NOpV=FGKJBNOI[IJV=>NS?AI [Fuü . õ÷ >M;=<=IJ9=[IJM9=B9lu[>@C@CBlDGP=>lKJYJIL9=@C>=9=?AIL@CT[>KbsCFG?ADGILBd@CNOFG?AQT>c?Z?ABd?ZI^Fuq4>NOB_ f>IL9cV=ILFGQRBNOFG[IJFGq4ILB9c>IJ9=DGIJ[>9=@C>UIJFG9cDGFGM DGP=>%KJF5?ABV=NSFGHH=B?AIJqrIJB9=>[I B=9=[> QTB=9=BDGNOBQRFG@CIJDGP=>0[IÌKJ<c9=jP=>=qrq4>0[YJB9=[F)[IJV=>NS?r>M¾IJ9ì@CNOFZ?AQWIL?A?rIJB9=>0?AI
(19) FGV=NSFG9=9B DGBKLB=NOIÛDGBQRH=KL>=QT>9c@CFGNOIúFGK NSB?A?ABMÛH=>NODG$P 6KLF DGBQTH=B=9=>9=@C>\NSB?A?AFV=IJ>9=> FG?A?ZB=NOUIJ@CFZ_ /. ⊥. CAPITOLO 2. 21.
(20) v-wyx]w v 7k8y|fcGyf~|hL89yy | {: <;<;yl{®d tu| ZZhyGf{ ] h|hy=;{¥c=L > ~Lf B9=?AIL[=>NOIJFZQTB=MoFG[>=?Z?ABMbIJKoDGFG?ABIJ9lDG<=IJMFpDGB9=@CFG@m@CBDGB9lIJKQTFG@C>=NOIJFGKL>FG9cIJ?rB@CNOBH=B K^IL;c<=IL[=BÚM¡2H=B?A@CF2<c9=F2K^FGQRIJ9=F2[=I¡QWFG@C>NOIJFGKJ>çI^?ZB=@CNOBHBç@CNOFG?AH=FGNS>9=@C> × DGDGNOBIJQR?A@C>(FGKLFGKJBá ×sCFGDGDG>pB@C@C[(IJDG>=FG?AQW>>QR9=H=@CIJ>pB(H=I^IJKnFGV=9c>>p@CNO>pBH=Ú FG[NSInFGILKL9=K^>[KJIJ> DZ>([=IJjIn<=NSNSILsCF NSFGq4_LüIJBÚ9=_ >u@ ?p>([=Io?AH=>?A?ABNS>%< ?AMoDGB9 fIkH=<< 4t[ILQRB?A@CNSFGNO> Ù ïDGP=>5IkDGB>=ssCIJDG&× IJ,>9=@CIk[IkØ NOIJsmKJ>?A?rILB9=>%H=>NTIJKkNOFGjjIJB,9=_kü,[I IJj<=NSF Ø _Lü Mf9=>KfDGFZ?ABp[=IfIJ9=DGIL[=>9=q®Fe9=BNOQRFGKJ>Mf?AB9cBoÖ , n −n n − n(θ ) r = ; r = ×Ø _ ý Ú m. ⊥. ⊥. ||. nm + n. ⊥. m. 0. nm + n(θ 0 ). [ BV=>å ¡IJK]DGB>sCsCIJDGIJ>=9=@C>d[I]NSILsCKJ>?A?rIJB9=>dH=>NKLFeH=BKJFGNOIJq4q4FGqrIJB9=>dB=NO[IJ9=FGNOI^F¡>åBA&A ILK DGB>sCsCIJDGIL>9c@C>p[=I]N·ILsCKJ>?A?rILB9c>pH=>NKJFeH=BKJFGNOIJqrq4FZq4ILBc9=>p?A@CNOFGBNS[IL9=FGNSILFZ_ 8kNOFGjjIn9=_ Ø C > h[I ILj<=NOF _JühP=FG9=9=B(<9DGFGQTQWI^9=B(B@C@CIJDGB([IJV=>NS?AB(>MnsC<BNSI[=FGK QTFG@C>NSIJFGKJ>MtsCFG9=9=B IL,9=@C>=NsC>NS>Ø 9=q4FG_(fIJF7å - ?ILKtDGB>sCsCIJDGIL>=9=@C> [I(NOIJsCKJ>?A?rILB9c>/Hc>N KLYJIJ9=@C>NOsCFGDGDZIJFÛFGNSIJEF D QR>q4q4B IJ?AB@CNOBHB=_(9=YJB 9=[=FÛDGP=> IJ9=DGIJ[> 9=BNOQRFGKJQR>=9=@C> ?Z<cK ?AIL?A@C>=QRFeNOFGH=H=NS>?A>9=@CFG@CBpIJ9 , IJj<=NSF Ø _LülPcF¡If?A>j<=>9c@CI]DGB>sCsCIJDGIJ>9=@CI][=IfNOIJsCKJ>=?A?ZIJB9=>=M NOIJ?AH=>@C@CILVcFGQT>9c@C>pHc>NKJFeDGB=QTH=B=9=>9=@C>pBNS[IL9cFGNOIJFe>p;c<=>KLKJF?A@CNOFGBNS[IJ9=FGNOIJFfÖ ⊥. tot F iδG = am+ F ⊥ e ⊥ I K ) L K M N O)O = N JH + N O)O δH 2. F. × Ø _Ù õ Ú [BV=> δ?Û KLBñ?AsCFG?rFGQW>9=@CBñ@CNOF IJK5NSFGjjIJBñ9=_ ù>ñILK%NOFGj=jILBñ9c_ Ø >ñV=FGK^> _Ü]> NO>=KLFGq®IJB9=I ×Ø _ Ù õ Ú*V=FGKJjB9B 9=>=KDGFG?AB IJ9èDG<=IKJ> δ Q = (4π S Q R Q ) P λ NOIJsCKL>?A?AIJB9=I QT<=KJ@mIJH=KL>u?AIJFG9cBp@CNOFG?ADG<=NSFGU=ILKJI^_ 0. Aria. Mezzo isotropo (nm). 2. 4 1. Cristallo Liquido. 5 3. dm. d. ¦A§ ¨ ©ªC«u¬® T °VU¹tÂ
(21) ²S¼Lº³Cµ:²:ÀºeµÈ·¸®¼ ³O¸¿¸Å¾´ µ¾Èy¿º ÈSÈÁ¸ ³ºt´XWhºTµ ¹=´µ:»Sºt´µk³Cµ ÎL³²m¶·µ¸¹cº¹YW·Å¾½W¿=¸®ÈÁ¼L¸t² »O¸¹=¼L²O¼J¼J¸W»S¸ ¹ïµ Àn»:³Cµ:È·¼L²mÀ À:¸À 8µ Z õ´®¸ Ë * ¹WÎJµ Æ=ó²
(22) È·¸ ¹=\¸ [JµÈ:µ Í µ À µÀSÉ ¸¹=´ ²µ ¹»:µ:´¥º¹c¼Lº ]Á_¯ ^gºÀSÉ ¸¹=´ ²³Cµ ÎyÀº ÈSÈ·² ÈSÃÀ ÀSɵ ¹=¼Jº³mÎÁ²S»O»mµ²R²:³Cµ:a² `Â
(23) º¶Á¶r¸aµ:È·¸ ¼ ³¸¿=b¸ ]L¬ ^ ÅfÀ·É ¸¹=´ ²ï¼ ³²OÈÂ
(24) º ÈSÈ·²¹=ºÀfº ¶ ¶r¸aµ:ÈS¸¥¼ ³¸¿=c¸ ]T:^dº Z ú À À² ³Cµ ÎLÀº ÈSÈS²´ ²:À ÀSÉ µ ¹=¼Jº³CÎ ²S»O»mµ²nÂ
(25) º ¶ ¶r¸µÈ·¸¥¼ ³¸¿<¸ `fe® ± ]g^nºÅ=µ ¹ ÎLµ ¹cºÅ=ÀSÉ ¸¹=´ ²a¼ ³²OÈÂ
(26) º®È·ÈS²o¹cº "À e \± ]h:^$Ë iA¸¹=¸ ÈS¼L²O¼Jº-¸ º ÈSÈ·ºbÀº³Cµ ÎLÀº ÈSÈ:µ¸¹¥µ4Â
(27) ÃÀ¼ µ ¿¥À:º Ë j IJQTHcBNO@CFG9=@C> ?AB@C@CB=KLIJ9=>FGNO>0DGP=>Mï9=>=KLKJ> BNS[IL9=FGNSIJ> DGB=9=[IJqrIJB9=I¾?AH=>NOIJQW>9=@CFGKLIJM¾KJF ?A@CNO<=@C@C<=NSF)[>=KLKJYJIJ9=@C>NSsCFGDGDZILFsCNOFKJFKLFGQRIL9GF)IJ?AB@CNOB=H=F)>ìIJKÌDGNSIL?A@CFGKJKLBìKJIJ;=<=IJ[=Bì)H=Ik CAPITOLO 2. 22.
(28) DGBQRH=KLIJDGFG@CFZ_ñ89XH=FGNS@CILDZBKJFGNS>Mñ?AB@C@CILKJI*?A@CNOFG@CI*[I*QTFG@m>NSILFGK^IñI^?ZB=@CNOBH=I × 8ò / M H=BK l ILQRIJ[>_^_L_JÚR?ZB=9=B)H=NO> ?A>9c@I ?A<=KLKJF5?Z<cH=>NOsCIJDGIJ>[>KJKJF,KJFZQRIL9=F5IL?AB=@CNOBH=F,DGP=>)IJ9 DGB9=@CFG@C@CB%DGB=9hIJKgDGNSIL?A@CFZKJKJBhKLIJ;=<=IJ[B_g89h;c<=>?A@CBhDGFZ?ABMgIDGB>sCsCIJDGIL>=9=@CI[INOIJsCKJ>?A?AIJB9=> N > N A&A9=B9(?AB9=B5H=I kt>=?ZHcNO>?A?AIg[FZKJKL>(?Z>=QTH=KJI^DGIgNS>KJFGqrIJB9=I ×Ø _ ý ÚMgQRFt[IJH=>9=[=B9=B [FGKLKJ>lDGFGNSFG@m@C>NOIJ?A@mILDGP=>l[=>=jKJI?A@CNOFG@CIb?AB@C@CIJKJIJ_89=BKJ@CNO>=M N > N A&A ?AB9BMbj> 9=>NSFGKLQR>9=@C>=M jNOFG9=[=>qrq4>2DGBQTHcKL>?A?A>_Tib>N,@CFGKJ>7QRB@CIJV=BMe9=>K?A>j<=IJ@CBM?ADGNOIJV=>NS>QTB2@C<=@C@C>7KJ> NO>KJFGq4ILB9cI]9=>K DZFG?ABpj>9=>=NSFGKL>pIJ9¡DG<=I N > N A&A=?AB9=Bp9c<=QT>=NOIfDGB=QTH=KJ>?A?rIL_ 8:KgsCFG@C@CBhDGP=>%KJYJB9=[Ft?A@CNSFZBNO[IJ9=FGNOIJFt>h;=<=>KJKLFBNO[I^9=FGNSILFtFGU=U=ILFG9cB%[<=>hDGB>smsCIJDGIL>9c@CI [IaNOIJsCKJ>?A?rILB9=>[IJV=>NS?AIa?r<=jj>NSIL?ADG><=9QTB=[B?Z>=QTH=KJIJDG>)Hc>NuQTIJ?A<=NOFGNS>KLY^FG9=jBKJB FGqrIJQW<=@CFGKL> φm [>Kf[=ILNS>@C@CBNS>pIL9u?r<=H=>NSsCILDGIJ>M DGBQT>u?AFGNSR[=>=?ADGNOIJ@C@CBp9=>=K û4Ø _ Ø _Ù4_ v-w v n|] ftfpG {®pf|f=; |+_;L|]~|( o| ~|f{o]Ld |]L93;f{ 5fL GLp~L|hy(y ;c|({® L|fcGq psrut3vxw f<=HH=B=9=ILFGQRB/[I(FGV=>NÞQRIL?A<=NSFZ@CB/KLYJFG9=jBKJB/FGq4ILQR<=@CFGKJ> φm [>=Kh[IJNO>@C@CBNS>/?A<=KLKJF ?A<=H=>NOsCIJDGIJ>%IJ9=[=IJV=IL[<cFG@CFl[FGKLKJY^IL9=@C>=NOsCFGDGDGI^Ft?A<=U=?A@CNOFZ@C5B D Üb`Mg?A>9=q4FFGV=>NTFZHcH=KLIJDGFG@CB DGFGQTH=Ip>cKL>@C@CNSILDZIpBáQRFGj9=>@CIJDGIL_u89á@CFZKLIuDGB9=[=ILq4IJB=9=ILMuILKu[IJNO>@C@CB=NO>áDGBIL9=DGI^[>DGB9 KL8Y yEz z M|{ yE}E~ M × DGsCN û Ù®_ Ú_ì8KìDGB>=ssCILDGIJ>9=@C > [Iì>9=>=NOjIJF [>K^KJYLFG9=DZBNSFGjjIJB FGqrIJQW<=@CFGKL> × DGsCN × Ù®_ Ù ý ÚÚH=<< 4ú>=?A?A>NS> [>=@C>NSQTIJ9c- FG@CB <=@CILK^IJqrq4FG9=[B K^F H=NOBDG>[=<=NOF [>?ADGNOIJ@C@mFe;=<=If[=If?A>j<=IJ@CBÖ ÕHH=KJILDGP=IJFGQRBM-?A<=K-DGFGQRHcILB=9=>M <=9,DZFGQTH=BQRFGj9=>=@CIJDGB × B>KJ>@C@CNSIJDGBÚï9=B@CB_ • ën?A?AB(j>9=>NSF<=9(QRBQR>=9=@CBh[=IgsCB=NOq4FDGP=>(DGNO>Ft<=9cF[IJ?A@B=NO?AIJB9=>h[cI s~z3 9=>KVcBKL<cQT>Máj>9=>=NOFG9c[BMá?A<=KJKJYJIL9=@C>=NOsCFGDGDZIJFGMá<c9èQRBQR>9=@CB [IçsCBNOq4F >KLFG?A@mIJDGBáDGP=>çNO<=B=@CFÞILKe[=ILNS>@C@CBNO>ç?A<=KLK^F2?r<=H=>NSsCILDGIJ>çsCIL9=DG<P 6ßILKeQRBQR>9=@CB >KLFG?A@mIJDGB 9=B9 UIJKJFG9=DGIJFG@CB [FZK QTB=QT>9c@CB [=I#sCBNSqrF [B=V=<=@CB FGKLKJYJFG9=DGBNOFGjj=ILB_ f>FGUUI^FGQTBFGH=H=KJIJDGFG@CB)<=9DGFGQRH=BQTFGj=9=>@CILDG B FG[<=9 FG9=jBKJB β DGB9,KLYJFG?r?A>sFZDGIJKJ>M-KJYL>;=<cIJKJILU=NOIJB@CNSF%I-[=<=>QRBQR>9=@mI [=I sCBNSq4F5 × DGsCN × Ù4_Jü Ø ÚÚ¥Ö Y ×Ø _Ù ÙrÚ (β ) = δφ µ χ [F2DG<=I¡B@C@C>9GILFGQRBáKJF2N·B@CFGq4ILB9=> δφm [>K¡[IJNO>@m@CBNS>áIJ9ç?A<=H=>=NOsCIJDGIL> × DGsCN × Ù4_Lü Ó~ÚÚ¥Ö µ χ Y (β ) ×Ø _Ù Ø Ú δφ = = Y (β ) ⊥. ⊥. ⊥. 22. 22. •. 0. 0. . ξ. [BV=>ut7KLF7DGB?A@mFG9=@C>>KLFG?A@mIJDZFç[Is ~z M χ- çKJYLFG9cIJ?AB@CNOBHcILF7[>KJKLF ?A<=?ADG>@C@mILV=IJ@CêQWFGj9=>@CIJDZF > - ILK DGB>=sCsCIyDGIJ>9=@C> [=I >9=>NOj=ILF [=I FG9=DGBNOFGj=jILBçFGq4ILQR<=@CFZKJ>_e`>KJKLYJ<cKJ@CIJQRBá@C>NSQRIJ9=>çFÞ[>?A@CNSFÞ9=>KJKLY^>;=<=FGq4IJB9=> 0>=?AH=NO>?A?rF0IJ9ßsC<=9=q4ILB=9=>Þ[>KJKLq F ¡¢<£=¤ M5¥¥ y§¦$~ ×M Ø z_ ÙN Ø y
(29) ¨=ÚMR©5KLy F0¥ ~NO©B¢ @CMFGq4IL¦3B=ª 9=> [δφ m >sIJ9=IJ@CFçIJ9 × Ù®_LünÙ4ÚÚ%> [>KJKJ« F ¡¢<£"¤ M5¥¥ y¬}E© M N M ¢ ¥ y × M
(30) y < £ ¢ ~ E } y = [ > C s L I = 9 J I C @ F J I 9 ® Ù _ ~ . Ú Ú _ I¯ L?A<=NSFG9=[BÞξKJ®F × NOB@CFGq4IJB9=> × δφmØ >ÞDGB 9=B=?ZDG>=9=[BÞKL>ÞDGB?A@CFG9=@CIR[>KRDGNOIJ?A@mFGKLK^B KLIJ;=<=IJ[BFGKJKJFñ@C>=QTH=>=NOFG@C<cNOF*FGKLKJFñ;=<=FGK^>FGUU=IJFZQRBöBH=> NSFG@CB>KJ>FGKJ@CNO> jNOFG9=[=>qrq4> IJ9 jIJBDGB × β° ÚMXHB?A?AIJFGQTB NOIJDGFGVcFGNO> IJKdDGB>sCsCIJDGIL>=9=@C>ú[=I FG9=DGBNOFGj=jILBpFGq4IJQT<c@CFGKJq > -_. CAPITOLO 2. 23.
(31) v-w vwyx n|] f({ L|fcc u|]{¥;2;ft~(G]L,~fy{¥yZG=f{¥|h{¥]~|¬psr±tv²w B9=?AIL[=>NOIJFZQTBd<c9psCFG?ZDGI^BdQRB9=BDGNSBQRFG@CILDGBdDGP=>d?AI]H=NOB=H=FcjF¡KL<c9=jBdKJYLFG?A?A> ¥ >dDGP=> %H=BKJFGNOIJq4q4FG@CBKJIL9c>FGNOQR>=9=@C>_-8K-sCFG?ADGIJBIJ9=DZIJ[>?A<%<=95?ZIJ?A@C>QWF%DGB?A@CIJ@C<cIL@CB,[Fh[<c> KLFGQWIJ9=>pIL?AB@CNSBH=>p@CNOFeKJ>u;=<=FGKJI]V=IJ>9=>pIJ9=?r>NOIJ@CBp<=9¡DGNSIL?A@CFZKJKLBpKJIL;c<=IL[=Bp9=>QRFG@CI^DGB_f9=F NOFGH=HNS>?A>9=@CFGq4ILB=9=>ú?ADGP=>=QTFG@CI^DGFá[>=KLK^FáDG>=KLK^Fá> [>IdsCFG?ADZIdNSILsCKJ>?A?rId[FGKJKJ> V=FGNOIJ> IL9=@C>=NOsCFGDGDG>5(QRB?A@CNOFG@mFhI^9 , IJj<=NOF Ø _ _i>=NeDGB=9=V>9=IJ>9=q4Fh[=INSFGH=H=NO>=?Z>=9=@CFGqrIJB9=>cM @C<=@C@CI-jKJI-FG9=jBKJI-NOFGHHcNO>?A>9=@CFG@CI-IJ9 , IJj<=NOF Ø _ )?AB9=B?A@CFG@CI->?AFGj=>NOFG@CI->,ILKNSFGjjIJB IL9=DGIJ[>9=@C>Þ&[I^?A>j9=FG@CB79=B=92H=FGNOFGKJKJ>KJB7FGKLKJY^FG?A?A> ¥ _Õö[cILsCsC>NS>9=q4Fß[>KT?rIL?A@C>=QRF NOFGH=HNS>?A>9=@CFG@CB IJ9 , IJj<=NOF Ø _Jü M(IJ9 DG<=I(K^FúKLFZQWIL9cFÛI^?AB@CNOBHcFÛFGV=>=V=FÛKJ> sCFGDGDG> H=FGNOFGKJKL>=KL>MR9=>Þ<c@CIJKJILq4q®ILFZQWBÞ<=9=F0DGB9ÞsCFGDGDG>Þ9=B9ßH=FGNOFGKJKL>=KL>_R89ß;=<=>=?Z@CBßQRB[=BÞILK sCFG?ADGILB2NSILsCKJ>?A?AB2[FGK^KJYLIJ9=@m>NSsFGDGDGIJF&FGN·ILEF D QT>=q4q4B2IJ?AB@CNOB=HB2&?A>H=FGNSFG@CB2[Fß;=<c>KLKJB NOIJsCKL>?A?AB [FGKJKJYJIJ9=@C>NOsCFGDGDGI^F QR>qrq4B IJ?AB@CNOBHc5B D Ü]` × IL9 , IJj<=NOF Ø _ M ?AB9=B NOIJ?AH=>@C@CILVcFGQT>9c@C>5IsCFZ?ADGIk9=_ïÙd>,9=_ Ø Ú_8:9cBKL@CNS>MIJKDGNSIJ?A@CFGKJKJB,K^IL;=<cIL[B5(DGB=9c@>=9=<=@CB sCNOFl[<=>tH=IJFG?Z@CNS>(IJ?AB@CNOBH=>(DGP=>(sCB=NOQRFG9=BMsCNOFl[InKJBNOB=M<c9tFG9jBKJB [InDGIJNSDGF _ 8:9%@CFGKQRB[BMIsCFG?ADGINSILsCK^>?A?AI[=FGKLK^Fh?A>DGB=9=[FhIJ9=@m>NOsCFGDGDGIJF Ü]´` D QTθ>³ q4q4B5IJ?AB@CNSBØ H÷ B dIJ9 IJj<=NSF _ Úg?AB9=BpFG9=DGP=YJ>?A?AIf?A>H=FGNSFG@CIf[FZIfsCFG?ADGI 9=_Ù¾>p9=_ _ ×óNO>FG9=jBj@CIfIJFG9=QT_füdBù>pDG9=B+_ ¶ 9 µù, ¸ > ·*jKJØ IFZ?A?AI,B=NO@CBjB9=FGKLI,9=>K,H=IJFG9=Bö[>KJKJYJIJ9=@C>NOsCFGDGDGI^F*Ø > FG?A?Z<cQRIJFZQTB/DGP=>/IJKh[=ILNS>@C@CBNO>/?AIJFÛBNOIJ>9=@CFG@CB*<=9=IJsCBNSQT>QR>9=@C>/BVc<=9;<=>M(DGB9 BNOIJ>9=@CFGQR>9=@CB%[>?ADGNOI^@C@CB5[FGj=KLIkFG9=j=BKLIkq®>9=IJ@CFGKJ> θm >%FGq4I^QT<c@CFGKJ> φm _kÜ]>5?A<cH=>=NOsCIJDGI IL9=@C>=NO9=>ç[=>KLKJ>7[<=>çH=IJFZ?r@CNO>7IL?AB@CNSBH=>ç?AB9=Bç@CNOFG@@CFG@C>7IL92QTB=[Bç[FßIL9=[=<cNONO>7<=9 FG9=DGBNOFGj=jILB%[>KJKLB%?A@C>?A?AB5@CIJH=B5>5FGKJKLIJ9=>FGQR>9=@mIk[=>Kk[=ILNS>@C@CBNO>%@CNOFtKLBNSB,H=FGNOFGKJKL>KJI^_ `>I]QT>@CB=[=IbNSILsCKJ>?r?ABQR>@mNOIJDGI]?ABKJBdKJYLIJ9=@C>NSsCFGDGDZILF¡@CNSF¡KJF¡KJFGQWIJ9=Fu8nIJ9 , ILj<=NSF Ø _ l>dILK DGNOIJ?A@CFGKJKJBpKLIJ;=<=I^[BpeNSIJKL>=VcFG9=@C>_ Raggio incidente. Angolo cuneo θW ≈2°. x. n. 1. n. 2 n. 3 n. 4. I. CLN II y. z. ¦A§ ¨ ©ªC«R¬4 gu° ¹SµÈ:µ:¸¹cºuÈS)» (cºÂ̲·¼ µ»O²´ ºÀ À²»OºÀ À:²´¥º À e® ± º7ºu´ ºµo³²mÆ Æ®µ ¸¥¼L¼ µ:»:µn³Cµ ÎyÀyº®È·È:µ ´®²:À À2 º [²m³Cµº µ ¹=¼Lº³mÎÁ²S»O»Sº®ËUO¹T»OÃC¹=º ¸ ´µ3e®± º,½f¿=¸ È·¼L¸ ¼ ³²k´ úoÀ:²:Âgµ ¹=ºaÈ·¸À µ:´¥º Å~¼ ³²OÈ:¿=²m³Oº¹c¼ µ~ºoµÈ·¸ ¼ ³¸¿=ºu» ¼ º²¼ ¼ ½ÁËS± ² À:²mµ ¹=´² ¼(=²À:ºaÎÁ²S»O»Oº¹=¸¹R¿c²m³²:À À:ºÀ:ºÅ»S¸®8È ¾k´ ²WÈ·º¿=²m³²:³º
(32) µ ÎÁ²SÈS»:µ]³Cµ ÎLÀº ÈSȵ²:À ÀºÈSú´¥Ã¥ºÈ·Ã¿cº³CÎLµ:»:µ » ³²:Æ®Æ µ ¹=ËJ¯ïº ¹=Ë
(33) ¬ ½C= ¿rÀ µg²m¹ Æ=¸À µÈS¸¹¸TÈ·¼L²O¼ bµ [¸À:Ã¥¼L²:Â
(34) º¹=¼JºTº®ÈÁ²mÆ=º ³²S¼ µgºaµ À Î ²OÈ·»mµ:¸aµ ¹»:µ:´ º¹c¼LºR½WÈ·¼L²O¼L¸ ´ µÈ·ºÆ ¹=²S¼L¸b¹=¸¹-¿=²m³²:À À:ºÀ:¸ ²:À ÀSÉ ²OÈSÈ·º¶o¿=º³]³Oº¹=´¥º³º]¿®8µ À8» (®µ²m³²fÀ:² ÎLµ Æ=ó¥²SË NOFGq4IJ>FGKJKJYJ<=?AB,[>KJKLFhKLFZQRIJ9=F%DGB95sCFGDGDG>9cB9HcFcNOFGKJKL>KJ>,>[>=KLK^F%sCBNSQRF%F%DG<c9=>B [>KJKLFçDG>KJKJFGMd?rIJFGQTB IJ9 jNSFG[B [IdHNO>=KL>VcFGNO> [ILNS>@C@CFGQR>9=@C> ILKdsCFG?ADZIJBúNSILsCKJ>?A?AB [FGKLKJY^IL9=@C>=NOsCFGDGDGIJF*QT>q4q4BöIJ?AB@CNOBH=5B D Ü]` × NOFGj=jIyBö9=_ Ø [I , IJj<=NSF Ø _ ÚMDcP=> DGB9=@CIJ>9=>pKJYJIJ9=sCBNOQRFGq4ILB=9=>p?A<=KLK^YJFG9=jBKJBpFGqrIJQW<=@CFGKL>¡[=>K][=IJNO>=@@CB=NO>_ CAPITOLO 2. 24.
(35) Õ ON IJjBNO>MhFG9=DGP=>*?A>*KJF NOFG[IJFZqrIJB9=>*IJ9=DZIJ[>9=@m>*?AI%HcNOBH=FGjF KJ<=9=jB*KLYJFG?A?Z> ¥ × H=IJ>jN<=HcNSF>9=[_IJlDGBsB=KLFGNONSQR>0FG9=FGBpKLKJYJILFG9=9@mj>=BNOsCKJFGI]DG[=DGILV=IJF>=NOKJ?AFZI]QR[=ILF¡9=Fq4>8ÁNSD BpDGNSDGILB ?A9u@mFGKJKJYLKLIJB09=@CKJ>IJ;=NSsC<=FGIJ[DGDGBILÚFeM¾FGIÌNOsCI^FGFE?ADfDGKJFGIuQWÙ5IL9=> F¡Ø8:_fó[II ,DGB9=?A>j<=Ø >9cqrFGM%I5DGB=>sCsCILDGIJ>9=@CI%[=I5NSILsCKJ>?r?AIJB9=>*>ñ[I%@CNOFG?rQRIJ?A?AILB=9=>ñ[F ;=<=>?A@CF IL9=@C>=NOsCFGDGDGIJFpIL?AB@CNSBH=Fd9B 9l?AB9=B(IJ?AB@CNOBH=IL_o`>DGB 9=?A>j<=>DGP=>t;=<=>?A@CFdIJ9=@C>NSsCFGDGDGILF H=NOB[=<=DG>á<=9=F2H=ILDGDGB=KLFÞQTB[=ILsCIJDGF2[>K^KJ>áH=BKJFGNOIJq4q4FGqrIJB9=I¡[>=IusCFG?ADZI¡@CNSFG?AQR>?A?rI¡B NOIJsCKL>?A?AI^_p@CI^KLIJq®qrFG9=[=B KJ>9cB@C> >?AH=NS>?A?AILB=9=Iu[>IuDGB>sCsCIJDGIJ>9=@CIu[IuNOIJsCKJ>?r?AIJB9=>> @CNOFG?AQRIJ?A?rILB=9=>9=>KJKLYJIL9c@C>NSsCFGDGDGIJFsCNSFI[<c>[IJ>=KL>=@m@NSIJDGIIL?AB@CNSBH=I Ù ÁMH=B?Z?AIJU=IJKL>=M H=>ÂN 4GMn[IJQRB?A@CNOFGNO>DGP=>(jKJIn>sCsC>@C@CIn[=InFG9=IJ?AB@CNSBH=IJFl[>IoDGB>sCsCIJDGIJ>9=@CIn[=InNOIJsCKJ>?A?AIJB9=> >@CNOFG?AQWIL?r?AIJB9=>?AB9=Bl[>=K@C<=@C@CB@CNOFG?ADZ<=NSFGUIJKJI;=<=FZ9=[BMDGBQR>9=>KbDGFG?ABlIJ9d>?AFGQR>=M jKLI]FG9=jBKJI][=I]IJ9=DGIJ[=>9=q4Fe?AB9=Bd@C<=@C@CI]IL9=sC>NSILB=NOI]F¡HcBDGP=Ibj=NOFG[IJ_]ib>N
(36) @CFZKJ>pQRB@CIJV=B=Mb9=>K ?A>j<=IJ@CB@CNOFG?ADG<=NS>NO>QRB;=<c>?A@CIoH=IJDGDGBKJIo>=sCsC>@C@CIo>lFG?Z?A<cQR>NS>QRBDGP=>IDGB>sCsCIJDGIL>9c@mI [I]@CNSFZ?AQRIJ?A?AIJB9=>pFG@C@CNSFGV=>=NO?ABpKJYJIL9=@C>NSsCFGDGDZILFFGNSILEF D KJFZQRIL9cFu8b?AB9=BpIJ?AB@CNOBHcIL_ > µ=_ BQR>&[=>?ADGNOIJ@C@CB fIJF KJYJFG9=jBKLB&@CNOFìKJYLFG?A?A>&[=>KWH=B=KLFGNSILq4q®FG@CBNO>&iá>&KJYLFG?r?Aà H=NO>DGφ>=Ý [>9=@C>QR>9=@C>M¾H=B?r?AILFZQRB ?ADGBQRH=BNSNO> IJK¾DGFZQRH=B >KJ>@C@CNOIJDGB0IL9cDGIL[=>9c@C> 9=>KJKLF DGBQRH=B9=>9=@C> ?A@CNSFGBNO[IJ9=FGNOIJF ×ÅÄ A&A Ú/>èIL9ê;=<=>KJKJF BNS[IL9cFGNOIJF ×ÅÄ Ú_áóBHBèKLF NOIJsCKL>?A?AIJB9=>ì[FGKJKJYJIJ9=@C>NOsCFZDGDGIJFQT>q4q4BìIJ?ZB=@CNOBH=5B D Üb`aMÌKJ>ìDGBQTHcB9=>9=@CI
(37) [ILV=>=9=@CFG9=B "rÖ A&A Æ N A&A YfDGB? Ú ôÆ Ä Ä × φÝ − φ m Y ?AIL9 × φÝ −φm Ú ×Ø _Ù4ü~Ú Ä ô N Ä [BV=> Ä Y&ÿKJYLFZQRH=IJ>q4q4Fÿ[>K DGFZQRH=Bæ@CNOFG?AQR>=?A?ABþFGKJKJYJIJ9=@C>NO9cBþ[>=KLK^FÿKJFGQRIJ9=F @CNOFG?AH=FGNO>=9=@C>)> N A&A> N ?AB9=B)IDGB>ssCIJDGIJ>9=@CI[=IaNOIJsCKL>?A?rIJB9=>_a9)QR>@CB[=BQRBKJ@CB ?A>QTHcKLIJDZ> > [=ILNS>@C@CB H=>N QRIL?A<=NSFGNO> KLYJFG9=jB=KLB FGq4ILQR<=@mFGKJ> φm [>K[ILNS>@C@CBNO> IJ9 ?A<=H=>NOsCIJDGIJ>%DGB9=?rIJ?A@C>h9=>KsCFGNRNO<=B=@CFGNO>%IJKH=BKJFGNOIJq4q4FG@CBNS>%iDGB9(V=>KJBDGIL@CuFZ9=j=BKLFGNS> DGB?A@CFG9=@C> ω_-Ü]YLFG9cjBKJB[ IH=BKLFGNSILq4q4FGq4ILB=9=> φÝ [ILVc>9=@CF%<=9cF%sC<=9=q4IJB9=>,KLIJ9=> FGNS>[>=K @C>QTHcBoÖ Mb[BV=> pKJYJFG9=jBKJB[>K^KLYJFG?r?A>B@C@CIJDGB[>KH=BKJFGNOI^q4qrFG@CBNS> NOIJ?AH=>@C@CBúφÝkKLYJôFG?Aφ?AÇ Ë > È&Ç É"µcÊ MlωFGKLK^YLI^?A@CFG9=@C¸ > φÇ È&Ç É ô/õ _ B9ú?A>=QRH=KJILDGIdHcFG?Z?AFGj=jIlFZKLj=>UNOIJDGIJMd?AI [ILQRB?A@CNSFìDGPc>&KLY^IL9c@C>9=?AIL@m[>K¾sCFG?ADZILB&NSILsCKJ>?r?AB × 8 Ì ô γ Bë ÌTBë Ì)ÍJÚuì<=9=FsC<=9=q4IJB9=> H=>NOIJB[IJDGFeDGB9usCNO>=;=<=>9=q4FeFG9=jBKJFGNO> Ø ω Î4Ö r ×Ø _Ù Ú I (t) = I0 [a 0 + b0 cos 2(ωt + φ iniz − φs )] [BV=1> Ï KLYJIJ9=@C>9c?AIL@Cï[>K sCFG?ADGILBuIJ9=DZIJ[>9=@C> ÐA>oÖ y Ñ ô × N A&A EÊ Ò N A&A Úî Úî Ø ×Ø _Ù4Ó~Ú ô × N N Ø â-<=IL9c[IJMKJYLFG9=j=BKLBlFGqrIJQR<=@mFGKL> φm [>=Ko[IJNO>=@C@CBNO>H=$< 4p>?A?A>NO>B=@C@C>9=<=@CB[FGKJKJFuQTIJ?A<=NOF [>KJKLFDGB?A@CFG9=@C>u[I sCFG?A>u[=>K]?A>j=9=FGKL>uB=?ZDZIJKJKLFG9=@C>u[=>=KLKJYL>=;=<=FGq4ILB9c> ×Ø _ :Ù Ú_ ÜbYJIL9c@C>9=?rIL@C ×Ø _Ù ~Ú V=FGKL> H=>=N*ILKßDGFG?ZB IJ9þDG<cIÞILKß[=ILNS>@C@CBNS> ?AIJFæB=NOI^>9=@CFG@CB <=9=IJsB=NOQR>QR>9=@C>h9=>=KgDZFZQRH=IJB9=>_89(;=<=>=?Z@C>(DGB9c[IJq4ILB9cILMnIJK[=ILNS>@C@CBNO>(l[=BV=<=9=;=<=> H=FGNOFGKJKL>=KLB5FGKLKJYJFG?A?A>5sCFGDGIJKJ>5>MH=>NSDGI 4GM φm ô φ IJ9 ×Ø _ Ù ~Ú_â-<=FG9c[B,(FGHH=KJILDGFG@CB5<=9 DGFGQTH=B >?A@C>NO9=B H=>N QRIL?A<=NSFGNO> KJYJ>9=>NSjILF [=IáFG9=DGBNSFGjjIJBM DGB=QTH=FGNS><=9=F ⊥. ⊥. ⊥. ⊥. ⊥. ⊥. I. A rigore I0 è uguale all’intensità del fascio incidente moltiplicata per il prodotto dei coefficienti di trasmissione t (aria-lamina I ) e t’ (lamina I-aria).. CAPITOLO 2. 25.
(38) [IL?A@CBNS?AILB=9=>p[>Kf[=ILNS>@C@CBNO>p9c>K]V=B=KL<=QR>_f8:9u;c<=>?A@CBpDGFG?ABM]IJK]DGFZKJDGBKJBp[>KJKLY^IJ9c@C>9=?AIL@C NOIJsCKL>?A?AF 9=B9*Hc<< 4 >?r?A>=NO>ñH=I k sCFG@C@CBñIL9/QRB[BñFG9cFGKLIJ@CIJDGBñQRF 9=>=DZ>?A?AFGNOIJB <=@CILKJI^qrq4FGNO>h<=9=FDGB=QTH=KJ>?r?AFtH=NSBDG>[<=NSFt9=<=QR>NSILDZF?AV=IJKJ<=H=H=FG@CFt[F Ô >NONO>=QRFG9 "ø ·_ ò FGKLIfDZFGKLDGB=KLIf?AB9=Bp?A@CFG@CIf>?A>j=<=IL@CIfNO>DG>=9=@C>=QT>=9=@C>u[FGK]9cB?A@CNOBdjNS<=HH=B ÎÁ_ j ?A@CFG@CB [ILQRB?A@CNSFG@CB5DGP=>Mg;=<cFG9=[B5tFGH=H=KJILDGFG@CB%<=9hDGFGQRHcB5QRFGj9=>=@CILDG B 7K^<=9=jB%KLYJFG?A?A > µcM KLF ×Ø _Ù Úk[=ILV=>=9=@CF]Ö Ý Ù Ú ×Ø _Ù YJÚ ( ) = Ý [Ü á +Û á Þ<ßà 2(ω Ú + φÖ ×sÖ Ø − φÕ − ∆φÓÁÔ)Ô )] [BV=â > y Yd> Ñ Yd?AB9=B DGB>sCsCIJDGIL>=9=@CIpILKdDG<GIdV=FGKJBNS> [ILH=>=9=[> [FGKLKJY^IL9=@C>9c?ZIJ@CÞ[=>cK DGFGQTH=BlFG H=H=KJILDGFG @CBM φã NOFGH=HNS>?A>9=@CFpIJKo9c<=BV=BV=FGKJBNO>l[>KJKLYJFG9=jBKJB[>=Ko[IJNS>=@C@CBNO>IJ9 ?A<=H=>NOsCIJDGIJ>([BH=BtKLFdNOB@CFcq4IJB9=> D Ú> - ÝÝ lIJKnH=NOIJ9=DGIJH=FGKL>>sCsC>@C@CB ?AH=<=NOIJB[=>KLKJF7[=IJ?A@CBNO?AIJB=9=>áIL9=[=Bδφ@C@CãoF7× φ[ã FGô K¡φDG FZQRδφ H=Bã _ B∆QRφ> ?rIu[>=[<cDG>[=FZKLK^YLFG9=FGKJI^?AI [>KJKLF ×Ø _ Ù YLÚM ∆φ- ÝÝ ?AILQR<cKJF <=9cF NOB@CFGq4IJB9c> FGH=H=FGNS>9=@C> [>K [=I^NO>@C@CBNS> ?A<=KLKJYJIJ9=@C>NSsCFGDGDGIJF DGP=>æ?AI0V=F FG[ FGjjIJ<=9=j>NS>æFGKJKLF NOB@CFGq4IJB9=> >sCsC>@C@CI^V=F δφã _ 9=YJ>?AH=NO>?A?AIJB9=>pFG9=FGK^IL@CI^DZFeFGH=H=NOB=?A?ZIJQRFG@CFe[cI ∆φ- ÝÝ Î4Ö _ Ù . Ú λ × Ø è êë ì 2φ ä ) ∆ φæçç = ( é 0. 0. 0. 2. 0. ( ) ξå 2. 2. 1. [BV=> Ñí p<=9lDGB>sCsCIJDGI^>9=@C>FG[I^QT>=9=?rILB9=FGKJ>M[=IJH=>9=[>9c@C>?ABKL@CFG9c@CB[FGjKJII^9=[IJDGI[=I NOIJsCNOFGq4ILB=9=>,[>=K Üb` >5[=>=KLKJF(KJFGQRIJ9=F(> î ô × ¢ Ê ¢ Úî Ø _ò ILHcILDGFGQW>9=@C>M Ñí ≈ Ø~ý _ / ?A?Z>=NOV=IJFGQTB=M&[FZKLKJF _ Ù:.~ÚM&DGP=> IJ9=V=>NS?AFGQT>9c@>æH=NSBH=BNSqrIJB 9FGKJ>æFZK ;=<=FG[NOFG@CBp[=>KLKJFeKJ<=9=jP=>×Ø q4q4Fe[I]DGB=>NO>9=∆q4φF- ÝQRÝ FGj9=>@CI^DGF ξ® >pDGP=>MfH=>NKJFe[>sCI^9=ILq4IJB9=> [I ξ® MïH=NSBHBNSqrIJB9=FGKJ> FGKï;c<=FG[NOFG@CB [>=KïDGFGQRH=B QRFGj9=>@CIJDGï B _¾ÜbYJFG9=[FGQR>9=@CB [>KJKLFNOB@CFGq4IJB9=> FGH=HcFGNO>9=@C> ∆φ- ÝÝ MìIL9 sC<=9=q4IJB=9=> [>=Kì;=<=FG[NOFG@CBÿ[>KDGFGQRH=B QTFGj=9=>@CILDGB=Ma,NSILHcBNO@CFG@CB)IL9 , ILj=<=NOF Ø _LÓ _ / ?A?A>NOV=FG9=[BKLF , IJj<=NSF Ø _JÓ MaHB ?A?AIJFGQWB sCFGNO>pKJ>p?r>j<=>9=@CI DGB9=?AIJ[=>NOFGq4IJB9=IÖ Ù4Ú ÜbFtNSB@CFGq4ILB=9=>%FGH=H=FGNS>9=@> ∆φ- ÝÝ [>Kg[=ILNS>@C@CBNO>h[IJH=>9=[>h;=<=FG[NOFG@CIJDGFGQR>9=@m> [FGKDGFZQTHcð B 7>MH=> NSDGI 4GMk Ñ M ¢ñ¦5~z ~ ¢<£ ¡~ Ñ ~ M [=FZKJKLF(NOB@CFGq4IJB9=>,NS>FGKJ>,[>=K [ILNS>@C@CBNS> DGsCN _Ù ÚÚMfDGP=>peK^IL9=>FGNS>uILò9 k_ ÚØ ∆φ- ÝÝ ?ZIaQT× FG9=@CI^×>Ø 9=>Ø IJ9=sC>NSILBNS>F õ _ õ Ù ÷ H=>NdDGFGQRHI
(39) QRFGj9=>=@CIJDGI
(40) ?AB@C@CBIÙ õ ó > _ Ó øÙ Õ?AîQRMïDGBNSNOIJ?AH=B9=[>=9=@C> FG[0<=90DGFGQTHcB [I¾IJ9=[<=q®IJB9=> QTõ FGj=9=× >≡@CILDGF ý Ô ô +õ ô Ù ò Ú_)80V=FGKJBNOI)[I ∆φ- ÝÝ NSILH=B=NO@CFG@CI)IL9 , IJj<=NSF Ø _JÓ DGBNONSIL?AH=B9c[B 9=B7FGKJKJFßQRFG?A?AI^QTF&NOB@CFGq4IJB9=>7FGH=HcFGNO>9=@C>MH=>NSDG<P 6ßDGFGKJDGBKJFG@mI DGB9ß<=9ßFG9=j=BKyBß[õI Ó ÷ @CNOF FG?A?A>ÞsCFGDZIJKL>ß>ßDGFZQTH=B=_TóFGKJKLF0>?AH=NO>?A?AIJB9c> FG9=FGKLIJ@mIJDGFlFGH=H=NOB=?Z?AIJQRFG@CFl[I ∆φ- ÝÝ ×CØ _ Ù . ÚMgH=B?A?AIJFGQRB(V=>[>NS>hDGP=>(KLYJFG9=jBKJB [öI Ó ÷ [IJKWQRFG?A?AILQRB >sCsC>@C@CB&?ZHc<=NOIJB_ BQR>ßV=>=[NO>QRB&9=>=KWHNSB?A?AILQRB DGFGH=IL@CB=KLBMR9=>KJKJ>ß9=B?A@CNO>ßDGB=9=[IJqrIJB9=IW?AH=>NOIJQR>9=@CFGK^ I *NOFGjjIJ<=9=j>=MRFGKRH=I kZM . _ Ù Ù õBô Õ?AîQ × Ô ô7õ _ 35.&ò Úe>0KLYJFG?A?A>0sCFGDGIJKJ>0sCBNSQTF)<=9ìFG9jB=KLB [I ý DGILNSDGFùø õ ÷ NOIJ?AH=>@C@CB FGKDGFGQRH=B_89;=<=>?A@C> DZB=9=[IJqrIJB9=IKJFùNOB@CFGq4IJB9=> FGH=H=FGNO>9c@C> ∆φ- ÝÝ [>K[IJNO>@C@CB=NO>M [BV=<=@CFèFGKJKJFè[IJ?A@CBNS?AILB=9=>M NOIJ?Z<cKL@mF IL9=sC>=NOIJBNO>lF õ _ õ õ Ø ÷ >[du[>Kb@C<=@C@CBl@CNOFG?rDG<=NSFGU=ILKJ>dNOIJ?AH=>@C@CBlFGIb@mILHcILDGIbNO<cQRBNSI ?AH=>NOIJQR>9=@CFGKJIfH=NO>=?Z>=9=@CIfI^9u;=<=>?A@CBp@CIJH=Bp[IfQRI^?Z<cNO>=_ ||. CAPITOLO 2. ⊥. 26.
(41) -3. ∆φapp ( x 10 ° ). 0 -5 φs = 45°. -10 -15 -20 -25 -30 0. 100. 200 2. 300. 400. 2. H ( KOe ). ¦A§ ¨ ©ªC«p¬® h+° * ð ¹ Z ú®ÈÁ¼y²RÎLµ ÆcóO²l½R³Cµ ¿=¸ ³¼L²S¼L¸¡À·É ²:¹c´ ²mÂ
(42) º¹=¼J¸(´µ µ ¹(Πù¥¶·µy¸¹cº(´±µ ù úcZ®Ã¥²:¹c´ ¸ ÀSÉ ²:¹®Æ=¸À¸a´ º À ´µ ³º¥¼L¼J¸³ºoµ ¹ÈÁÿcº ³CÎJµ:»:µ:ºÅZ³CµÈ¿=º ¼J¼J¸²mÀ À·É ²SÈSÈSºnÊd»y´µ ³º¶·∆µφ¸¹c÷øºaø ´ ºÀf»O²:¿¸Â̲:Æ ¹cº¥¼ µ»S¸_½yÅf½ φû À » hZÅn²
(43) ¼JºÂn¿=º³²S¼Ló ² e:½-Ã¥¼ µ À µ ¶·¶4²S¼ µ¹=ºÀn»S²mÀ:»S¸ À¸-¹cú³Cµ:»S¸ üdý:þ5ÿ Ë * ¿=²m³²:º ¼ ³Cµ¿cº ³gµ ÈS¸¹¸g ¹
(44)
(45) ü ¯ ¯ OÅ=¹ ¯Á h®¬ ú8ú ü T4 Tp¯ ú χ÷ ¯ ü T gd 5ÿ ¯ "!L #ÈSȷõ:²:Â̸¾Á» (=ºkÀ·É ²m¹¥Æ=¸ À¸¾¼ ³² ÀSÉ ²SÈSÈSºÎÁ²S»mµ À:ºÌºµ Àb»O²:¿¸
(46) È:µ:² ´ 3µ g:h$ Ë¥±gÉ µ ¹c´ µ»OºÌ´µc³Cµ ÎL³²m¶Áµ¸¹=º
(47) ´ ºÀcº¶·¶4¸gµ:È·¸ ¼ ³¸¿¸
(48) ½&¹ % ü ¯ h¯aºgÀ² À:ù oÆ (=º¶Á¶r²g´=É ¸¹=´ ²´ º À4Î ²OÈS»:µ:¸µ ¹»:µ:´ º¹c¼Lº ½ λ' ü)( T®¬4 +*,-Ë `>K?A>j=<=IL@CBÛDGB9=?AIJ[>NS>=NO>QRBÛ?A>QRH=NO>Û@CNOFG?ADG<=NSFGUILKJ>ÛKJFNOB=@CFGqrIJB9=>ÛFGH=H=FGNS>9=@C> [BV=<=@CFFGK^KLF[=IJ?A@BcNO?AIJB9=>ì[IÌ @ -
(49) IL?A@C_
(50) 89;=<=>=?Z@C>ìDGB=9=[ILq®IJB9=IJMÌK^YLIJ9=@C>9=?rIJ@C5[>cK ∆φ- ÝÝ sCFG?ADGILB5NOIJsCKL>=?Z?AB%IL9%H=NO>=?A>9=q4Fh[>KJK^Fh[I^?A@CBNO?AIJB9=>,[=I @ -¾IJ?r@Ìh[FG@mF([Fh<c95?r>j9=FGKJ> B?ADGILKJK^FG9=@C> [=IßH=<=KJ?ZFGq4IJB=9=> MßDGB 9æ<=9=F DGB?Z@CFG9=@C>þ[IßsCFG?A>þDGP=>þ[ILH=>=9=[> ?ABKLFGQR>9=@C>[=FGK V=FGKJBNS>[>=KLKJYLFGØ 9cωjBKJB[>=K [IJNO>@C@CBN·>IJ9,?Z<cH=>NOsCIJDGIJ> φma× >=;=_ ×Ø _ Ù YJÚ DGB9 ÝÝpôfõ Ú_ó<=9;=<c> MKLYJFG9=jBKJB7FGq4IJQT<c@CFGKJ>2[=>=Ke[=ILNS>@C@CBNO>2IL9ß?Z<cH=>NOsCIJDGIJ>MIJ9 H=NO>?A>∆9cφqr- F) [>KÌDGFGQRH=B0QTFGj=9=>@CILDGB=M¾H=<< 4)>?A?A>NS>ìB@C@C>9=<=@CB0[FGKJKJFQRIJ?A<=NOF[IJNO>@C@mF [>KJKLFDGB?A@CFG9=@C>u[I sCFG?A>u[=>K]?A>j=9=FGKL>uB=?ZDZIJKJKLFG9=@C>=_ 8:KQR>@CB[B(NOIJsCKJ>=?A?ZB=QT>@CNSIJDGB([>?ADGNOI^@C@CBhsCIJ9=BhFG[(BNOFll?A@CFG@CBhH=NSBH=B?A@CBh[FZKg9=B=?A@CNOB jNO<=H=H=BìFGKLDG<=9=IFG9=9=I
(51) sCF ÎÓ Á_
(52) 8K
(53) QR>@CB[B>?A@CNO>QTFGQR>9=@C>?A>=QRH=KJILDZ>>[IJNO>@C@CB=_ 8:9csCFG@C@CILM,KLF/QRI^?Z<cNOF*[=>KJKJYJFG9=jB=KLBöFGq4IJQT<c@CFZKL> [>K,[=IJNO>@C@CBNS>ö?AI,NSIJ[<=DZ>öFGKJKJF ?A>QTHcKLIJDZ>QWIJ?Z<cNOFh[=>KJKJFhsCFG?A>,[I<=95?r>j9=FGKJ>Bφm?ADZIJKJKLFG9=@C> ×Ø _ Ù YJÚ_-89=BKJ@CNO>M-H=>=NeKLF QTIJ?A<=NOF[I φm M
(54) 9=B99=>DG>?A?rFGNOIJFKJFDGB9=B?ADG>9=q4F[>IH=FGNOFGQR>@CNOIDGFGNOFG@C@m>NSIL?A@CI^DGI [>KW?A<=U=?A@CNOFG@CBßIJ?AB@CNOBHcBÞ>ß[>KWDGNOIJ?r@CFGKLKJBßK^IL;=<cIL[=B=MRDGP=>ßIJ9=sCKJ<=>9=q4FG9=Bß?ABKLFGQR>9=@C> KLYJFGQRH=IL>q®q4F Ñ Yl[>Kl?A>=j=9=FGKL>ÛB?ADGIJKJKJFG9=@C>úIL9 ×Ø _Ù YLÚ_89=sCIJ9=>Mj=KLIl>sCsC>@C@CI?AH=<=NSI [BV=<=@CIFGKJKLFu[=IJ?A@CBNO?AIJB9=>l[>=Ko[=IJNO>=@C@CBNO> × ∆φ- Ý/Ý . õ _ õ õ Ø ÷ Ú-?AB9BlFGKLQR>9=Bl@NS>lBNS[IL9cI [Ibj=NOFG9=[>q4q4F ~ ¢ {sM N ~© N ~~F¡;=<=>KJKJIbH=NS>?A>9=@CIb9c>IbQR>@mB[I]DGB9=V=>=9=qrIJB9=FGKJI]<=@CILKJIJq4q4FG@CIbI^9 FGKL@CNSIÌKJFGUBNOFG@CB=NOIJMÌDGP=>ì?AsCNO<=@C@CFG9=BìKJ>0H=NSB H=NOIJ>@C%[ >KJKLFNOFG[=IJFGq4IJB9=>ì@CNOFG?AQR>=?A?AF)[=FGK DGNOIJ?A@CFGKJKJBpKLIJ;=<=I^[B × FG[p>=?r>QRH=IJBM]DGsCN ý DkÙ Ù ·Ú_ â-<=>?A@CBpQW>@CB[BMfH=>ÂN 4GMfP=FeFGKJDG<c9=IfIJ9=DGB9=V=>9cIL>9=@CIÖ ÜbYJIL9c@C>9=?rIL@C ×Ø _ :Ù YJÚ,[>KJKLFNSFG[IJFGq4IJB9=>úNOIJsCKL>=?A?AFç[FGKJKLY^IL9c@C>NOsCFGDGDGI^FKJFZQTIJ9=F • IL?AB@CNSBH=EF D Ü]`ß¡9BNSQTFGKJQR>9=@C>dQRBKJ@CBdH=ILDGDGB=KLFG_]â-<=>?A@CBdsCF¡? 0bDGPc>lNO<=QRBNOI [BV=<=@CIFGKJKLFlH=NO>?A>9=q4F[cIKJ<=DG>h[cILsCsC<=?AFH=B=?A?ZB=9=B%[FGNS>h<=9tDGB9=@CNOIJU<=@CB(9=B9 ?A>QTHcNO>p@CNOFG?rDG<=NSFGUIJKJ>_ 85NSFGjjI(NSILsCKJ>?A?rI([FZKJKL> V=FGNSIL> IJ9=@C>NSsCFGDGDG> [=>KLK^F DG>KLK^Fú[>V=B9cB/>=?Z?A>=NO> • ?A>H=FGNOFG@CIk?AH=FGq4IJFGKJQR>9=@C>%H=>NQTIJ?A<=NOFGNS>5?ABKJFGQW>9=@C>,KJY^IL9=@C>=9=?AIL@Cd[>=KkNOFGjjIJB NOIJsCKL>?A?AB[FGKJKLY^IJ9=@C>NOsCFGDGDGI^F%QR>q4q4BIJ?AB@CNOB=H5B D Ü]` × NOFGjjIJB9=_ Ø [I , ILj<cNOF ⊥. CAPITOLO 2. 27.
(55) _ I 4eeB@C@C>9=<=@CBp<=@CIJKJIJq4q4FG9=[Bp[<=>pK^FGQRIJ9=>pIJ?AB@mNOBHc>p[I]DG<=If<=9=FGMf;=<=>KJKLF Ø[FG_ ~KLKJÚF H=FGNO@C>ú[>KsCFG?rDGIJBúIL9=DGIJ[=>9=@C>=M?rILFáDGB9úKL>úsCFGDGDG>Û9=B9úH=FGNOFGKJKJ>KL>=_ â-<=>?A@CBá@CIJH=Bç[IeKLFZQRIL9cFÞ9=B972sCFGDGILKJQW>9=@C>áNS>=H=>NSILUIJKJ>á>[72H=IJ<=@C@CB?A@mB DGB?A@CB?AFG_ Õ DGFG<=?AF [>jKJIæIL9=>=V=IL@CFGUcILKJI >=sCsC>@C@CIþ?AH=<cNOI × [IJsCsC<=?AILB9=> [IþKL<=DZ>=M • [IL?AB=QTBj=>9=>IJ@Ce[=>=KoHcBKLFGNSILq4q4FG@CBNO>lNOB@CFG9=@C>MFG9=IJ?rB@CNOB HcILFpNS>?AIL[=<=FZMo?A>H=Hc<=N QTIJ9=I^QTFGMg[>=KJKJFtKJFZQTIJ9=Ft@CN·FG?ZHcFGNO>9=@C>_J_J_LÚMgKJYJFGDGDG<cNOFG@m>q4q4Ft[Ig;=<=>?A@CBhQT>=@CB[B [IgQRIJ?A<=NOFl[>KJKLY^FG9=jBKJB%FGq4IJQT<=@mFGKJ>%[cILH=>=9=[>%sCBNS@C>QR>9=@C>%[=FGKgDGB=9=@CNOFG?A@CB δ1 Ñ YLÅî y Y Ñ Åî y DGsCN ×Ø _ i:Ù >= NOYLDGÚÚ
(56) I 4G>M2[%K^YL(FGDZQRDGB<=KLNS@CFGB%@C>NOq4IJ[q4BF @C@CFt[>9=KÞ>KkQTDG>FZ@C?AB=B5[B DGP=> [ILH=δ>=1 9=?A[=IL>F QTô B=KL @CB QR≈IL9=B=NO >
(57) [× I Ù®_2 H=>?AFG9=@C>QR>9=@C>ì[FGKJKJ>ìDGFZNSFG@C@C>NOIJ?A@CIJDGP=>ìB@C@CIJDGP=>ì[>KJKJF)KJFZQRIL9=FIJ?AB@CNOBHcF)>M ;=<=IJ9=[ILMKLI^QRIL@mF IJK@CILH=B [IQT>=q4q4IDGP=> H=B?A?AB9=B >=?Z?A>=NO> <=@CIJKJIJqrq®FG@CI^_tÕ[ >?A>QRH=ILBMí43 ?A> K^FùK^FGQRIJ9=FùP=Fù<c9IL9c[=ILDG>ö[INSIJsCNSFGq4ILB9=>H=FGNOIâ F ¢@? ô Ñ IJ9%>=;=<=FGqrIJB9=> ×H=¢ B?A2 ¢?AIL× U=θIL KJÚ> Ú FGMkKLDGKL<=Ft9=;=F <=FGQR9=IJ@C?AIJ@C<c NSFÛ [=I(FG9=jBKJB FGq4ILQW×Ø <=_@CÙ FG~K^ÚÌ>/[DGIJV=B=IL9 >=9=;=>5<=9=><=?AK^@CKJB F(>%QT9=>=B=@CB9%[B NOIJsCKL>?A?ABQR>@CNSIJDGB_ i>Ne<=9cF%[IJ?ADG<=?A?AIJB9=>,FGDGDG<=NSFG@CF%[I-;=<c>?A@CI-FZ?ZHc>@C@CILM-NSILQRFG9=[=IJFZQRBFGKJKLFhNO>=s>=NO>9=q4F "·_ v-w vw v n|] f({ L|fcc u|]{¥;2;ff~|h~fy{¥yZG { oy;={ B;==o{¥]= 5n>=DG>9=@C>=QR>9=@C> ÎÁMu2?Z@CFG@CBáH=NOBHB?A@CB<c9QR>@CB[BáFGKL@C>=NO9=FG@CIJV=B Hc>N)>V=IJ@FGNS> KLYJ<=?ABh[=IK^FGQRIJ9=>(DGB9(sCFGDZDG>h9cB9(H=FGNSFGKLKJ>KJ>(>[(FG?r?AIJDG<=NOFGNS>(IJKQWFG?A?rILQRB(DGB=9=@CNOFG?A@CB IJ9cFe<=?rFG@CB_ × BδQT1 > ô Ù4H=ÚgNSILIL9=QR[=FGILMdH=>sC9cFG[DG>DG9=I^FG@CQR>QRB >IL9=9c@CDG>pIL[[=>=FGNOKf> @mILH=<=Bp9 [=sCIfFGKJ?AFGDGQRIJBú QRB9=B=DGNOBQRFG@CILDGB ?A<=KdDGFZQRH=IJB9=> [BH=BêFGV=>NOjKJIçsCFG@C@CBêFG@C@CNOFGV=>=NO?AFGNO>ê<=9 H=B=KLFGNSILq4q4FG@CBNO>êib_çÜ]>êH=I^FG?Z@CN·>êDGP=> NOFGDGDGP=IJ<=[B9=BIJK 9=>QRFG@CILDZB?AB9B>9=@CNSFGQTU=>DGB9?A<=H=>NSsCILDGI-H=FGNOFGKJKL>=KL>>sCBNOQRFG9=B @CNOFç[IpKLB=NOB <=9 DG<=9c>BúDGB=9 <=9FG9=jBKJB [IpFGH=>NS@C<=NOF θ ³ ≈ Ø ÷ _d`a>KpDGFG?ABú[cI IL9=DGIJ[>9=q®F 9=BNSQTFGKJ>MhI%[<=>*NOFGjjIJM5NSILsCKJ>?A?rI5NSIJ?rH=>=@C@CILV=FGQR>9=@C>ñ[FGK^KJYLIJ9=@C>N·sCFGDGDGILF FGNOIJEF DfQR>q®qrBùIL?AB@CNSBH=Bö>öQR>q®q4BöIJ?AB=@NSBH5B D Üb`aM?AI5?ABV=NOFGH=H=B9=jB 9=B=MQRF/IJK sCFG?ADGILB&NSILsCKJ>?A?AB&[FGK^KLFìIJ9c@C>NOsCFGDGDGIJFìFGNSIJEF DfQR>q®q4B&IJ?AB@CNSBHB × 9c_dÙIJ9 , ILj<NOF Ø _ Ú QTFG9=@CIJ>9=> KLF ?A@C>?r?AF H=BKJFGNOIJq4q4FGqrIJB9=> [>KæsCFG?ZDGIJB IJ9=DGIJ[=>9=@C>MæF DGFG<=?rF [>KJKLY^IL?AB@CNSBH=IJF[=>KLKJYJIL9=@C>=NSsCFGDGDGIJFG_af>Ma;=<=IL9c[ILMasCFGDZDGILFZQRB)H=FG?A?ZFGNS>)INOFGj=jINOIJsCKJ>?A?AI FG@C@CNOFGV=>NS?ABì<=9FG9=FGKJIJq4qrFZ@CBNS>ìÕMÌIJ9=DGNOB=DGILFG@CBìDGB9)ibM
(58) ?AFGNO%H=B?A?AILUcILKJ>UKLB=DZDGFGNO>ìI^K NOFGjjIJB%9=_ïÙ4_kiBILDG<P 6GMkDGB=QT>%9=>KkQR>@CB[B%H=NO>DG>=[>9=@C>MkIJKkH=BKJFGNOIJq4qrFG@CBNS>5iìNS<=B@CF ÚMnFG9=DGP=>(Õß[B=VNO¡NS<=B@CFGNO>t?ZB=KLIJ[FGKJQT>=9=@C>(DGB9tiH=>=NWQRFZ9=@C>9=>NS?AI FG× φ[pÝ->=ô ?A?AφBpÇ È&Ç ÉIL9=Ê DGNSBωDZILFG@CB=_ / ?A?Z>=NOV=IJFGQTB DGP=> KLYJFZ9=FGKLIJq4q4FG@CBNO> UKLB=DZDGP=>NO FG9=DGPc> IJK sCFG?ADGIJB NSILsCKJ>?A?AB [FGKLKJY^IL9=@C>=NOsCFGDGDGIJF*QT>q4q4BöIJ?AB@CNOBH=5B D Ü]` × NOFGjjILBö9=_ Ø [I , IJj<=NSF Ø _ Úß?ABKJB ;=<=FG9=[B(KLFHcBKLFGNSILq4q4FGq®ILB9c>h[>KsCFZ?ADGIJBhNSIJsCKL>=?A?ZBt?rFGNOu<=j<=FGKJ>(Fl;=<=>KJKJF[c>KnsFG?ADGIJB IL9=DGIJ[>9=@C>[=FG@CFd[Fdib_oâ<=>?A@CBtFGV=V=IJ>9=>t;c<=FG@C@CNOB(VcBKL@C>?Z<l<=9FG9=j B=KLBtjILNSBt>tDGIJB ;=<=FG9=[BÛKJYLFG?A?A>Û[=Iiù?AIl@CNSBV=FH=FGNOFGKJKL>KJBÛBÛBN@CBj=B 9=FGKJ> FGKJKJFH=NSBIJ>qrIJB9=>Û[>=K [ILNS>@C@CBNS>(?A<=KJKLY^IL9=@C>=NOsCFGDGDGI^F × DGsCN û4Ø _ÙrÚ_n89tB j=9=IFGKJ@CNOBtDGFG?ABMn;=<=>?A@CFlB9=[=FlNOIJsCKL>?A?rF P=F<=9=FHcBKLFGNSILq4q4FGq4ILB9c>hK^>jj>NSQT>=9=@C>h[IJV=>NS?ZFl[=Fl;=<=>KJKJFIL9cDZIL[>9c@C>(FlDGFG<c?AF[>cI [ILVc>NO?AIDGB>sCsCIJDGIL>=9=@CIe[=IeNSILsCKJ>?A?rIJB9=> × N A&AW> N Ú>7?rFGNO0@CNOFZ?AQR>=?A?AFßFG@C@mNOFGV=>=NO?AB KLYJFG9=FGK^ILq4q4FG@CBNO>pÕ_ iFGNS@C>9=[Bö[FGKJKJ>ö>;=<=FGq®I^B9=I ×Ø _ Ù4ü~ÚM,NOIJDGFGV=ILFGQRBùKJYJIL9=@C>9c?AIJ@CÛ[>K5NOFGjjIJBö[B=HB KLYJFG9=FGK^ILq4q4FG@CBNO> Î4Ö ⊥. ⊥. CAPITOLO 2. 28.
(59) ×Ø _ Ù:~Ú. I r (t ) = I 0 c0 [1 − cos 4(ωt + φiniz − φs )]. [BV=>1} ô × N −N A&A Úgîgø _ / ?A?Z>=NOV=IJFGQTB DGP=>=M(FG[>?A?ABMtKLYJIL9c@C>9=?rIL@Cç[>K(sCFG?ADGIJB NOIJsCKL>=?A?ZB ú<=9=Fús<=9=q4IJB9=> H=>NOIJB[IJDGF2[>cKu@C>cQTH=BçDGB9çsCNS> ;=<=>9cqrFÞFG9=jBKJFGNO>¬ ω_¡Õ9=DGP=>áIJ9ç;c<=>?A@mBáDGFG?AB KLYJFG9=jBKJB FGqrIJQR<=@mFGKL>[>Kp[=ILNS>@C@CBNO> H=<< 4ç>=?A?A>NO>B@C@C>9=<=@CB [IJNO>@C@CFZQR>9=@m> [FGK^KLF QTIJ?A<=NOF[>=KJKJFeDGB=?A@CFG9=@C>u[=I]sCFG?A>u[>K ?A>j9=FGKJ>uB?ADZILK^KJFG9=@C>_ fB@C@CBKJIJ9=>IJFGQTBpDGP=>pI^K]DGBc9=@CNOFG?A@CB δ1 e?A>QRH=NO>u<cj<=FGKL>uFG[5ÙWFeHcNO>?ADGIJ9=[>=NO>u[FGKLKJ> H=NOB HcNOIJ>@CRB=@@CIJDGP=>p[>=KLKJFTKLFGQWIL9cF¡>p9cB9ueH=I k9=>DZ>=?Z?AFGNSILBuKJYJ<=?ABp[=I]K^FGQRIJ9=>uFesCFGDGDG> 9=B9dH=FGNSFGKLKJ>KJ>_â-<G>?A@C>dDZFGNOFG@C@C>NSIL?A@mIJDGP=>lsCFG9=9=Bl? 0]DGP=>lIJKbQR>@CB[BdNOIJsCKL>=?A?ABQR>@CNOIJDZB DGB9pHBKJFGNOIJq4qrFG@CB=NOIbIJ9=DGNSBDGILFG@mI]?rILF¡H=I k¡sCFGDZILKJQW>9=@C>dFGH=H=KJIJDGFGUILKJ>dNSIJ?AH=>@C@CBdFGKfQT>=@CB[B DGB9X<c9X?ABKJB HcBKLFGNSILq4q4FG@CBNS>Mñ[>?ADGNOIJ@m@CBXH=NO> DG>=[>9=@C>QR>9=@C > × DGsCN ûrØ _ Ø _ÙrÚ_ iB?A?AIJFZQTB=MIJ9=BKJ@CNO>=M[=ILQRB?A@CNOFGNS> DGP=> KLFö;=<cFc9=@CIL@C N −N A&A M)HNSB H=B NSqrIJB9=FGKJ> FGKLKJYJFGQRH=IJ>q4q4F[=>=KLKJYJIJ9=@C>9c?ZIJ@C ×Ø _ Ù Ú¡[>KÌ?A>j9=FGKJ>0[BHB0KJYLFG9cFGKLIJq4qrFG@CB=NO>MÌ[ILH=>=9=[> H=BDGB[FGIáH=FGNOFGQR>@CNSIB@C@CIJDGI[=>KLK^F KJFGQRIJ9=F IJ?AB@CNSBH=F >[IJH=>9=[=>MIJ9=V=>DG>=M [FGKLKJY^FG9=IL?AB@CNSBH=IJFe[>jKJIfIJ9c[IJDGIf[=IfNOIJsCNOFGq®ILB=9=>p[>K DGNSIL?A@CFGK^KJBpKLIJ;=<=I^[B_ Õ9=FGKLB=jFGQT>=9=@C>7FGKTQR>@CB[B7DGB=92<=92?ABKJB7H=B=KLFGNSILq4q4FG@CBNO>=MeKJY^FGH=H=KLIJDGFGq4ILB=9=>2[IT<=9 DGFGQTH=B)>?A@C>NS9=BMDGPc>[=>@C>NOQRIJ9=F<=9cF[=IJ?A@CBNO?AIJB=9=>)[\I s ~zBg9=>KaV=BKL<cQT>>)<=9=F NOB@CFGq4IJB9=>,[=>K[=IJNO>@C@CBNS>,?A<=KJKJYJIJ9=@C>NOsCFGDGDZIJFGMkFGKJ@>=NSF(KJ>jj=>NOQR>9=@C>5IkDGB>sCsCIJDGIJ>9=@CI[cI NOIJsCKL>?A?AIJB9=>MaDGB?rILDGDG<P 6,KJYJ>?AH=NS>?A?AILB9c> ×Ø _ Ù ÚTH=>NdKJYLIJ9=@C>9=?AI^@Ch[>K ?Z>=j9=FGKJ>)[=BH=B KLYJFG9=FGK^ILq4q4FG@CBNO>æIJ9=DGNOBDGIJFZ@CBþ9cB 9æÿH=I k >?AFG@C@CFG_ 8K&H=NSIL9=DGIJH=FGKJ>æ>sCsC>@C@CBþ[>KJKLF [IL?A@CBNS?AILB=9=>ú[=ð I s²~zDZB9=?AIJ?A@C>MdDGBQR>ú9c>KLKJYJFZKL@mNOB QR>@CB[BMpIL9 <=9=FçNB @CFGq4IJB9=> ?A<=H=>NOsCIJDGIJFGKL>áFGH=H=FGNO>=9=@C> ∆φ- ÝÝ [>=Kp[=IJNO>=@C@CBNO>DZP=> ?AIpV=F7FG[FGj=jIL<=9cj>NO>FGKJKLF NOB@CFGq4IJB9=>(NS>FGKL> δφã _niB=?A?ZI^FGQRB([=IJQTB=?Z@CNSFGNO> "¾DGPc>(KJ>t[IJsCsC>NO>9=q4>tNO>KJFG@mILV=>t@CNOF KLF0NSB@CFGq4ILB9c>ß?AH=<=NOIJF09=>KWQT>=@CB[BßDGB9&<c9&?ABKyBßH=BKJFGNOIJqrq4FG@CBNS>ß>ßKJF0NOB @CFGq4IJB9=> ?AH=<=NOIJF09=>KWQT>=@CB[BßDGB 9&[=<=>ßHBKJFGNOIJq4qrFG@CB=NOIWIL9=DGNSBDGIJFG@CIR?AB9=B&IL9=sC>NSILB=NOIWFáÙ 7õ 68 _ i>NSDGI 4GM FG9=DGP=> H=>N ;=<c>?A@CB ?A>=DGB9=[B QR>@CB[BM V=FGKLjB=9=B KL> ?A@C>?r?A> DGB9=?AIL[=>NOFGq®IJB9=I5NSILj=<=FGNO[FG9=@CI ∆φ- ÝÝ _%8:9*HcFGNO@CIJDGBKLFGNS>M59c>KLKJ>ñ9=B?A@CNS>ñDGB9[IJq4ILB9cI ?AH=>NOIJQR>9=@CFGKJIJMaIJKaV=FGKJBNO>[I ∆φ- ÝÝ 5IL9=sC>=NOIJBNO>F õ _ õ õ Ø ÷ >[GMa;=<cIL9=[IJMa[>=Ka@C<=@C@CB @CNOFG?ADG<=NOFGUcILKJ>_ ⊥. ⊥. v-w r. |] ftfpG {®pf|fy9yffL%=GLp =y|(G | {:8;L|(3;=| {®=cu|fcc 8QR>@CB[=Ib?A@CFG9=[=FGNS[lH=>N
(60) KJFuQWIL?A<=NSF¡[>KJKLY^FG9=jBKJBlFGq4ILQR<=@CFZKJ>l?AsCNO<=@C@CFG9=BdKL>lH=N·BH=NOIJ>@C [I@CNSFG?rQTI^?A?rILB9=>d[I<c9dsmFG?ZDZIJBl[Fu<=9cFuKJFGQWIL9=Fu @ -
Documenti correlati
Il progetto da me realizzato può essere definito come tale perché il “cervello” del sistema preso in esame è il modulo wi-fi ESP8266, esso acquisisce dal sensore DHT22 (sensore
tati nelle virtù, nei lavori e negli uffizi proprii della nostra Congregazione, si facciano loro osservare tutte le nostre Costituzioni. Chi si dimostrasse
La perdita di energia non dipende dalla massa della particella incidente. dipende dalla carica e dalla velocità della
Tipi di dato e numeri interi Tipi di dato e numeri interi Variabili e costanti con nome Variabili e costanti con nome Struttura di un programma Struttura di un programma.. Capitolo
3.17, dato un fascio laser a velocità costante che incide sulla superficie ceramica, si ha che una percentuale consistente dell’energia incidente viene assorbita
Si parla di modi TE nel caso in cui il campo elettrico dell’onda piana incidente risulta disposto lungo un piano parallelo alla superficie di incidenza, si parla invece di modo TM
Vista la dipendenza delle prestazioni di un sensore SPAD dalla dimensione dell’area attiva e dalla lunghezza d’onda della radiazione incidente, appare ovvio che la possibilità
Le prove successive sono state condotte aumentando la pressione di 1 bar alla volta e generando sempre un onda PWM alla Frequenza di 500 kHz e Ampiezza 1 kV. Per pressioni superiori
