s v>3,,~1, -+ 01- =f,i'je...
TRANSCRIPT
'Phi '>S-~L-
ASs';0nV"'e<1-t ~ S\:) I L,II' 0 " j (i~
I. I\s v>3,,~1, S -+01- w',i~ =f",i'Je -(:OAcl'O/l,
Here ;AC"),,,,-t ,~) Co v -<c , S
E . ~ ,(Ie-r-wi)-,~,' toc-
-: E ' ( 1< L (c>S Eo + k x: s' '" 0 - co-c )0 e
~ ~ ,(I<'{ T 1<0)< -c-v-i)~ l-oC
A+ t: 0 (plo.e =f'\ .,wt
erlkiC) cdd cJrofF:'S co}
E ; kG?"-0 eCjC+ E(x/ cOJ 0\ =
SoG-ofer-lkrc
--f'c\ "ci 0 " I S
0 (,<; 2J) ::
if ) Ie8 X0 e
C)
((,,« !y)
( else')
ILO 1<: t)
",I e e vi -f'C-l"s-Foc"", v~.l kx / (cL)
~I0 + c: A(x/'Q) :: F ,kQ;<~ 0 e "" pc, I::, e
-r:~ ~ (-I ' co "
'St) A_, elk/(- k0b J [ Ic'oL
J~/-i..( kx, Ieb\ - Eo b L S, f' c- L S ' " C T
I/o s' " 5 i (10,,,<;, Ie,-+ , 0 ~ e (0 r e r-f I
@
1- r c-- v-. ~ "C> fe r to r t/1A '" r Q "-J,ves
AJ(x;7J)= ~~ Jl(~x) :~)
£' C - ' ; lco1 i Ie ( '<Lor,,1' );.2 0{IOf - -, e e
Herc- kA ( kx ~'o
):: F bL
.
[ (/-1<:8)1). (~ J~ "') d -0 SI(\L L jS/Y\(l2-d
-~ to6L 'S",c [ k{x-8&b J'
[ ~L ]?-M 51(\C- Ld
G0c.A
'-
~/c~
bLLL '2. '-[k (x-eJ)b j , ,[ IC~LJ l/I) J L IEo I ~ If'\C :? d , <;In C.--~ cA
C e. "fe, ("'J c,-t x = f)J / (J ~ 0
50 ce"t'er -T,c-ue,(s ",,-T C"j(e 6J/
0,";. clc""'-ed
(
/-r0y~7r '
I E--- d -"
':I
0Z. G) i=(eS(\el ~')e/
f(x,~)~)~ A~(x,"o\ S S f\(Xj Y) 0Jx-X) '0- y) dX cJ Y
{or ~()< ) - - -L ) r~ ,k: (x~+'oL)1 I'i:J - 7\ d e e 201
Ac) =- ~~ ~;~J Is J £(X-c \ <;(y) ~d-r(,-)<) L. ('d- y) 'Jf;,~ J xJ Y
T SS ~(X-tC-)~(Y~ C'-,~[r><-X)'-;«a-Y)'J/<dcdX:JYj
::: --'- ,/eJ< ;1c[(x-e-)L-t'IJL1l,v{ ;k[(x-t",)L-/(a'-l/2u1~~ e {e ~e )
- 1- ; loA ~ I«X<4LO'-)/2J~ -,' /ce, x/o-( ~ kc,)<~ ?~oAc e (e- +L )
r:-- 2:reA = - /\~
~~o--I 1k:(XL~(ul);?oi
(t~M
e e cos_~ ~{b~ F.C,l/J h ho-fe( )
he"" J Jl{lcx/r,,)
i=roM tc.1 (e)C
(\ -It C\
<:, X-"'-) ~ e x
l ( \" T,'k"i) X-! Co ) -) e
<;:, (co') ~ 1-
SoA(I<x) ~6):::
;!cxc, -'~Xc,(
\c: -f e ::; 2 (' 0 s lex"")
TLe". (y"",')
A ( \ ~ -~ , ~",{ ) Ie Td J / kx bt} )d\ '//'t) - :::\",( ~ e V-'--l uIJ "I
{jj
--- ---]i ;I-<>i;k (x'-tG')
(kxe;
)Ad e e 20-1 Co'; d
Sc~c cs FreSne I!
Me. Ice,> <;<:05<=' i-f') J-,Die <; ; r e -) 0" Fro, ~ ~ to" -('~ r-
\)e. I; d -Po r u"/ 0{
C 0(\ S " J e r i;e IJvv,i h
olors
Fo>i5
(or" Vl-OU - )
J;~f(,,'evi ""(0"5><
~~~) X, :;>< 13
><,~0
~
3. .1 "e of' oi:dc3 fo;,,-f <)OLCCe IS A'II f,,-+h> (,..,
AJ (/):: C [kr2c, T,(KfC\)J
-for k 1t-f -f
D()\--'\ "")
C= co0",ic-At, cJoesn'-!- >'V'"-+te r
A J (f ') = f T ( )kf f) I 2 f'
(b
I~~f'Ai(X)'=
4--r( !<x[)\
k)< i) JI. z:r-)-
(';rsl ~t°-+
A "2(x ') ::Lf-f: -
[ k (x-e')!,>
]- J -krx-fS)i) I 2-(.' - Sf:' (0 -J sf o-t
[2"3,{H 1)
""~ ~ + 2 ~~ ~"" - I) ] 2
~)1.4
1.2
-5 0 5 10 15 20
----
1=0 ( c.\ +oic./"(
I 0( 1/\ -t All
b') j 0< / L '1A,r --t lA, I
So Ffo+ I 2-J (1A1i) I{-){" -ruc+ vt (. 0 <--5 v:(", t) (v.-?f)
(Malee Sy",,",,-f(;C j siSo
<Jrci h I S fre+l-y)
0.8
0.6
0.4
0.2
0-15 -10
f3 ::9.2- of
IZO ::
CL~
2TT
ik e~ [~) J2-t [ ~j<,,-n ]'t
'" 4 2 ~,- ;:p(o+
D)[ ~ \ J 2~ [ ~ J I ~k - nJ
t
0" 1 f.A- ~1.5
v = 3.::'
0.5
0-15 -10 -5 50 10 15
---
Pe=h SCf'o..(c--tee-i \J~ 3.0
50 k:fSD--- -
2f' -3.0
6 0
6-(--1"-i) -
(,.?11
@)
Ai=' C¥lQ=L~I
20
~{'
[) r~6 A~lD
- -~-~----
See Th<i pe.(cs sefc(C1<::o-t- V='4-.b
Dr k I3D4-. 6'----- -
2.f-
[iC\+ (,,~ Co oR e .
CA.)
u ~ [-100.1:200.1J/10;v ~ 4.6:a1 ~ 2*besse1j(1,u+v/2)./(u+v/2):
a2 ~ 2*besse1j(l,(u-v/2))./(u-v/2);ir ~ (a1+a2) .'2: <:---plot(u,ir):hold onv ~ 4:
a1 ~ 2*besselj(1,u+v/2)./(u+v/2):a2 ~ 2*besselj(1,(u-v/2))./(u-v/2):ir ~ (a1+a2).'2;plot(u,ir):v ~ 5:a1 ~ 2*besselj(1,u+v/2)./(u+v/2):a2 ~ 2*besselj(1,(u-v/2))./(u-v/2):ir ~ (a1+a2) .'2:plot(u,ir):
Lt. r:-,<,: ~hel~rt'(O><; """ ,"'f;"""
LA '5 ~ Cor"Jol~-(;v",
CDb)
u ~ [-100.1:200.1]/10:v ~ 3:a1 ~ 2*besselj(1,u+v/2)./(u+v/2):a2 ~ 2*besselj(l,(u-v/2))./(u-v/2):ir ~ (a1.A2+a2.'2):~plot(u,ir):hold on
v ~ 3.3:
a1 ~ 2*besselj(1,u+v/2)./(u+v/2);a2 ~ 2*besselj(1, (u-v/2))./(u-v/2):ir ~ (a1.'2+a2.'2):p1ot(u,ir):v ~ 2.7:
a1 ~ 2*besselj(l,u+v/2)./(u+v/2):a2 ~ 2*besselj(1,(u-v/2))./(u-v/2);ir ~ (a1.'2+a2."2):p1ot(u,ir):
-to ( ""
bv>-r SL IJ'0 F'ceSnel c..ft'{Ox,,",,~-l;o,,)
E'xf'cncA 5'tv-q~ (00'1
AJ>()<I'o::: S A{x) Y) hCx-x} (J-Y') x cA'1. . . (x'+(J)
hc=-L 1lcoA ,Ie.
-- 'Ao1 B e-
-, 1<JX"n.,,,,>
H"'r A(x Y\= Eo----
II< Jx>. y'
JJ;X>-,'i' -"3
X""1101-+
- Fh<S-e2,) If'
J 'r- denoW';rc.iO!
<;uA (x/ Y) ~ E
0
-;1001 -, Ic(x>" y>\/"cJe e --Iccj
ev
AJ (X-"d) =
,
I I - , Ie0'1~ ,<CC'I e
:>.,c\ e E ~0 l<c..I
)< S5Ie. > » ,k r / X\
~
( v\ 'J-'2;;-(X..,Y -I'2'YL(>(- +'0-' cAXcJYe C'
txfc;"J S').t-oleJ -fer",,:,:
- - ~ ) )~\ (x <,OJL) r ' (~ -t k I>- 'y )2T1d~ E" e JJ e-' ~{X e>-i JXcAY
Re (DJn~'le ;,,1eo(.o.1 c;S0r-o,-,c:er t{c.f'c,-f'or~
0-('p lof" c :rc~ lor 0Fe,i"re.
J ",:,f r; ke 0~o-f ,--,e d:,) fl' e-i"ss (O,,(j c,'teJ
i~~-j {e')",(T
b1d
x:: t (oS 1>y:: ! S 'f r cp
00c-c. Ic ~ Ie. -f,' 0 f1 -tor ~b':: (:) J :) ; '" e
AO:)</~b) ,S c,/l;hc1(;~«(,/
'S'("' "'-+c;c
Go -t (OG ;-1-c,5o""
Letc'
LV r >\ (" Ie =k><
Ie =)< 01 '0
6)
I\[e-.. J"2 T1 D/z- ' IS
C -, eX/CDS cjJ
) e / of! c) 1>(';) 0
cp ;" i "'J'" I S' J e<,8~S5C'( ~~ci, o~
2",
\ -,k",?(os c:PJ e cJep-=-c) 2 T] To (i<x t )
The" t ;1'1e) «,1 'JIveS
D/L
2 TT So To (I<-"f) I dt =
3,
2iT
J<}
IcJ>~
j To (h \ ~ cJ ~0
- Z"Iex' J' ( ~o \ \ex DI b ) 2:
- ~ - (r-"D \
)ex J I '-)
So/ AJ (x, ~ =- - ~2 E ~ ~ ()(~(,/) 1T Dol (~ )l;J 2 n~ 0 e \< ~1 2~f'
,---'--- DL ,£..(y,,~'v'\
[2o1
( kfD\~iA; ("';'3)= -; L+oA l Ev e 201 I~ J, ~ JJ
,-- -
J c-st I: /ee. ~(c..~V' k",,1er (eSto,(+ --f'c,r Ilc~(' ~"-v-('
'l"c~J€',,1 OY1 Ie" 5 w:tk f'=~
-----
(jji)
s- ~) 1\( e eJ -+(,,"nS-f'O(~ =-t' ;>1:)c,(O~'I
A (x,'Q'):-
N-I
2-N-I
Zb.Jx- nc,/ ~-~C>.)n~ 0 ~'o
lA:Jhere A, (x,'Q\::~- 0 (Ix/<:;, lor"?)
( e ISc )- 0
Ii e"--4J ~x, Ieoj co S S
-;(k,,)(-tr,(j)A(x/\)J e d-Y d<a
<: ~ = \ -i(k-"x-<fc'o'o)C J S At ()<-nc,> "crY>\c,) c cJ>< d't-"/~ -ct)--
IXO; X-y;c-
'6'= '-6-"'0,
~) x ~ ><'~ Yl e;
=) d ' ~~ Me;
A (r", rb) ::
, L \ b/, b/>- '( , L ')
~ -1(k:x"C>.-rJC"",,"-) \' <; -I Ie"x."",'} / ,L E J J EDe. vi x Jr
"1M -b/e - ";e
-2.
-;(/cxnc.-tk"..."je I <-' lex ~, Ic." Ie,
CJ ,;;,flC T S'nC ~h,~
-b2<;IfI(
kx ~ ~~)-s:- Sine: l
"I-I
:f e -, k-xn"
f'\1-I
i. e-;ic""",,,,,~o /'h'CJ
:: 62. Icll~, h~ (I-e-:k-"'N
(1-e.-:/rvON
)SIY'LySlrC2 -'I-;k-,c- I
-'~,c.-c- -e
---Sc-~t I; Ice
A(kxJ~\ :
O',-t-r,c, <:f; o~
If\),IL~
b't
)/01~
[I)
,~ C Ie-s~ C:;6
.
(N-'
)11- -llcxc;.T ,-L
( "I-I)
, N/cx~
\) p ",-(_Co - -;),-L-- C -0 . ).. "2-
s:" ~2.
, NI<~aS 'r ?
5-" ~2
, .I Icx ~)
,
( I::..b \>< c, I (1 C(. T c, 'kC 'T)
(J ~ *E' ( '"' -------.-----------.----------...--
. L ( k-X ~\ I. ( k'6 ~)S' f'\ c.. ~) S'0( ~2. I\lkxc. )
.
(Nic'cro,
)<;;" (~ 5",) ~~
( l'Xc, \ ( ~\SI,,2 ~) 5",,' )01)
x
-
b') /" -fo{c,1
Loob
f Ic~ e, je-f
)
(AJ ( ~:-rL cJ ~ -f'F ",1-+cr~
(: Iee : . . . . .
I{? 0 ~ s;" c -F'k ~ C-l, enS
. . .. . ..f', Ihr ~I'-"-i. .'- _I
5"J,""(e.. '...
To-/~I wJ+J.,.
-:::: '{"f -- 2:J.-t'
kb -- b. . . '.~)
Sfcc;",,:>
- 2TI' -p :\-P--J<:G; c"