Page 1

   "! % # $'&)(+*,.-+$'/102435*607*68)9:(;-=<>(+9 Diffraction - geometry for the Fresnel formula

O r o -r' dS'

ro r'

Origin

? Each @BADC=EGF)element HJofILK=spherical MONDPofQ>area @OR.ETwaves: SVUXdS' WT@ZYD[\ofthe YVthe]^S`signal _4SaVFdetected Wcb=acts EGYDC=ADasbataSL[SVdeFEGWTC=ETFLM>f6SVUgbhFXiZFXjkFX[lW monqp aperture source YV]JOWcisb;FrtheSLdqsum FXEGWcC;ET(asFsUdS' YD[tWTtends ET@Zu;C;WcFXtovwWTzero, YxWcb=FytheWcYLintegral) WgSVi.z=FiZm{ofSLWWTb=FsYDu=vTFXEGaLSLWT@ZYD[\deYD@Z[tW}|M all these contributions.

HJILK~gN


€b=FX[Sy_4SaVF @Zvm;@BRqEcSVUWcFmut‚SV[kSVdqFXEGWTC=ETF„ƒ…†SLv^vGb=Y‡_w[@Z[?@BADC=EGFwHˆIK=MBNV…‰vGY WTb+SLW WTb=FyYDET@BAD@Z[=SVie_ŠSaDF @Zv4d;i‹SV[=Fy@B[Wcb=FsSLdqFXEGWcC;ETFV…+FSVUgbŒvTd=b=FXET@BUSVi._ŠSaDF vGWcSVEGWT@Z[=A]EGYDj Ž‡ SV[=mŒYDu=vGFE"aDFmhSLW Ž„ @ZvwYV]JWcb=Fy]YDEGj ‘’+“ ŽX”T•G–6— ™Jš Ž„˜ ›œŽ šžŸZ ¢¡£‹¤‰¥¦ §©¨T¤‰§«ªZ¦ ¬  _wb=FXETFsWcb=F vTFXUYD[;m+SVEG‚\vGYDC=EGUF vGWcEGF[=ALWcb­… ˜ …o@Bvd=ETYDdeYDE"Wc@ZYV[+SVi.WTY`WTb=FrSVjkd;iZ@BWTC=m=F>YL] WTb=Fsd=ET@Bj®SVE"‚k_ŠSaDFrSLW Ž  M ¯°]4WTb=F®d=EG@ZjkSVEG‚±_4SaDF®b+SVvSŒUYD[;vGWgSL[lWSVjd=iZ@OWcC=m=F`Y‡aDFXErWTb=F®EGFiZFaLSV[tW)EGFAD@BYD[­… _1F`USV[_wET@OWcFWTb=FWcYVWcSViˆz=FiZm²SLW Ž„ SVvsSvGC=j7Y‡aDFXE SViZiJWcb=FxvGFUYV[=m+SVE"‚_4SaDFXiZFWcv… YDEX…=@Z[³WTb=FsiZ@Zj@BW…‰SVv´SV[\@Z[tWcFXADEcSVi ‘“ ŽX”T•G–µ— ¶ ™Jš Ž„˜ ›œŽ š ŸZ ¢¡L£‹¤‰¥¦ §©·X¤‰§ ª ¦ ¬  — ¸¹cºZ»½¼:¾°ºO¿4Àl¾Á'ÃĺZÅÇÆ'ÈˆÉ ™Jš Ž˜ “Ë›œÊ Ì– Ž  š  ŸZ ¢¡£‹¤‰¥¦ §©¨c¤‰§ ª ¦ ¬ moÍ  — ˜ ¸¹cºZ»½¼:¾°ºO¿ŠÀl¾Á'žÃκBÅÇÆ"ÈÉ ™Jš ŽN ›ÏŽ  š‹ŸZ ¢¡£‹¤‰¥¦ §©¨c¤‰§©ªB¦ ¬ moÍ  _wb=FXETF Ž‡ @Zv SkdeYD@Z[tW}YD[±Wcb;F)d=EG@ZjkSVEG‚_ŠSaDF]ETYD[tWrÍÐSV[=m±moÍ  @ZvwWcb;FSVEGFS®FXiZFjF[tW YV]ÑÍÒSW Ž„ M ÓrÔJÕ=Ö×hÕ+ØJÙÐÕ+ÚÏۈܫݞބßJÙJ× |>[=Fw]C=EGWTb=FE^m=FWgSV@Bi=Wcb+SLW1?+ETFXvT[=FXie]YVC=[=m®[;FUFXvTvTSVEG‚_4SLv1WcYs_wET@OWcFWcb;F}UXYD[=vGWcSV[tW ˜}à SVv1á ™ ‘ àâ Iãхl_wb;FETF>‘ à @Bv1WTb=F jkSVAD[=@OWcC=m;F´YL]­Wcb=F}FiBFUXWTET@BU´z+FXiZmYV[kWcb;F m=@OR.ETSVUXWT@Z[=A ä'å­æ„çŠè©é'êÎç"ëLé'ç^ìíqî‡êÄïVð°ñé'ò«êÎìëyò©ììóyñwôñgõìXðèËò«çGöyíÌìð©÷­ñøð°î>÷ùê¢ò©æ ò©æ„ç1öú„û„üÎêÎéGñgò«êÎìë êÄëkýGþþÿ4ìøí ò«æ„çŠèËëLñøö„ö„êÎü ´ò©ê¢ò©üÄçTî û Lñgò©æ„ç"ð ð©ñëé'çTè«é"ì ñøð©êÎñ ð©êÄôñøü î‡ê ËýGþý °ýGþXþ ð«êÎôñøü î‡ê ìûè«ç"ð çTî1é"ìüÎìú„ð©çGîŠî‡êÄïVð°ñé'ò«êÎìë4íÌð©êÄë çGèeñgòoò©æ„ç:ûVìú„ëîñøð©êÄçTè+ìøítèËæLñî‡ìg÷:è+úLèËêÎë ÷ùæ„êÄò«ç:üÎê æò :çG÷ ò«ìXë ‡ð«çGöLçTñgò©êÄë ð©êÄôñüÎî‡ê è­ç ‡öLçGð«êÎô4ç"ëò©è ñXèËóXçGî Xñøð©çˆëìøò­ò«æ„çð°ñ ‡è.ìøí lê æòùêÄë>öñXè«è«êÄë 1û ò©æ„ç çGî XçGè:ñëîsè«êÎî„çGè:ìí qì‡î‡êÎçGè VûLçGëXòÑèËç çGð©ñüDò«êÎôŠçTèJûLñé°ó÷.ñð©î>ñëî íÌìð©÷.ñð©îè „÷ùêÄò«ærñô4ìøò«êÎìëyüÎêÎóç ò«æñøòùìøí;ñë eç"ü :ëLî î„ìŠëìøò­ò«æ„çò©æ„ð«çGç „ð©êÄë XçGè­ìí;é'ìXüÄìXú„ð î lê æòùôŠçGëò«êÎìë î}ñð«ê è«çJíÌð©ìôè«úé°æ ûLçGëî‡êÎë Xè :çG÷­ò«ìXë`ë„ç Xç"ð ìøò^ò«ìsò©æ„ç´ûVìøò«ò«ìXô%ìíùò«æ„ê è oñøëîxëç çGð^ñé°óë„ìg÷ùüÎçGî çGîrò©æ„ç´÷­ñ ç ò«æ„çGìð ìøí:üÎê XæXò4ç Xç"ëxò©æ„ìú æ`êÄò÷.ñXè^ñ gñøêÎüÎñû„üÎç ý çGñð©è^ûLç"íÌìð©ç}æç}ö„úû„üÄê è«æ„çGîæ„êÎè 6êÎë ý :çî‡êÎî´ë„ìøòqò©ñóç:ú„ö´ò«æ„çˆ÷.ñ Xç­ò«æ„çGìð 4êÄëwü ñgò©ç"ðqçGî‡êÄò«êÎìëèqìøí oêÄë ý ý ˆìðý ‡ý ìðeêÎë ò«æ„ç1ý ÑçGî„ê¢ò©êÄìXë é"ìð©ð«çTéÇò©çGîŠû 1ò©æ„ç Jú‡ò«æìð èqìg÷ùë Jñëî ‡ñøëîwüÄç"í ò.ûVç'íÌìXð«ç:æêÎè JçTñgò©æ´÷ùêÄò«æò©æ„ç .ììXó‡èËçGüÄüÎç"ð :ç çGðËò©æ„ç"üÎçGè©è †èËìXôŠçìí.æêÎè1èËöVçGé"ú„üÎñøò«êÎìëèÑæLñ ç Ìë„ì ö„ú„ëêÄëò©ç"ëî‡çTî èËò«ð©ìë >÷­ñ ç ì çGðËò©ìë„çTè „ìXð:ç „ñôŠöüÄç „êÄë>æ„ê è:î‡ê è©é'úè©èËêÎìëLè­ìøí;ò«æ„ç6ç"ò«æ„çGð:æ„ç6ñXèËóXçGî ˆú„çGð +ê èùë„ìò Jê èËêÎìë öLçGðËíÌìXð«ô î4é°æ„êÄç Šû 1ò«æç JêÎû„ð°ñgò«êÎìëLè+ìøíDò«æêÎè yçGî„êÄú„ô ç ò«çGëî‡çTîŠò«ìò©æ„ç:ûVìøòËò©ìô ìøíDò©æ„ç Xçùû ò«æ„ç :ñ ‡è:ìí lê æò tñëîyö„ð©ìöñ Xñøò«çGî ò©æ„ð©ìú Xæyò«æ„ç4è«ìüÎêÎî VöVç"üÎüÄúé"êÎîrñøëî ú„ë„êÄíÌìð©ô .ñøö„êÎüÄüÎêÎôŠçGëò©ñ ìøí†ò«æ„ç ˆö‡ò©êÎé°ó :ç"ð çTè­êÄëò©ì1ò©æ„çö„ü ñé"çìí ‡ç"ëè©ñgò©êÄìXë HJILK~"I 

   !" $#% & (')* ,+  "-/.'0'132 -45%768 59':*-

;=<>5%?2@6$?0AB#C'ED; 

GF

EV

[Z

W@J

]\

3W

a

cb

I

KJ

ML

ONP

E

?^

OZ

OZ

0W

V

gU _cX UYF

%W

V

}%

`

W

X

T

EV

OUYX

%W

>P

[\

V

E

$e

W

W

r<lD;" 0m

g\

@p

tZ

%S

c_Tx

vI

RW

ysRQz

|Z ?^

W

n n

tZ

[U0UUU dg_

nRs RZ

vu

V fL

r{

V

k<lD] 0m

wZ

OZ

W

W

j

Z

?^

|\

OV

g\ `

OZ

V

a

Y`

Z

W

iW

_

V

OV

noj%Uqp

nQRo

H_

7F

V

RQTS U=J

W

5dfe

W dg_hX

!~

HF

%W

W

8b

€

V

r{


vGC=EG]ËSVUXFVM }YLWcFyWcb+SWWcb=FXETFs@ZvwSxd=b+SLvTFsUgb+SV[=AVFrYV]Jã â I)@B[³Wcb=FsF †d=EGFvGvT@ZYV[­M^€ FyUSL[ @BAD[=YDEGF`WTb=@Zvsm=FWgSV@Bi©…ˆSVvs_ŠFkvTb+SViBi6SViB_ŠS‚‰v)iZY‰Y SWr@B[tWcF[;vT@BWT@ZFXvr@B[²WTb=FkFX[=m­…ÑvGY{WTb=@Zv d=b=SVvTFs@Z[†]YDETjkSLWc@BYD[®_w@BiZi.ueFsiZYDv"WM b+SLW´AD@OaDFXv´C;v}SxEGFU@BdqF>]YVEUYDjd=C;WT@Z[=AWTb=Fyz+FiBm{SW´SV[t‚³dqYV@Z[tW´SVv´SxETFvGC=iBWwYL] S l[=Y‡_w[±d=EG@ZjkSVEG‚_ŠS‡aVFVM {Ý Ž ÔˆÔ BÖ Ž„Ž × Þ‡Ý eØ b=F³vGFUXYD[=md=ETYVu=iZFXj@BvrWcb=SLWWcb;FETF³[;Yu+SVU t_4SLETm†~°ADYD@Z[;A±_4SaVFiZFWcv ²_wbt‚ m=Y‰Fv WTb=F _ŠSaDF LFFXdjkY‡a‰@Z[=Ax]YDE"_4SLETm=v b=Fru=SVvT@BU)SV[;vG_1FE>@BvwWTb+SLW´Wcb+SW @O]ˆ_1F)m=YWcb=F jkSLWcb;v´d;ETYDdeFEGiB‚ “ y@BETUgb=b=YLR – _1Frz=[=mhSV[{F ‰WcETSk]ËSVUWcYDE´@Z[\Wcb=F @Z[tWTFADETSVi:@Z[taDYDiOa‰@Z[=A WTb=F SV[=ADiBFvYV]JWcb=FsvGYDC=ETUXF~°d=ET@Bj®SVE"‚®_ŠSaDF)vGC=EG]ËSLUFyaDFXUXWcYVE SV[;mŒWTb=Fsd=ET@Bj®SVE"‚k_ŠSaDFø~ vGC=EG]ËSVUXF~°YDu=vTFXEGaLSLWT@ZYD[{dqYD@B[tW}aVFUXWTYDE}_w@OWcbŒWcb=F _4SaDF)vTC=E"]ËSVUF @O]Wcb;F)vTYVC=ETUXF)@Zv´@Z[ iB@Z[=F _w@OWcb³Wcb;F UXF[tWcEGFrYL]ˆWTb=F SVdqFXEGWTC=ETFyWcb;@Zv 1_ŠYDE lv}YDC†WWcY`uqF “ –^— IN “"N UYDv„“ –G– _wb=FXETF Œ@BvyWcb=FkSV[=ADiBFxYV]ŠWTb=FYDC;WcAVYD@Z[=A³_ŠSaDFk]EGYDj WTb=Fk[;YDETjkSViWTYŒWTb=Fkd;ET@ZjkSVE"‚ _ŠSaDFX]EGYD[tWM v®iZYD[=A SVv_ŠFSaVYD@ZmÐiZSVETAVF±SV[;ADiZFXv…Š_1FhUSL[ WgS LF “ – WTYÏueFÏND…wSV[;m Wcb=F SVd;d=ETY †@ZjkSLWc@BYD[ ‘“ Ž„X”T•G–— ˜ ¸ ¹cºB»½¼:¾°ºB¿4Àl¾Á'žÃκBÅÇÆ"ÈÉ ™Jš ŽN ›ÏŽ šžŸZ ¢¡£‹¤‰¥¦ § ¨ ¤‰§©ªO¦ ¬ moÍ   @BvySVm=F ‰C=SLWcFkSVvsSV[²SVd=d;ETY †@ZjkSLWc@BYD[±WcYŒSV[ F =SLUXW vTYDiBC;Wc@BYD[YV]6Wcb;F`_ŠSaDFF lC+SLWT@ZYD[ _w@OWcb³Wcb=F SVd;d=ETYDd;ET@‹SWcFyueYDC=[=m+SLEG‚³UXYD[=m=@OWc@ZYV[=vM ¯°]_1Fs@ZAD[;YDETF>WTb=Fsm=@Zv"WgSV[=UXFsm=FdeF[=m;F[=UXF)YV]JWcb=F SVjd=iB@BWcC;m=FV… ‘“ Ž„”T•G–— UXYD[=v"WgSV[tW ¸ ¹cºZ»½¼:¾°ºO¿4Àl¾Á'ÃĺZÅÇÆ'ÈÉ ŸZ ¢¡L£‹¤‰¥¦ §©¨T¤‰§ ª ¦ ¬ moÍ  YDEX…=@Z[\UXYDjkd;ETFvGvTFXm±[=YVWcSLWc@BYD[ ‘ — UYD[=v"WgSV[tW ŸÎ¡£ ¸ ¹TºZ»½¼:¾°ºB¿ŠÀl¾ËÁ'žÃĺZÅÇÆ'ÈˆÉ L¤lŸ ¥ m+Í _wb=FXETFrÊx@ZvWcb=F m=@BvGWgSL[=UFs]ETYDj Wcb=Frd=ET@Bj®SVE"‚®_ŠSaDFX]EGYD[tW WTYkWcb;FrdeYD@Z[tWwYV]ÑYDu=vTFXEGaLS~ WT@ZYD[­M M„

‡

ˆ

rŠY‹Œ

‰

Š

‰

ŽŠ

‡

†

‘’‡

•–T—5˜Ž™Tš›˜œyž@Ÿw ›¡Rœ?•%¢

£

Ž¤

¦

§£

…

…

HJILK~


\Ý Ž Õ Þ„Ý eØۈÕ;ÞÞ‡× Ž ØÒÕ;ÞÜ eØ Ž Õ+Ø e× ?+YDE´vT@Bjkd=iB@ZUX@BWǂD…+WcS VF)WTb=FYDEG@ZAD@B[{YL]Wcb=FUXY†YVETm=@B[+SLWcF vG‚‰v"WcFj7SLW WTb=F)UXF[tWcEGFxYV]Wcb=F SVdeFE"WcC=EGFVM b;F[±WTb=F)m=@BvGWcSV[=UFs]ETYVj Wcb=FrdqYV@Z[tWr“  ”  ”  – YD[\Wcb=Frd=ET@Bj®SLEG‚®_ŠSaDFø~ ]EGYD[tWWcYxWcb=FsYDu;vTFE"aLSLWc@BYD[{deYD@B[lW @ZvÊ — š Ž„› Ž  š vGYWTb+SLW Ê —  %“ L›  – “ 6›  – ” SV[;mh@B]_1Fm=Fz+[=F 7SVv}Wcb=Fm;@ZvGWcSV[=UXFYV]Wcb;FYDu=vGFEGaLSLWT@ZYD[±dqYD@B[tW ]ETYVj5WTb=FUXF[tWcEGF YV]JWcb;FrSLdqFXEGWcC;ETF —    vGY ʗ › I  V› I     ƒ _wb=@BUgb{@Bv…=F †d+SV[=m=@B[=A=… Ê › V  ›   “ ” – _wb=FXETF>WTb=F>[=YVWcSLWc@BYD[ ®“ – m;F[=YVWTFv ¢WcFXETjv4YV]:YDEGm=FEXpBM6¯°]ùWcb;FsSVdqFXEGWTC=ETF>@Bv4vTjkSViBi©…t_ŠF jkS‚@ZAV[=YDETF>WTb=FyWcFXETjv@Z[ ‰ SL[=m  M b=FX[­…@BAD[=YDEG@Z[=A®WTb=FxaLSVET@ZSLWc@BYD[YV]ŠSVjkd;iZ@BWTC=m=F)_w@OWcb²m=@Zv"WgSV[;UFV…JSV[;mÏSVu;vTYDEGu=@Z[=A WTb=Fsd=b+SVvGFrUgb+SL[=ADF YD[ŒWTb=F d+SLWcbŒiZFX[=AVWTb 5@Z[tWTY`WTb=F UYD[=v"WgSV[tW´WcFXETjŒ…=_ŠF b+SaDFsWcb=F UXYDjkd=SVEcSLWT@BaVFiB‚kvT@Bjkd;iZF>EGFvTC;iBW ‘ — UXYD[=vGWcSV[tW ¸  ŸZ Î¥ ª Ǩ ¥ ª «¨ ¬ moÍ  «

‹

‰

ŽŠ

¬Š

¨

®²

¥

¯

²$¥

°

²

³°

´

´

¶µ ´

®

²

²

¯

¥

²

¯

¥

²

¯

°

²

°

¥

°

¥

²

°

y¸ ²

²·

°

°

¯

f¹º´

¯

´

¥¼»

°

´

² °

¯

²

¯

²

²

°

‡

¾´

¸ Á4Â

¿

À

¸ Á

Ã

Ä

Ã

²

±é"ð«úLé'ê ñøüDöLìXêÄëòùê è.ò«æñøò­êÄí;ò«æ„çÑêÎëXò©ç Xð©ñøò«êÎìëwì Xç"ð éGñøë ûLçÑç gñüÄúñøò«çTîwêÎë .ñðËò©çGè«êÎñë}é'ììXð©î‡ê ëñgò©çGè ò«æ„çêÎëò«ç ð°ñøüté"ñë ûVçÑíOñé'ò«ìXð«ê "çTî „ìðùûð«ç êÄò ‡÷ùð©êÄò«ç ñøëî è«ìŠò«æñøò Œé'ìXëèËò©ñøëò ¸ î ¸ î ñøëîwê¢í‰÷.çð«çGôŠçGô^ûVç"ðeò«æñøò.êÎëwò©æ„çè«ö„êÎð«êÄò­ìøítò«æç ð©ñú„ë„æ„ìíÌç"ð.üÄêÎô4ê¢ò­÷qçñøð©ç:ò©ð«çTñgò«êÎë ^ò«æ„ç÷.ñ XçGèoñXè ê¢í;ò«æç ´÷.ç"ð©çö„üÎñë„ç LèËìŠò«æLñgò:÷.çôñ w÷ùð©êÄò«ç ÅOe

W

OZ

OW

OV

ÊÑ%Ò"Ó

É

Ð

V

tUYF

¬RZ

Ê?Û Ü Ý

V

7ÈɳÊË Ì

Î Ñ%Ò"Ó

Î Û0à áTÝ

Î ÑCÔ ÕÞÖ ØÙß

Ê ÑCÔ Õ×ÖgØ&Ù?Ú /F

RZ

W

â

ÈÉ

ñøëî èËìŠò©æñgò

â

³é"ìëèËò©ñëXò ¸ É

Ê Ñ%Ò"Ó ÊEÑCÔ Õ

Ê â

ÍÉ

Ð

0P

ÍkÉÏÎ Ë Z Ì

Î

î ¸

Ê?Û 3Ü Ý Ö ØÙã

HJILK~ÇK

Î ÑCÒÓ Î ÑCÔ Õ

î

Î Û0à á Ý"å Ö Ø&Ù ä

V


Ö ÜËÝžÞ JY vTFXFb=Y‡_5Wcb=@Bv_1YDE lv³YDC†W@Z[ d=EcSVUWc@BUFV…iBFXW®C=viZY‰Y z+EGvGW\SW®Wcb;F±m=@OR.ETSVUXWT@ZYD[ d+SWTWcFXET[³YV]JSrvT@Z[;ADiZF}vTiZ@OWMˆ¯°]ù_ŠFyYDu;vTFE"aDF SLW4SV[³SV[=AViZF ‰…=SV[;mWcb=F>vGiZ@OWŠ@BvŠd+SVETSViZiBFi+WcY WTb=F S †@Bv1SL[=maVFE"‚kiBYD[=A=…DWTb=F´m=@BRqEcSVUWc@BYD[xd+SLWGWcFEG[k_w@BiZi=m=FXdqFX[=m®YV[=iB‚xYV[ L â ±M¯°] _1FsYDu=vTFXEGaVF)SLW´SL[{SL[=ADiZF )WcYxWcb=Fy[;YDETjkSVi©… V ⠗ vT@B[:“ – M b=FX[{_1Fsj®S‚®_wEG@BWTFV… ]YDEwSxvGiZ@BW4YV]ˆ_w@Bm;Wcb +… ‘ — UYD[;vGWgSL[lW ¸ Ÿ ¥ »½Æ '¬ ª m  — Uá ™YD[;vTvG@B[:WgSL“ [l–W “©IL¤ á – vT@Z[­“ ™ ^vT@B[ù“ – â I – b+SW}@Bv…;WTb=Fs@Z[tWcFX[=vT@OWǂaLSVET@BFvwSVv »½Æ Diffraction - Single Slit T v B @ [ ¥ @Z[:“   '¬ .“ –6— q“ – G v – ¥ b=FrETFvGC=iBWT@Z[=A@Z[tWTF[=vG@BWǂ\d+SLWGWcFXET[±@BvwvTb=Y‡_w[hADETSVd=b=@BUSViBiB‚®@Z[\z+ADC=EGF)HJILK=MÎI†…oSV[;m SVv´Sxd+SLWGWcFXET[ŒYV]iB@ZADbtWwSL[=m\m+SVE ®u+SV[=m=v´@Z[z=ADC=ETF HJILK=M ;M çæ=èéêré

‡

¯

´

¯

´

¾ì

¸ ²

í

¸ ²

¯

ï 5À

í

ì

‡

µ

ð

sin

‡

I( θ , λ , d)

Ž¤

ð

2 . π . d . sin ( θ )

óò

·

í

î ²

ôõ

²

Ä

Ž¤

2

² í

λ

2 . π . d . sin ( θ )

λ

1

0.8

0.6 I( θ , λ , d ) 0.4

0.2

0

15

10

5

0

5

10

15

2 .π .d .sin ( θ ) λ

? @BADC=EGF}HJILK;M I†P b=F}aLSVEG@‹SLWT@ZYD[`YV]­@Z[tWcFX[=vT@OWǂx_w@BWcb®SV[=ADiBFw@Z[`Wcb=F}m=@BRqEcSVUWc@BYD[`d+SLWTWTFEG[ YV]Sx[+SVEGETY‡_ vGiZ@BWM $‡

Fraunsli.mcd

1

11/03/99 12:52

HJILK~ ö


Fraunslj.mcd

? @BADC=EGF4HJILK=M ;P b=FiZ@BADbtWSV[;mxm+SVE u+SV[;m=v@Z[)WTb=Fm=@OR.ETSVUXWT@ZYD[rd+SLWTWTFEG[xYV]qS [+SVEGETY‡_ vGiZ@BWM b=Fx@B[lWTF[=vG@BWǂ{_w@ZiZi:ueF FXETY_wb=FX[=FXaVFEsWcb=FxSLETADC=jF[tWyYL]Wcb=FxvG@Z[h]C=[=UWc@BYD[h@Z[ WTb=Fs[‰C;jkFXEcSLWTYDE@ZvwSxjC=iOWc@Bd=iZF}YV]ã…†Wcb+SLWw@Bv_wb=F[ ™ vG@Z[ù“ –6— ã I _wb=FXETF @Bv´SV[\@Z[tWcFXADFEXM b=F z=ETvGW XFETYYV]ˆ@Z[tWcFX[=vT@OWǂ³@ZvwSW ™ ^vT@Z[­“ – — ã I YDEX…+SVvWcb;FrSL[=ADiZF )_w@BiZi­ueFyvTjkSViBi©… — Iã ⠙ — â }YLWcFŠWTb+SLWWTb=F4UXF[tWcETSVi;deFS @ZvJWcb=FŠb=@ZADb;FvGW…tSV[=mxu;ETYtSVm;FEˆWTb+SV[WTb=F4vTC;u=vT@Bm=@‹SVE"‚ deFS lvXM b;FyvTC=u=vG@Zm=@ZSVEG‚kdeFS lvwm=FUXETFSVvTFs@Z[SVjkd;iZ@BWTC=m=F´_w@BWcb³m;@ZvGWcSV[=UXFyS_4S‚]EGYDj WTb=FsUF[tWTETFVM b=F1vTC=UXUFvGvT@OaDFdeFS lv“m=@BRqFEGF[tW Œ– SVEGF l[=Y‡_w[`SVvJm=@BRqFEGF[tW ùYL]+m=@BRqEcSLU~ WT@ZYD[­M 1

11/03/99 13:27

‡

ì

Ž¤

÷

ø÷

ì

¤

„

‡

ì

úù

ì

Ä

÷

HJILK~

•%¢Oû›üR¢ ý

1B24 Waves Optics and Acoustics Lecture 24 of 33 (UCL)  

1B24 Waves Optics and Acoustics Lecture 24 of 33 (UCL), astronomy, astrophysics, cosmology, general relativity, quantum mechanics, physics,...

Read more
Read more
Similar to
Popular now
Just for you