Diffction k f c f Th Huygn-Fnl Pincil tt: Evy unobtuct oint of vfont, t givn intnt, v ouc of hicl cony vlt (ith th m funcy tht of th imy v. Th mlitu of th oticl fil t ny oint byon i th uoition of ll th vlt (coniing thi mlitu n ltiv h. Hnc to tmin th vfil byon n illumint g of lit, n to u th ffct of hicl v ouc in th vicinity of th lit o tu. ck Wvnumb Funcy Wv Wv o inut Z = Wv imnc P ZA An infinitimlly thin lit ( t, To infinitimlly thin lit Young oubl lit x Coin Rul: o o i( k t co 9 in co 9 in ( t, x co i( kt i( kt in in Aum -it ik (, t Binomil xnion: 8 in 8 in ik ik 8 i k in i k in -it (, t ik 8 -it (, t co k in A co k in v o Hnc mxim hn k in n n i n intg in n n in k Only th h tm ill vy ignificntly hn n Euivlnt gomty i vlt ouc t th m ngl (i.. ln v but t by in Ph iffnc k in Thi only ok bcu Ph iffnc k in o o in co 9 in co 9 ix co x ix Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE
Th iffction ttn of finit ith lit Th nlyi of th oubl lit cn b xtn to inclu i of infinitiml lit hich cov th hol tu ith k 8 Dfin A/ in thi c to b th illumintion mlitu unit lngth of th tu Auming ik ik in ik in -it A i.. fom Doubl lit nlyi, but u - it ik ik in ik in Funhof o lin h ith i( k- t ik ik in ik in Thi intgl cn b imlifi into to gim: i( k- t i( k- t ik co ik in ik in k in i( k- t in kin k in A in kin kin contnt A ; Fnl o utic h ith o in kin kin Hnc o hn: i( k- t ik i( k- t i t t C( co t t S( in t t i( k- t co t iin t t A C( is( Fnl Intgl Th cn t b vlut xctly, but cn b vlut numiclly k in n n k in n i non-o intg n k k B( x log x in x lim x x Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE
Gnli Fnl vfil W cn iv th Fnl gim vfil fo mo gnl gomti, n ly thi to tmin th iffction ttn of knif g. Coni th unifomly illumint tu to xtn fom to. Ding not to cl! Aum Pythgo Thom If ll A in th viou xml, th ffct of th utic tm in ill only ffct th h ignificntly n not th mlitu k i( k- t i co,, C( co t t S( in t t i( k- t t iin t t A C( C( is( is( o fo knif g, Coni ubtitution A C( C( is( is( t t t, i( k t ik (, t (, t i( kt Fom th Conu Sil on cn tht S C A i C( is( o if bov th knif g by (th thn blo mut xchng it ign. Sinc i ootionl to : A i C( is( S( S( C( C( Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE 3
F-fil (Funhof iffction ttn of gting ( n ( n ( n... Aum th gting i unifomly illumint, n conit of lit of ith, t by cing. ( t, (, t ( n ( n n it Aum f-fil (Funhof cnio i.. in in i( k t n ik in t n n (, i( k t ik in ( t, n ik in (, t i( k t ik in n n n n n n A ik i( kt ( t, Coin ul: co in i.. ln v iving t, iknin ik ( nin x i( k t ik in n (, t ik ( n in ik in ik in in t (, t kin i (, i( k t ik in ik in ik ( n in in kin kin kin n in (, t kin n i( k t ik ik in n i( k t ik in ik ( in ik in Th lt t u th fomul fo th um of gomtic i ik in... n n n n n n i( k t ik in i k in i k in i k in kin ik in i k in i k in i k in in i( k t in (, t k (, t in i k in i k in kin ik in i kin i k k ik in k in in in k k in in in in in i( k t in in in in (, t k k A in in in in k k A Zo t: in in in in in in n n, n in n in in in m m in m in kin k Mxim ( gting lob t: vnumb in in Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE
F-Fil iffction ummy Thi i th ctul fomul fo th iffction ttn v o. It incoot ll th mxim n minim ffct cib bov. A in in in in in in in m, n, Zo t: Mxim t: intg Envlo u to finit lit ith n in ; n Mxim u to lit cing in in.8 o in 9.5 o Fin tuctu u to numb of lit (i.. ovll i of tu Zo t: But mxim hn m in intg Thi on h vy fin tuctu inc i lg in 3 o in 3.6 o Almot ll of th iffction ffct ult in min lob of ngul ith (in in h i chctitic lngth of th gting, lit tc. Fo ny oticl intumnt, th olving o i likly to b iffction limit. So thi tio giv th minimum ngul vition tht to objct coul b olv vi n oticl ytm. * c-con i /36 of g.g. fo th Jm Wb c tlco, = 6.5m. So fo Inf-R light of vlngth 3.5mm, i bout. c-con*. Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE 5
Bgg l of X-y iffction fom tom in cytl lttic Pth of incint X-y Rflct X-y fom th cytl Molling gnl iffction ffct fom finit ith lit W cn u comut to vlut th vfil in th vicinity of finit ith lit hich i unifomly illumint. W thfo not tict to th limittion of th Funhof n Fnl gim co in in in Atomic lttic cing Rflct y ill contuctivly intf hn th th iffnc btn th y flcting off nby tomic ly i n intg multil of th vlngth of th X-y in n x co ik A it (, t Th i i to vlut th vfil o t viou n vlu. Th intgl i oximt by um b on lg numb of finit vlu In th xml blo : 5 in B ltiv to th mximum Bgg l cn b u to tmin tomic lttic cing ( inc X-y vlngth cn b tmin fom th oti of th ouc, n th iffction ngl cn b mu vi otting cytl (o tcto hon X-y tcto X-Ry ouc Cytl lttic Si Willim Hny Bgg 86-9 Dcibl uful mu of o ov lg ng of vlu B( x log x All th lot viulition of th m vfil o in nomli cibl. Phyic toic hnout Diffction D An Fnch..clcticon.info PAGE 6