7/30/2019 [Fsica per a multimdia] PAC 1

1/8

J Q @ A N ] E R N D U C X @ D H @ N

KF R H @ C C F I A O E Q X E Z E

A A B P $ I A $ Q N

7/30/2019 [Fsica per a multimdia] PAC 1

2/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l 2&?

> @dnl`ieu ~ue fd}c`u uin an` n ab`an he : ad he afqxnx ndbxfdq hfr

n E }reqqeu ec zfcud he cn an` n ei ui`xnxq hec Q`qxedn@ixerina`finc ` ei ifxna` a`eixj`an

: ad 4 =#=: d /=#=: d)1 4 2#>: >=$8 d 1

b Xei`ix ei afd}xe ~ue anhn xfd hfr dequrn n}rf `dnhndeixuiq =#1 id he h`dexre ` jeix cn qu}fq`a` ~ue qi }erjeaxndeixeqjr`aq# ancauceu ~unixq xfdq o` anbei q` eq afccf~uei hejfrdn frheinhn# jfrdnix ceqxruaxurn ~ue q`ih`an n cn j`lurn >

J`lurn > Ed}n~uexndeix hecq xfdq hfr }er n cn}nrxnx b

]er n qfcua`finr n~ueqx e era`a` coe h`z`h`x ei 1 h`deiq`fiq }er n ~ue ec

acauc q`lu`dq ja`c heixeihre Q` qu}fqed ~ue ecq xfdq eqxni nc`ienxq ei ci`n nc ccnrl he =#=: d xei`d ~ue;=#=: d ; =#1 >=$0d 4 2 >=? xfdq ei ci`n

]er n afizerx`r n` n 1 h`deiq`fiq# of oe ducx`}c`anx }er q` dnxe` 1 af}q `ec requcxnx q;

/2 >=? )1 4 ? >=28

]er xnix# ec ifdbre hxfdq ~ue an} nc aub he : ad he afqxnx q ? >=28

a Afiq`hereu ~ue cfr ~ue xei`u afrreq}fi n c`qxf} dq eqxnbce#ndb >? ieuxrfiq Ancauceu cn dnqqn he cn an` n

/deipq}reeu cn dnqqn hecq eceaxrfiq)

Q` }nrx`d he ceq dnqqeq qeleixq;

]rfx; >#:=$2#:=$2

7/30/2019 [Fsica per a multimdia] PAC 1

3/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l 1&?

2 Eiudereu 1 dnli`xuhq eqancnrq# 1 dnli`xuhq zeaxfr`ncq# ceqh`deiq`fiq he anhn dnli`xuh ` uin ui`xnx ei ~u eq }ulu`idequrnr

Dnli`xuhq eqancnrq Xed}ernxurn; cn qezn h`deiq` q G ` cn ui`xnx hec Q@ q ec Gecz`i @ixeiq`xnx; cn qezn h`deiq` q @ ` cnui`xnx hec Q@ q cnd}er Xed}q; cn qezn h`deiq` q X ` cn ui`xnx hec Q@ q ec qelfi

Dnli`xuhq zeaxfr`ncq

Jfrn; cn qezn h`deiq` q J ` cn ui`xnx hec Q@ q ec Ie|xfi Naaecerna`; cn qezn h`deiq` q n ` cn ui`xnx hec Q@ q ec d&q2

@ixeiq`xnx ccud`ifqn; cn qezn h`deiq` q @ Z ` cn ui`xnx hec Q@ q cnanihecn

1 Ecq e }er`deixq he cCOA# cnaaecernhfr ~ue on hexeaxnx ceq }nrxauceq dq afd}nx`bceq ndb ce `qxia`n hec Bfq he O`llq#leiern >5 }exnbpxeq /]B) he hnheq cnip Eq}ea`j`~ueu cfrhre hednli `xuh hec ifdbre he HZH huin an}n /8#< LB) ieaeqqnr`q }ereddnlnx{ednr xfxn n~ueqxn `ijfrdna`

> ]B 4 25=B

8#< LB 4 8

7/30/2019 [Fsica per a multimdia] PAC 1

4/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l 8&?

n Hexerd`ieu ec zeaxfr zecfa`xnx

]nrx`ix hec jex ~ue eqxed hnznix ui dfz`deix reax`c`i` ui`jfrde# xei`d;

Ccnzfrq#

b Hexerd`ieu ec zeaxfr he }fq`a` hec db`c nc an} hui d`iux

Cn }fq`a` ei juia` hec xed}q ei ui dfz`deix reax`c`i` ui`jfrde q;

> d`iux 4 := qelfiq# }er xnix;

a Afiq`hereu ~ue zfceu }cnqdnr n~ueqx dfz`deix n cn }nixnccn hecfrh`inhfr# ndb uin reqfcua` he >2?= ?== } ecq# jeixaf`ia`h`r cfr`lei he cnix`a QR ndb cn anixfinhn `ijer`freq~uerrn he cn }nixnccn Ec q`qxedn he affrheinheq hec

}rflrndn hni`dna` eqx fr`eixnx qelfiq cn j`lurn 1# ndbcfr`lei n cn anixfinhn qu}er`fr eq~uerrn Xei`ix }reqeix xndb~ue ui dexre eqx re}reqeixnx }er 5 } ecq# hexerd`ieu ceqaffrheinheq hec db`c nc an} he >= qelfiq honzer afde inx ndfureq /Ancauceu ceq ifzeq affrheinheq ux`c`x{nix ceq jrduceqhe cn}nrxnx > 5 hec dhuc >$ aniz` he q`qxedeq he rejeria`n#afiq`hernix nilceq }fq`x`uq ei qeix`x nix`ofrnr`);

J`lurn 1 Q`qxedn he affrheinheq QR ux`c`x{nx nc }rflrndnr` hni`dna`

7/30/2019 [Fsica per a multimdia] PAC 1

5/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l 5&?

]er n afdeinr# ancauced ceq affrheinheq ei ec }r`der q`qxedn he rejeria`nux`c`x{nix cn dnxe` n jrducn ~ue ei cn}nrxnx b;

N afix`iuna`# afizerx`d ecq dexreq n } ecq;

]er xnix# xei`d ec zeaxfr }fq`a`;

Nrn jed ec aniz` he q`qxedn he rejeria`n# ~ue q uin rfxna`;

Ec zncfrh 2> q ?== ec hp 2>q = }er~u ec ifu fr`lei he affrheinheq eqxnc }uix /?==#=) Cnilce q he $0= }er~u q ei qeix`x ofrnr`

]er xnix# ceq ifzeq affrheinheq qi;

5 Ui afx e qurx heq hec re}q ei ui dfz`deix reax`c`i` ` ei 5 qelfiqa`raucn n 5=gd&o Ancauceu cnaaecerna` /ei d&q 2) ` cn h`qxia`n ~ueon reafrrelux ei n~ueqxq 5 qelfiq

7/30/2019 [Fsica per a multimdia] PAC 1

6/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l :&?

: Hexerd`ieu ceq affrheinheq ei juia` hec xed}q /x) p/x) hui }uix he cn a`raudjeria`n e xerin huin rfhn he 2= ad he h`dexre~ue l`rn n hueq rezfcua`fiq }er qelfi /r}q) ei qeix`x ofrnr`# q` ecaeixre he cn rfhn eqx q`xunx n ceq affrheinheq _425 ad P41= ad

req}eaxe hui QR Afiq`hereu ~ue if o` on heqjnqndeix eiafdeinr ec l`r

Ei ui dfz`deix a`raucnr jed qerz`r ceq e }reqq`fiq qeleixq;

N` ~ue q` afiq`hered ~ue if o` on heqjnqndeix# xei`d;

< Ui qnxcc`x he xeceafdui`ana`fiq he 2== gl heqar`u uin rb`xna`raucnr nc zfcxnix he cn Xerrn n 15= gd hncnhn Heq}rq huine }cfq` nc qeu `ixer`fr ec qnxcc`x eq h`z`he` ei hfq xrfqqfq he 5= gl` he >5= gl he }eq ^u`in qer cn zecfa`xnx frb`xnc hec aeixre hednqqeq hec afikuix hecq hfq jrnldeixq he qnxcc`x6 N ~unixq~u`cdexreq hncnhn heqar`ur crb`xn n~ueqx aeixre he dnqqeq6Afiq`hereu ~ue cn dnqqn he cn Xerrn q d X 4 5#0? >=28 gl# ~ue ecrnh` he cn Xerrn q r X 4 :1

7/30/2019 [Fsica per a multimdia] PAC 1

7/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l ) he 5== l eqx q`xunhn qfbre uin }`qxn he lec# eire}q# n > dexre he cn }nrex Uin ncxrn bfcn /bfcn 2) he 2== l fanafixrn eccn n 5= ad&q ` ced}eip an} n cn }nrex

J`l urn 8 Cn bfcn 2 qn}rf}n n cn bfcn > ei uin qu}erja`e qeiqe jrelndeix

Qu}fqnix ~ue ecq faq qi ecqx`aq ` ~ue if o` on jrelndeix ~uerehue` ` cn zecfa`xnx he ceq bfceq# hexerd`ieu;

n ^unix he xed}q xr`lnr cn bfcn > n fanr afixrn cn }nrex6

]er n ancaucnr ec xed}q }r`der qon he ancaucnr cn zecfa`xnx ~ue x`ihr cn bfcn >heq}rq he ~ue cn bfcn 2 f~u` ndb eccn Ei xrnaxnr$qe huin afcc`q` ecqx`anqeiqe jrelndeix xei`d ec qeleix q`qxedn he~una`fiq;

Q` jnaxfr`x{ed ` ceq afdb`ied ndb cn cce` he afiqerzna` he dfz`deix xei`d;

Heq}rq he afdb`inr ceq hueq e~una`fiq xei`d ~ue;

z >j 4 =#2?5< d&q /an} n ceq~uerrn)` z 2j 4 =#2>81 d&q /an} n cn hrexn)

Nrn kn }fhed ancaucnr ec xed}q n }nrx`r he cn jrducn he cn zecfa`xnx

7/30/2019 [Fsica per a multimdia] PAC 1

8/8

Jq`an }er n ducx`dh`n]NA >

Kfrh` Ccfiao Eqxeze AA BP$IA$QN ]l ?&?

b ^unix he xed}q xr`lnr cn bfcn > n xfrinr n fanr afixrn cn bfcn 2heq}rq he rebfxnr afixrn cn }nrex ei cn dnxe` n h`reaa` }er eiqeix`x afixrnr`6 ]er afdeinr anc qnber cn }fq`a` `i`a`nc he cn bfcn 2 ~uni cn bfcn > xfan cn

}nrex;

N afix`iuna` `lunced ceq h`qxia`eq he anhn bfcn ed}rnix cn dnxe` n e~una`hec dfz`deix reax`c`i` ui`jfrde ` eqbr`ied ec xed}q ei ~ue eq }rfhu`rc`d}naxe# kn ~ue ceq hueq eqxnrni n cn dnxe` n }fq`a`;

Cn bfcn > xnrhnr28 qelfiq ` d`l ei xfrinr n fanr afixrn cn bfcn 2 heq}rqhe rebfxnr afixrn cn }nrex

0 Ui ncxnzeu edex uin fin qfifrn he >= $: \&ad 2 ^u`i i`zecch`ixeiq`xnx ei hea`becq /hB) edex cncxnzeu6

>= Heq`xled jer uin ni`dna` ei cn ~unc ui fbkeaxe ei re}q anuheq h uin ncnhn he >= d# qelu`ix ecq rn`cq qeiqe jrelndeix h uinduixnipn ruqqn ^u`i qer ec dhuc he cn qezn zecfa`xnx n uinncnhn he 5 d6 Afiq`hereu l4>= d&q 2 ` ielc`l`u ~uncqezfc x`}uq hejrelndeix

]er n }fher ancaucnr cn qezn zecfa`xnx n 5 dexreq onured he ancaucnr }r`der ec

xed}q ~ue xnrhnr ei nqqfc`r n~ueqxn ncnhn d`xkninix ceq jrduceq hec dfz`deixreax`c`i` ui`jfrdedeix naaecernx;

N afix`iuna` njel`d ec xed}q fbx`ilux ei cn jrducn he cn zecfa`xnx;

N` hfiaq# cfbkeaxe ei an`luhn cc`ure x`ihr uin zecfa`xnx he>= d&q an} n bn`