Práctica 4: Lentes delgadas

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Ckhtks `kcij`js

J. Jrtura Dnrjh`j _asktk, Orkh`j N. \jjvk`rj _kyks y Kerjnh I. Lah`ks Cuhj

Mukvks 6; `k Djrza `k ?6:;

Jostrjlt

Nh tbns rkpart wk wncc try jh` h` tbk ealjc `nstjhlkae skvkrjc ckhsks (tbrauib vjrnaus dktba`s) oatb `nvkr-ikht jh` lahvkrikht. tbns wntb tbk nhtkht ae lahstrultnhij tkckslapk jh` j dnlraslapk, jh` dkjsurnhi tbknr dji-hnljtnah pawkr.

_ksudkh

Kh kstj prêltnlj ousljdas dk`nr `k `nvkrsjs eardjscj `nstjhlnj ealjc `k ckhtks tjhta lahvkrikhtks lada `n-vkrikhtks. Ksta lah cj nhtkhlnüh `k pastkrnardkhtk kh-sjdocjr uh tkckslapna y uh dnlraslapna utncnzjh`a `nlbjsckhtks y dk`nr sus patkhlnjs `k djihnljlnüh.

Nhtra`ullnüh

Aomktnvas

:. Dk`nr cj `nstjhlnj ealjc `k ckhtks lahvkrikhtks y `n-vkrikhtks dk`njhtk vjrnas dîta`as.

?. Lahstrunr uh snstkdj üptnla quk euhlnahk lada uhdnlraslapna.

<. Lahstrunr uh snstkdj üptnla quk euhlnahk lada uhtkckslapna.

Jhêcnsns tkürnla

[hj ckhtk `kcij`j ks jqukccj quk par sus prapnk`j`kspuk`k skr ljrjltkrnzj`j lada uh aomkta uhn`ndkhsnahjc(n.k. snh irasar, sndpckdkhtk lah jcturj):.Var cas trjojmas rkjcnzj`as par Ijuss sjokdas quk kxnstk

:Bktlb, ?66?

uhj rkcjlnüh khtrk cjs `nstjhlnjs ealjc, aomkta k ndjikhpjrj uhj ckhtk `k tjc djhkrj quk=

:

e   4

:

sn+

:

sa(:)

A, ca quk ks ca dnsda=

e  4sa  ¹  sn

sa  +  sn

(?)

@k kstj rkcjlnüh ca quk pa`kdas hatjr ks (aoskrvjock kh?), k ndpartjhtk pjrj hukstra `ksjrracca kxpkrndkhtjc,quk kstj rkcjlnüh ha ks uhj euhlnüh, n.k. sn tkhkdas uhpjr `k vjcarks quk ludpckh kstj rkcjlnüh, djtkdêtnlj-dkhtk ha bjlk `nekrkhlnj kh kc rksuctj`a lujc `k cas `ashýdkras larrkspah`k j quk `nstjhlnj (Ksta ks kc euh`j-dkhta `kc dîta`a `k puhtas lahmuij`as).[h dnlraslapna y uh tkckslapna sah, kh kskhlnj, kc dnsdasnstkdj üptnla7 cj ýhnlj `nekrkhlnj khtrk jdoas skrê cjpasnlnüh `kc aomkta, pjrj uh dnlraslapna tkh`rkdas uhaomkta pkqukúa y j palas lkhtädktras `k hukstras ckh-

tks, dnkhtrjs quk kh kc ljsa `k uh tkckslapna tkhkdas uhaomkta j uhj `nstjhlnj ca sulnkhtkdkhtk irjh`k ladapjrj quk kc jhêcnsns ca puk`j lahsn`krjr uh uh puhta khkc nhhnta.

@ksjrracca kxpkrndkhtjc

? Ckhtks lahvkrikhtks.

: Ckhtk `nvkrikhtk.

: Ukrhnkr.

: Eckxüdktra.? @njerjidjs.

: Vjhtjccj

:

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: Cêskr.

: Cêdpjrj lacndj`j.

? @njpasntnvjs.

: \astîh `k `njpasntnvjs.

\apartks ladpckmas.

\apartks skhlnccas.

@j`a quk rkjcnzjdas `nvkrsjs dk nlnahks, tkhkdasdýctnpcks jrrkicas kxpkrndkhtjcks quk pralk krkdas j`kslrnonr.

Cky `k Ijuss.

Vrndkra, pjrj cj dk`nlnüh `k cj `nstjhlnj ealjc `k uhjckhtk lahvkrikhtk par dk`na `k cj klujlnüh `k Ijuss=

Eniurj := Dk`nlnüh par dk`na `k cj cky `k Ijuss.

Lahsnstk kh cj cêdpjrj lacndj`j y cj pjhtjccj saork kx-trkdas apukstas `kc rnkc, dnkhtrjs quk cj ckhtk lahvkrikh-tk sk khlukhtrj khtrk jdojs. J`kdês, erkhtk j cj cêdpjrj

sk khlukhtrj kc sastîh `k `njpasntnvjs lah uhj `njpasntnvjkh îc. Kc aomktnva `kc kxpkrndkhta ks khealjr cj ndjikh`k cj `njpasntnvj saork cj pjhtjccj y dk`nr cjs `nstjhlnjsrkckvjhtks.

Vuhtas lahmuij`as.

Vjrj cj skiuh`j dk`nlnüh quk rkjcnzjdas vacvkdas jtkhkr cj pjhtjccj y cj cêdpjrj kh kxtrkdas apukstas `kcrnkc, lah cj `njpasntnvj musta erkhtk j cj cêdpjrj. Kh

kstj aljsnüh hklksntjrkdas quk cj `nstjhlnj –pjhtjccj-`njpasntnvj— skj 0 vklks djyar j cj `nstjhlnj ealjc qukljclucjdas pjrj cj ckhtk usjh`a kc prndkr dîta`a.

Eniurj ?= Dk`nlnüh par dk`na `k Vuhtas lahmuij`as.

Hukvjdkhtk ousljdas khealjr cj ndjikh `k cj `njpasn-tnvj saork cj pjhtjccj, sjcva quk kstj vkz ousljrkdas kcpjr `k vjcarks dkhlnahj`as kh cj nhtra`ullnüh.

Aomkta jc nhhnta

Kstk jrrkica kxpkrndkhtjc lahsnstk kh praykltjr saorkuhj supkrlnk cj ndjikh `k uh aomkta duy ckmjha usjh`auhj ckhtk lahvkrikhtk y, pastkrnardkhtk, dk`nr cj `nstjh-lnj `k skpjrjlnüh khtrk cj ckhtk quk praykltj y cj supkr-lnk

Dnlraslapna.

Kh kc ljsa `kc dnlraslapna lacaljdas cjs ckhtks (`k`nstjhlnjs ealjcks sndncjrks) j uhj `nstjhlnj mj (6.:5d+6.:>d Wcj cahintu` `kc –nhstrudkhta— djs cj sudj `kcjs `nstjhlnjs ealjcksT) `kc cj`a `k cj djyar, pahkdas

kc aomktnva j su `nstjhlnj ealjc (6.69d) y `kc cj`a `k cjdkhar pahkdas kc aomkta j aoskrvjr j cj `nstjhlnj `k cjckhtk (.:?d)

?

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Eniurj <= Kc dnlraslapna.

Pkckslapna.

Kh kc ljsa `kc tkckslapna, hklksntjdas ckhtks lah djyar`nekrkhlnj kh sus `nstjhlnjs ealjcks (.<5 y .69d), kstjs sklacaljh j cj sudj `k cjs `nstjhlnjs, y kc aomktnva vj `kccj`a `k cj dkhar skpjrj`j j su `nstjhlnj ealjc (6.69d)

Eniurj 0= Kc tkckslapna.

_ksuctj`as aotkhn`as

@nstjhlnj aomkta WldT @nstjhlnj ndjikh WldT>.; <0.2

<0.><0.5<;.6<;.:<0.>

:6.6 <?.<<:.5<?.9<?.5<0.><<.0

:0.6 :5.?:5.0

:5.6:;.>:5.::5.<

Pjocj := Dk`n`js pjrj Cky `k Ijuss

sa   sn   Krrar   e    Krrar>.;6 <0.22 6.65 9.09 6.6>

:6.66 <?.>? 6.0? 9.59 6.:6:0.66 :5.:; 6.69 9.;6 6.6?

Pjocj ?= Vradk`nas pjrjCky `k Ijuss

@nstjhlnj ealjc WldT (º?)9.;9.59.<9.;9.99.;

Pjocj <= Dk`n`js `k e 

lah aomkta jc nhhnta

<

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C @:¶ Dk`n`j :56.6 :00.<

:56.6 :00.0:56.6 :00.?

?¶ Dk`n`j :;;.6 :<>.?

:;;.6 :<>.::;;.6 :<>.<

<¶ Dk`n`j :;6.6 :<0.<5:;6.6 :<0.>:;6.6 :<0.:

Pjocj 0= Dk`n`js `kVuhtas lahmuij`as

C @ Krrar e Krrar:56.6 :00.<6 6.62 9.05 6.6?:;;.6 :<>.?6 6.62 9.;6 6.6?:;6.6 :<0.:6 6.:5 9.;< 6.6?

Pjocj ;= Ujcarks `kVuhtas lahmuij`as

sa,:   C   sn,?   e ?(ma):9 < ?0 5:9 < ?0.< 5:9 < ?<.2 5:9 < ?0.? 5:9 < ?<.9 5:9 < ?<.> 5?6 0 :9.: 5?6 0 :9.? 5?6 0 :9.? 5?6 0 :9.: 5?6 0 :9.0 5?6 0 :9.< 5:2 ; :0.> 5:2 ; :; 5:2 ; :0.2 5:2 ; :0.2 5:2 ; :0.9 5:2 ; :0.> 5

Pjocj 5= Ckhtk `nvkrikhtk

Jhêcnsns `k rksuctj`as

Lada sk puk`k jprklnjr kh cjs tjocjs ?, < y ; ta`js cjdk`nlnahks lah lahsnstkhtks lah uhj ckhtk `k   9.;  ld `k

`nstjhlnj ealjc (quk ks cj `nstjhlnj rkpartj`j kh kc djrladktêcnla `k cj ckhtk). @k kstj eardj, pa`kdas jskiurjrquk kstj ks, `k bklba, cj `nstjhlnj ealjc.

LahlcusnahksCairjdas khlahtrjr cj `nstjhlnj ealjc pjrj cjs ckhtks

utncnzj`js kh kstj prêltnlj. J`kdês, lah kstj nheardj-lnüh, pu`ndas lahstrunr cas snstkdjs quk jltujrah ladadnlraslapna y tkckslapna.

_kekrkhlnjs

Bktlb, Aptnls, 0½ k`. J``nsah Ykscky= Vkjrsah k`u-ljtnah, ?66?.

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