10. Ogib Svjetlosti i Atomski Spektri

SVEUČILIŠTE JOSIPA JURJA STROSSMAYERA U OSIJEKU ELEKTROTEHNIČKI FAKULTET

Razlikovna godina

Kolegij:Fizika 2 Seminarski rad

OGIB SVJETLOSTI Darko Brežnjak  David Kuzminski Filip Kraus

Glorijan Bagić Goran Ivoš Ilija Majdenić Ivan Benke

Ivica Čabraja Kristijan Radočaj Marko Zetović Tomislav Šapina Zvonimir Balent Osijek, 2014.

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Sadržaj 1.

UVOD........................................... ................................................................. ............................................ ............................................. .......................................... ................... 1 1.1

2.

Uvod u seminar ........................................... .................................................................. ............................................. ......................................... ................... 3

EKSPERIMENTALNI EKSPERIMENTALNI DIO ........................................... ................................................................. ............................................ .............................. ........ 5 2.1

Određivanje valne duljine monokromatske svjetlosti pomoću optičke rešetke  .......... 5

2.2 Određivanje propustljivosti zadanih optičkih filtara fi ltara pomoću ručnog spektroskopa ..... 14 3.

................................................................. ............................................. ............................................. ............................ ..... 18 ZAKLJUČAK ..........................................

4.

ZADACI ........................................... ................................................................. ............................................ ............................................ .................................... .............. 19

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1.

UVOD

Svjetlost je jedan od oblika energije. energije. Ali je i pojava u obliku energije, čestice, čestice, fotona, i vala. Kako se svjetlost u određenim okolnostima može razmatrati ili kao val ili kao skup čestica govori se o dualnoj prirodi svjetlosti. Pa se tako i fizikalna optika, to jest dio fizike koji

 proučava elektromagnetske elektromagnetske valove  u smislu njihovih svojstava i pojave, dijeli na valnu i čestičnu, to jest korpuskularnu. U valnoj optici svjetlost je elektromagnetski val, koji predstavlja istodobno širenje električnog i magnetskog polja u prostor. Kao što je prikazano slikom 1. 1 ta dva polja su i međusobno okomita i okomita na širenje vala , stoga se može govoriti   o transverzalnom obliku vala.

Slika 1.1: Širenje elektromagnetskog vala

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magnetskog polja.

Te se, u vakuumu, kreće najvećom brzinom u prirodi koja iznosi

299.792,458 km/s. Kada se opisuju valovi koriste se pojmovi poput perioda, amplitude, frekvencije te valne duljine. Period je fizikalna

veličina kojom se iskazuje trajanje jednog ciklusa periodične promijene.

Frekvencija se opisuje kao broj titraja u jedinici vremena i jednaka je recipročnoj vrijednosti  perioda.

Valna duljina je udaljenost nakon koje se val ponavlja, odnosno odgovara fizičkoj

udaljenosti između dva susjedna brijega (ili dola). Amplituda je najveći otklon od srednje vrijednosti,

ravnotežnog položaja. položaja.

Kao što je prikazanom slikom 1.2 e lektromagnetski valovi se rasprostiru velikim spektrom frekvencija, no ljudsko oko može vidjeti samo mali dio

tog spektra, točnije u području valne

duljine od oko 380 nanometara pa sve do oko 780 nanometara,

i to na načina da različite

valne duljine unutar tog raspona predočuje kao različite boje . P ri čemu je ljubičasta boja val sa valnom duljinom oko 380 nanometara, a crvena val sa valnom duljinom od oko 780 nanometara.

Slika 1.2: Spektar elektromagnetskih vala.

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samo jedan izvor valova. Dakle promatramo kako valovi koji dolaze iz istog izvora interferiraju jedni sa drugima. Interferencija valova jest svojstvo algebarskog

zbrajanja dva ili više vala. Da bi došlo do

interferencije valovi moraju biti koherentni, odnosno moraju

imati identične valne duljine i

amplitude, te razliku u fazi koja se ne mijena u vremenu.

Slika 1.3: Ogib svjetlosti na pukotini

Kao što je prikazano slikom 1.3 kada svjetlost naiđe na pukotinu nastaje interferencija. Ona je konstruktivna na mjestima gdje su

valovi u fazi, valovi označeni   sa 1 i 2 na slici. A

destruktivna gdje su valovi međusobno pomaknuti u fazi za 180°(π), valovi označeni sa 3 i 4. 1.1

Uvod u seminar

U ovom seminaru

izvesti će se dva eksperimenta. U prvom eksperimentu cilj je odrediti valnu

duljinu izvora svijetlosti koja pada pada na optičku rešetku. rešetku. Kao izvor postavljen je laser laser (λ=632.5 nm), a optičke rešetke pomoću kojih se određuje val na duljina imaju konstante od d=10 -5 m i d=1.66667*10-6m.

U drugom eksperimentu se uz pomoć priručnog eksperimenta treba

odrediti spektar izvora svjetlosti te propusnost zadanih filtara. Cilj prvoga eksperimenta jest provjeriti preciznost

ovakvog načina mjerenja te moguće

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se kemijskih elemenata sastoji izvor te

na koji način funkcioniraju filtri i kako ih se može

koristiti.

Kao analiza rezultati eksperimenata će biti obrađeni i statistički i grafički te će biti obrazloženi mogući uzroci odstupanja, pogrešaka, od zadanih, poznatih, vrijednosti.

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2. EKSPERIMENTALNI EKSPERIMENTALNI DIO U ovom dijelu biti će objašnjen način provođenja pojedinog eksperimenta eksperimenta i oprema, te t e će biti  priložena matematička matematička podloga za izračun određenih vrijednosti. 2.1

Određivanje valne duljine monokromatske svjetlosti pomoću optičke

rešetke Optička rešetka sastoji se od međusobno jednako udaljenih, i paralelnih pukotina u jednoj ravnini na kojima se ogiba upadni val. Ogibom upadnog vala svaka pukotina postaje izvor

vala kao što je prikazano slikom 2.1. Pri prolasku svjetlosti kroz optičku rešetku dolazi do ogiba na svakoj od pukotina,zbog čega nastaje interferencije valova koji izlaze iz rešetke.

Slika 2.1: Optička rešetka

Obično je napravljena tako da je na staklenoj zarezan niz jednako udaljenih paralelnih zareza.  Na mjestima gdje je staklo zarezano svjetlost ne prolazi, već prostorom između dva zareza.

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Slika 2.2: Ogibna slika

Relacija za izračun valne duljine ima

slijedeći oblik:

               

(2-1)

Gdje je λ valna duljina monokromatske svjetlosti, n redni broj ogibne točke, Δ Zn položaj n-te

ogibne točke, d  konstanta optičke rešetke, a  L udaljenost od rešetke do zastora.

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Postupak mjerenja sastoji se od nekoliko koraka. Prvo je potrebno provjeriti eksperimentalni  L od zastora. Nakon toga se  postav, potom je potrebno postaviti postaviti optičku rešetku na udaljenost udaljenost  L od

optička rešetka treba postaviti na put snopu laserske svjetlosti kako  bi se na zastoru prikazale ogibne točke. Potom je potrebno izmjeriti udaljenost između centralnog i svakog od prva tri ogibna maksimuma . Nakon čega se mijenja udaljenost

optičke rešetke od zastora.

 Nakon mjerenja potrebno je uz pomoć relacije (2 -1) i izmjerenih vrijednosti izračunati vrijednosti valne duljine

monokromatske svjetlosti, te usporediti sa stvarnom vrijednošću

valne duljine He-Ne lasera ( λ=632,8nm). Tablica 2.1 prikazuje rezultate mjerenja pri =1·10-5m. korištenju optičke rešetke sa konstantom d =1

Tablica 2.1: Rezultati mjerenja valne duljine monokromatske svjetlosti sa d =1 =1·10-5m

Broj mjerenja

1

2

3

4

5

6

7

8

9

10

11

12

L[m]

0,1

0,2

0,3

0,4 0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

ΔZ1[mm]

7

14

19

28

35

40

47,5

53

60

71

76

82

700 700 633 700 700

667

679

663 667 710 691 683

14

69

81

95

107 122 143 153 166

700 700 683 688 690

675

679

669 678 715 695 692

λ 1[nm] ΔZ2[mm] λ 2[nm]

28

41

55

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Uz pomoć tablice 2.1 možemo napraviti grafičku analizu mjerenja.

ΔZn 0,3

0,25

y = 0,2127x - 0,0017

0,2

ΔZ1 ΔZ2

0,15 y = 0,139x - 0,0008

ΔZ3

Linear (ΔZ1) Linear (ΔZ2) Linear (ΔZ3)

0,1

y = 0,0688x - 0,0004 0,05

0 0

0,2

0,4

0,6

0 ,8

1

1,2

1,4

L/[m]

Slika 2.4: Grafički prikaz ovisnosti Δ Z n=f(L)

Iz grafičke analize vidljivo je da su ogibni maksimumi linearno ovisni o udaljenosti optičke

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Tablica 2.2: Prvi ogibni maksimum metoda najmanjih kvadrata

i

ΔZ1[m] L*ΔZ1

L[m]

(L)²

(ΔZ1)²

1

0,1

0,007

0,0007

0,01

0,000049

2

0,2

0,014

0,0028

0,04

0,000196

3

0,3

0,019

0,0057

0,09

0,000361

4

0,4

0,028

0,0112

0,16

0,000784

5

0,5

0,035

0,0175

0,25

0,001225

6

0,6

0,04

0,024

0,36

0,0016

7

0,7

0,0475

0,03325

0,49

0,002256

8

0,8

0,053

0,0424

0,64

0,002809

9

0,9

0,06

0,054

0,81

0,0036

10

1

0,071

0,071

1

0,005041

11

1,1

0,076

0,0836

1,21

0,005776

12

1,2

0,082

0,0984

1,44

0,006724

n

Σ(ΔZ1) Σ(L*ΔZ1)

Σ(L) 7,8

0,5325

0,44455

Σ(L)² 6,5

Σ(ΔZ1)² 0,030421

(ΣL)² 60,84

(ΣΔZ1)² 0,283556

Uz pomoć relacija (2-2), (2-3) i (2- 4) možemo odrediti jednadžbu pravca u eksplicitnom obliku koji predstavlja najbolju prilagodbu na izmjerene podatke. Nagib pravca (a  ): ):

   ∑   ∑   ∑        ∑   ∑  

(2-2)

Odsječak na osi y ( b ): ):

     ∑   ∑   

(2-3)

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Usporedbom relacije (2-1) sa eksplicitnim oblikom pravca dobivenog gore navedenim

 jednadžbama primjetno  jednadžbama primjetno je da se jednadžba pravca pravca može izraziti i kao: kao:

    

(2-5)

Pa ako se usporedi sa osnovnom jednadžbom pravca koja ima oblik:

 Gdje y Gdje  y odgovara  odgovara



, a x a  x odgovara  odgovara L.  L. Tada se može primijetiti

(2-6)

da nagib pravca a zapravo

ima oblik:

   

(2-7)

Prema tome slijedi da valna duljina monokromatske svjetlosti iznosi:

         

(2-8)

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Tablica 2.3: Treći ogibni maksimum metoda najmanjih kvadrata

i

ΔZ1[m] L*ΔZ1

L[m]

(L)²

(ΔZ1)²

1

0,1

0,021

0,0021

0,01

0,000441

2

0,2

0,042

0,0084

0,04

0,001764

3

0,3

0,063

0,0189

0,09

0,003969

4

0,4

0,084

0,0336

0,16

0,007056

5

0,5

0,102

0,051

0,25

0,010404

6

0,6

0,125

0,075

0,36

0,015625

7

0,7

0,145

0,1015

0,49

0,021025

8

0,8

0,164

0,1312

0,64

0,026896

9

0,9

0,187

0,1683

0,81

0,034969

10

1

0,219

0,219

1

0,07961

11

1,1

0,234

0,2574

1,21

0,054756

12

1,2

0,252

0,3024

1,44

0,063504

n

Σ(ΔZ1) Σ(L*ΔZ1)

Σ(L) 7,8

1,638

1,3688

Σ(L)² 6,5

Σ(ΔZ1)² 0,28837

(ΣL)² 60,84

(ΣΔZ1)² 2,683044

Izračun relativne pogreške u postotcima:

  (  

(2-9)

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Iz tablice 2.4 je vidljivo da je pri mjerenju i računanju došlo do pogreške. Razlika između rezultata mjerenja i stvarne vrijednosti ima nekoliko uzroka.

Prvi uzrok je razlučivost pri mjerenju, što se može primijetiti na slici 2.2. jer su ogibne ogibne točke  poprilično velike što što otežava točno točno očitavanje. Drugi Drugi uzrok jest taj što su se sva mjerenja mjerenja zaokruživala na milimetar što može dosta pridonijeti pogrešci kada je riječ o mj erama reda nekoliko stotina nanome tara. No ako se pogleda spektar valnih duljina može se primijetiti da

su odstupanja unutar crvene boje, jer crvena boja se nalazi između 625 i 740 nanometara valne duljine. Prema izračunu najtočnija vrijednost valne duljine jest

za prvi ogibni

maksimum sa relativnom pogreškom od 8,72%. Tablica 2.4 prikazuje rezultate mjerenja pri korištenju optičke rešetke sa konstantom d =1,66667 =1,66667·10-6m.

-6

=1,66667·10 m Tablica 2.4: Rezultati mjerenja valne duljine monokromatske svjetlosti sa d =1,66667

Broj mjerenja

1

2

3

4

5

6

7

8

9

10

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0,25

0,2 y = 0,0204x + 0,0216

0,15    Z

      Δ

ΔZ1

0,1

0,05

L[m]

0 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55

Slika 2.5: Grafički prikaz ovisnosti Δ Z n=f(L)

Tablica 2.5 prikazuje rezultate mjerenja za prvi ogibni maksimum sa optičkom rešetkom konstante d =1 =1 10-5

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Uz pomoć relacija (2-2), (2-3) i (2- 4) možemo odrediti jednadžbu pravca u eksplicitnom obliku koji koji predstavlja najbolju prilagodbu prilagodbu na izmjerene podatke.

Nagib pravca pravca a  ima

vrijednost a=0,4073, odsječak na osi y b=0,00124, a koeficijent korelacije  R=0,9999.  R=0,9999.

2.2 Određivanje propustljivosti zadanih optičkih filtara pomoću ručnog spektroskopa

U ovom eksperimentu potrebno je odrediti područje propustljivosti zadanih optičkih filtara  pomoću ručnog spektroskopa. Spektroskop je jednostavan instrument za promatranje spektra vidljive svjetlosti. Sastoji se od

optičke prizme ili optičke rešetke, koja služi za rastavljanje svjetla na spektar. Slika 2.6  prikazuje princip rada spektroskopa, dok slika 2.7 prikazuje izgled koriš tenog spektroskopa.

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Slika 2.7: Spektroskop iz eksperimentalnog postava

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Filtri rade na principu propuštanja samo valova određenih valnih duljina. Tako žuti filtar  propušta samo valne duljine koje se nalaze u spektru od ~565 -740 što se u bojama očitava kao spektar žute narančaste i crvene. Dok zeleni filtar propušta samo valne duljine ~500 -565 što se kao što vidimo u tablici 2.6 u bojama očitava kao spektar ze lene boje. Slika 2.8  prikazuje spektar spektar boja vidljiv pomoću spektroskopa spektroskopa bez filtra.

Slika 2.8: Spektar boja bez filtra

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Kako izvor svjetlosti nije živina izbojna žarulja, već fluorescentna rasvjeta očitane valne duljine ne odgovaraju valnim duljinama na energetskom dijagramu žive prikazanom slikom 2.9 stoga rješenja će biti približna. Slika 2.9 prikazuje energetski dijagram žive sa prijelazima i valnim duljinama  prikazanim u mjernoj jedinici 10-10m.

Tablica 2.7: Izmjerene spektralne linije žive (fluorescentne svjetiljke) i odgovarajući

energetski prijelazi

Boja

valna duljina λ [nm] [nm]

energetski energetski prijelaz

ljubičasta

445

   

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3.

ZAKLJUČAK 

U prvom djelu eksperimenta bilo je potrebno izmjeriti valnu duljinu monokromatske

svjetlosti na način da se svjetlost iz lasera propusti okomito na optičku rešetku koja je udaljena od zastora za udaljenost „ L“ te da se izmjere udaljenosti od ogibnog maksimuma nultog reda do ogibnih maksimuma prva tri reda.

Tijekom mjerenja primijećeno je da

 preciznost otežava veličina i ud aljenost ogibnih maksimuma, preciznost mjerne vrpce i  preciznost ljudskoga ljudskoga oka. Što je dovelo do pogreške pogreške od 12,02% 12,02% . Drugi dio eksperimenta odnosio se na određivanje valnih duljina spektralnih linija sa ručnim spektroskopom. To jest bilo je potrebno usmjeriti spektroskop prema izvoru svjetlosti, fluorescentne

rasvjete, te na mjerilu unutar spektroskopa uočiti spektralne linije na mjeri.

Potom očitati sa mjere valne duljine uočenih spektralnih linija i njihove boje. Svaki izvor

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4. ZADACI 1. Zadatak

Okomiti na optičku rešetku s 500 zareza po milimetru duljine upada snop monokromatske svjetlosti valne duljine 500 nm. Odrediti  još

može vidjeti ako svjetlost pada okomito na rešetku  i pod kojim kutom se otkloni

drugi ogibni maksimum( α2).

Rješenje: d =1 =1·10-3/500 m=2·10-6 m

λ=500 nm=5·10-7 m_____ a) k max max=?  b)

najveći red spektra k koji se

α2=?

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Rješenje:  λ=520

nm

 L=  L= 1 m n=1

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LITERATURA [1]

Fizika 2  – PREDLOŽAK  –  PREDLOŽAK

ZA LABORATORIJSKU VJEŽBU, 2010./2011. g. , Ogib

svjetlosti [2]

Atomic spectra and Atomic Structure –  Gerhard  Gerhard Herzberg, New York, 1944.