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7/29/2019 P2 - week 9 - Wave nature of light
1/22
Youngsdoubleslitexperiment
Natureoflightunclearforalong0me Doesitconsistofpar0clesorwaves? Firstsolidevidenceofwavenaturearrivedin181:
Youngsdoubleslitexperiment
A
B
C 1
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InterferenceFringes
2
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Demonstration
hGp://phet.colorado.edu/en/simula0on/wave-interference
3
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Questions
Dothefringesappearforallcoloursoflight? Yes,butthedistancesbetweenthemaredifferent
Howfarapartarethefringes? Itdependsonthewavelengthofthelight,onhowfarthescreenwiththedoubleslitsis,andthedistancebetweenthetwoslits
Howisthedistancebetweenthefringesrelatedtothecolour(wavelength)oflight?
Otherthingsbeingequal,longerwavelength(lowerfrequency)meansgreaterdistancebetweenthefringes
Bymeasuringthedistancebetweenthefringes,wecandeterminethewavelengthoflight
Whydowenotseethisinterferenceoflightineverydaylife? Fringedistanceis0nyandsourcesareincoherent. 4
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Theorybehindtheexperiment
Pathdifference:thedifferenceindistancetraveledbythetwowavesfromtheirrespec0vesourcestoagivenpointonthe
paGern
AtpointO,thepathdifferenceisBO-CO=
B
C
d
D
M O
5
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Theorybehindtheexperiment
B
C
d
D
M O
P
x
2Etc
PathdifferenceatP: Forabrightfringe:
BP-CP=m (wherem=,1,2)
6
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Theorybehindtheexperiment
B
C
d
D
M O
P
x
PathdifferenceatP: Forabrightfringe:
BP-CP=m (wherem=,1,2)
Foradarkfringe: BP-CP=(m+1/2)/2
3/2 Etc
7
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Separationofthefringes
BQ=BPCP=pathdifference=m(forabrightfringe) BCtoosmallcomparedtoBP,sowecanassumeCQmeetsBPatrightangles
Fromtrigonometry(triangleBQC):sin()=BQ/BC=m/d Fromtrigonometry(trianglePMO):tan()=OP/OM=x/D is0nyso:sin()=tan()m/d=x/D=xd/mD(wherem=,1,2..)
B
C
d
D
M O
P
x
Q
8
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Separationofthefringes
=xd/mDx=mD/d Forthe1stbrightfringe(m=1):x1=D/d Forthe2ndbrightfringe(m=2):x2=2D/d
etc
B
C
d
D
M O
P
x
Q
9
y=xm-xm-1=D/d
Distancebetweentwo
consecu0vefringes
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Example
InaYoungsslitexperiment,thesepara0onbetweenthefirst
andfihbrightfringeis2.5mmwhenthewavelengthusedis
6.2x1-7m.Thedistancefromtheslitstothescreenis.8m.
Whatisthesepara0onofthetwoslits?
1
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Fringeposition
11
O
m=
D
d
D
d
m=1m=-1 m=2m=-2
2D
d
3D
d
m=-3 m=3
2D
d
3D
d
Red=longer
Blue=shorter
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Fringeposition
12
O
m=
D
d
D
d
m=1m=-1 m=2m=-2
2D
d
3D
d
m=-3 m=3
2D
d
3D
d
Red=longer
Blue=shorter
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Theelectromagneticspectrum
Theelectromagne1cspectrumistherangeofallpossiblefrequenciesofelectromagne0cradia0on
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Wave-particleduality
Wave-par1cleduality:Theamountofenergyaphotonhascancauseittobehavemorelikeawaveormorelikeapar0cle
Wearenottalkingaboutadifferenceinwhataphotonis,butabouthowitbehavesatdifferentenergies
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Thevisiblespectrum
Thevisiblespectrumistheregionoftheelectromagne0cspectrumconsis0ngofphotonswithwavelengthsfrom
approximately4to7nm
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Whyistheskyblue?
BluerwavelengthsgetscaGeredmorebyatmosphericmoleculesthanredwavelengths(RayleighscaGering)
Mostofthelongerwavelengthspassstraightthrough Shorterwavelengthsgetabsorbedbytheatmosphericmoleculesandre-emiGedinrandomdirec0ons
ItisscaGeredallaroundtheskysoinwhicheverdirec0onyoulook,someofthescaGeredbluelightwillreachyou
NearerthehorizonbluelightgetsscaGeredevenmore
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Example
Apairofscreensareplaced13.7mapart.Thefirstscreenhas
twothinparallelslitscutintoitwhichare.96cmapart.
Monochroma0clightshinesontothescreenwiththeslits.A
thirdorderfringeisobservedonthesecondscreen,2.5cm
fromthecentralfringe.Determinethewavelengthofthislight.Roughlywhatcolourisit?
17
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Example
Ifayellowlightwithawavelengthof54nmshinesonascreen
withdoubleslitswheretheslitsarecut.1mmapart,what
istheanglefromthecentralfringethatyouneedtoturnto
observethesecondorderfringe?
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Thesinglesliteffect
Youcans0llgetfringesevenifyouuseasingleslit Theslitbehavesasthoughithasalargenumberofpointsourcesspreadevenlyacrossthewidthoftheslit
Thewavefrontsfromthedifferentendsoftheslitwillbearrivingatdifferentpointsontheendscreenatdifferent0mes
Yous0llgetconstruc0veanddestruc0veinterference
19
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Interferencebythinilms
Coherentsourcesofwaves(constantphasedifference)produceaninterferencepaGern
InterferencepaGernsarealsoobservedwhenlightpassesthroughathinfilmofatransparentmedium(e.g.oil)andgets
reflectedback
2
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Interferencebythinilms
Coherentsourcesofwaves(constantphasedifference)produceaninterferencepaGern
InterferencepaGernsarealsoobservedwhenlightpassesthroughathinfilmofatransparentmedium(e.g.oil)andgets
reflectedback
21
2oildcos(
2)= m
1
2
"
#$
%
&'
Construc0veinterference:
2oildcos(
2)=m
Destruc0veinterference:
7/29/2019 P2 - week 9 - Wave nature of light
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ToDo
Readsec0on18fromthebook[upto18.3p.341-p.348PhysicalOp0cs]
HomeworkAssignmentwk9:ques0ons7.4,7.6,7.7,7.8,7.9,7.2
Handitinnolaterthan4:00pmnextWednesday-LATEWORKWILLNOTBEACCEPTED
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