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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?

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Example

Ifayellowlightwithawavelengthof54nmshinesonascreen

withdoubleslitswheretheslitsarecut.1mmapart,what

istheanglefromthecentralfringethatyouneedtoturnto

observethesecondorderfringe?

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Thesinglesliteffect

Youcans0llgetfringesevenifyouuseasingleslit Theslitbehavesasthoughithasalargenumberofpointsourcesspreadevenlyacrossthewidthoftheslit

Thewavefrontsfromthedifferentendsoftheslitwillbearrivingatdifferentpointsontheendscreenatdifferent0mes

Yous0llgetconstruc0veanddestruc0veinterference

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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

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2oildcos(

2)= m

1

2

"

#$

%

&'

Construc0veinterference:

2oildcos(

2)=m

Destruc0veinterference:

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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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