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March 17, 2016 CH 36 Diffraction
I.
Diffraction:
A. Example:
B. Diffractionisawaveeffect.Thatis,itoccursbecauselightisa
waveanditoccurswithothertypesofwavesaswell.
C. Diffractioncanbedefinedratherlooselyastheflaringoflightasit
emergesfromanarrowslit.Morethanjustflaringoccurs,however,
becausethelightproducesaninterferencepatterncalledadiffraction
pattern.
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March 17, 2016 D. FresnelBrightSpot
1.
Lightwavesflareintotheshadowregionofasphereastheypassthe
edgeofthesphere,producingabrightspotatthecenteroftheshadow,called
FresnelBrightSpot.
II.
Diffractionfromasingleslit,locatingtheminima:
A. Let’slookatthedestructiveinterferencefromtheslit:
1.
First,ifwementallydividetheslitintotwozonesofequalwidthsa/2,
andthenconsideralightrayr1fromthetoppointofthetopzoneandalight
rayr2fromthetoppointofthebottomzone.FordestructiveinterferenceatP1,
First minimum only Page2
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March 17, 2016 2.
Onecanfindtheseconddarkfringesaboveandbelowthecentralaxis
asthefirstdarkfringeswerefound,exceptthatwenowdividetheslitinto
fourzonesofequalwidthsa/4,asshowninFig.36‐6a.
3.
Ingeneral,
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(minima  dark fringes) [SHIVOK SP212]
March 17, 2016 B. SampleProblem:
1.
Aslit1.00mmwideisilluminatedbylightofwavelength589nm.We
seeadiffractionpatternonascreen3.00maway.Whatisthedistance
betweenthefirsttwodiffractionminimaonthesamesideofthecentral
diffractionmaximum?
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March 17, 2016 III.
DiffractionbyaCircularAperture:
A. ExamplePicture:
B. (first minimum  circular aperture) Vs Page5
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March 17, 2016 C. Resolvability
1.
Rayleigh’sCriterion:
a)
Twoobjectsthatarebarelyresolvablewhentheangular
separationisgivenby:
(Rayleigh’s criterion) Page6
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March 17, 2016 D. SampleProblem:
1.
Nuclear‐pumpedx‐raylasersareseenasapossibleweapontodestroy
ICBMboosterrocketsatrangesupto2000km.Onelimitationonsuchadevice
isthespreadingofthebeamduetodiffraction,withresultingdilutionofbeam
intensity.Considersuchalaseroperatingatawavelengthof1.40nm.The
elementthatemitslightistheendofawirewithdiameter0.200mm.(a)
Calculatethediameterofthecentralbeamatatarget2000kmawayfromthe
beamsource.(b)Bywhatfactoristhebeamintensityreducedintransittothe
target?(Thelaserisfiredfromspace,sothatatmosphericabsorptioncanbe
ignored.)
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March 17, 2016 E. SampleProblem:
1.
Abeamoflightofasinglewavelengthisincidentperpendicularlyon
adouble‐slitarrangement,asinFig.35‐10.Theslitwidthsareeach46μm
andtheslitseparationis0.30mm.Howmanycompletebrightfringes
appearbetweenthetwofirst‐orderminimaofthediffractionpattern?
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March 17, 2016 IV.
DiffractionGratings:
A. Adiffractiongratingissomewhatlikethedouble‐slitarrangement
buthasamuchgreaternumberNofslits,oftencalledrulings,perhaps
asmanyasseveralthousandpermillimeter.
B. Thepathlengthdifferencebetweenadjacentraysdeterminesthe
interference.
1.
(maxima  lines)
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March 17, 2016 C. DiffractionGratings,WidthoftheLines:
1.
2.
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March 17, 2016 D. DiffractionGratings,GratingSpectroscope:
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March 17, 2016 E. SampleProblem:
1.
Adiffractiongrating20.0mmwidehas6000rulings.Lightof
wavelength589nmisincidentperpendicularlyonthegrating.Whatarethe
(a)largest,(b)secondlargest,and(c)thirdlargestvaluesofθatwhich
maximaappearonadistantviewingscreen?
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