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Remarksforinstructors:Answer(1).Theangularpositionofthemth-orderbrightfringeinadouble-slitinterferencepatternisgivenbydsinθm=mλ.Thedistanceymofthemth-orderbrightfringefromthecenterofthepatternisgivenbyym=Ltanθm,whereListhedistancetothescreen.ThespacingbetweensuccessivebrightfringesisΔy=ym+1–ym=L(tanθm+1–tanθm)≈L(sinθm+1–sinθm)=L[(m+1)-m]λ/d=Lλ/dbecausetheanglesaresmall,andforsmallangles(inradians)sinθ?tanθ.AsLincreases,thespacingΔyincreases.AplanemonochromaticlightwaveisincidentonadoubleslitasillustratedinActiveFigure37.1.Astheviewingscreenismovedawayfromthedoubleslit,whathappenstotheseparationbetweentheinterferencefringesonthescreen?1.2.3.4.5.Itincreases.Itdecreases.Itremainsthesame.Itmayincreaseordecrease,dependingonthewavelengthofthelight.Moreinformationisrequired.[ActiveFigure37.1]
Remarksforinstructors:Answer(2).Fromourresultabove,weseethatasdincreases,thespacing?ydecreases.AplanemonochromaticlightwaveisincidentonadoubleslitasillustratediActiveFigure37.1.Astheslitseparationincreases,whathappenstotheseparationbetweentheinterferencefringesonthescreen?1.2.3.4.5.Itincreases.Itdecreases.Itremainsthesame.Itmayincreaseordecrease,dependingonthewavelengthofthelight.Moreinformationisrequired.[ActiveFigure37.1]
Remarksforinstructors:Answer(2).Theanglesintheinterferencepatternarecontrolledbyλ/d,whichweestimateineachcase:(a)0.45μm/400μm≈1.1×10?3(b)0.7μm/400μm≈1.6×10?3(c)and(d)0.7μm/800μm≈0.9×10?3FourtrialsofYoung’sdouble-slitexperimentareconducted.(a)Inthefirstrial,bluelightpassesthroughtwofineslits400mmapartandformsaninterferencepatternonascreen4maway.(b)Inasecondtrial,redlightpassesthroughthesameslitsandfallsonthesamescreen.(c)Athirdtrialiperformedwith
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