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Interference vs. diffraction patterns
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[QUOTE="vetgirl1990, post: 5455270, member: 573977"] [h2]Homework Statement [/h2] The centres of two slits of width [I]a[/I] are a distance [I]d[/I] apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light, the ratio a/d is equal to: ANS: 1/4 [h2]Homework Equations[/h2] Here are the various interference conditions for interference and diffraction: [B][/B] Interference conditions for [I]double slit[/I]: MAX: dsinθ = mλ MIN: dsinθ = (m+½)λ Diffraction conditions for a [I]single slit[/I]: MAX: asinθ = (m+½)λ MIN: asinθ = mλ Diffraction conditions for [I]diffraction grating: [/I] MAX: asinθ = mλ MIN: asinθ = (m+½)λ [h2]The Attempt at a Solution[/h2] I will walk through my reasoning... I've classified the diffraction component of this problem as [I]diffraction grating[/I] rather than [I]diffraction through a single slit[/I], because based on this setup, there are two slits for diffraction to occur through. While we normally see grating in the order of 2500grates/cm, 2grates/cm would still be considered grating. So based on that logic, the conditions for minimum for both are: Diffraction: dsinθ = (m+½)λ, where m=1 Interference: asinθ = (m+½)λ, where m=4 Now, when I plug in all the values for m, and cancel out all the similarities (sinθ, λ): asinθ=(1+½)λ --> a=1.5 dsinθ=(4+½)λ --> d=4.5 The ratio I get for a/d = 1.5/4.5 = ⅓ HOWEVER, I noticed that if I cancel out ½ rather than adding it to m like I did above, then the ratio for a/d=¼. What am I doing wrong? [/QUOTE]
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Interference vs. diffraction patterns
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