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Interference vs. diffraction patterns

  1. Apr 26, 2016 #1
    1. The problem statement, all variables and given/known data
    The centres of two slits of width a are a distance d 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

    2. Relevant equations
    Here are the various interference conditions for interference and diffraction:

    Interference conditions for double slit:
    MAX: dsinθ = mλ
    MIN: dsinθ = (m+½)λ

    Diffraction conditions for a single slit:
    MAX: asinθ = (m+½)λ
    MIN: asinθ = mλ

    Diffraction conditions for diffraction grating:
    MAX: asinθ = mλ
    MIN: asinθ = (m+½)λ

    3. The attempt at a solution
    I will walk through my reasoning...
    I've classified the diffraction component of this problem as diffraction grating rather than diffraction through a single slit, 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?
     
  2. jcsd
  3. Apr 26, 2016 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    Could you please check again in the original problem, is it minimum or maximum?
     
  4. Apr 26, 2016 #3
    The original question does indeed say minimum.
     
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