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Relation between intensity and amplitude

  1. Jan 29, 2015 #1
    When superposing waves in say double slit interference from two slits, I seem to have come across two approaches:
    1. Sum the two waves in complex form to get the resultant amplitude, take the real part, and square to get the intensity, i.e I=[Re(A)]2
    2. Sum the two waves in complex form to get the resultant complex amplitude. Then take the modulus squared to get the intensity, i.e I=AA*.
    What is it that makes these two approaches give the same result. Mathematically they seem to be different to me. Also, where does the second come from? I know I=cε0E2 but this doesn't involve the modulus does it?
     
  2. jcsd
  3. Jan 29, 2015 #2

    RUber

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    If you think of the complex A in the exponential form, ## A = r e^{i \theta} ##, then ## [Re(A)]^2 =( r \cos \theta) ^2##.
    Also, ## AA^* = r e^{i \theta}r e^{-i \theta} =r^2##, therefore these are mathematically the same only when you are approaching head on (angle = 0 or pi).
     
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