1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

E&M plane wave interference

  1. Dec 18, 2008 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Find out the condition for two-plane-wave interference. The two plane waves are given as

    \vec{E}_1 = E_0\vec{A}\exp(ikz - i\omega t) + c.c.

    \vec{E}_2 = E_0\vec{B}\exp(ikz - i\omega t + i\phi) + c.c.

    where [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] are complex. All other variables are real.

    2. The attempt at a solution
    Here is how I do the problem. I first let

    [tex]\vec{A} = A\exp(i\alpha)[/tex]

    [tex]\vec{B} = B\exp(i\gamma)[/tex]

    and define
    [tex]F = kz - \omega t, \qquad G = kz - \omega t + \phi[/tex]

    \vec{E}_1 = E_0A \left(\exp[i(F + \alpha)] + \exp[-i(F+\alpha)]\right)
    = 2E_0 A\cos(F+\alpha)

    \vec{E}_2 = E_0B \left(\exp[i(G + \beta)] + \exp[-i(G+\beta)]\right)
    = 2E_0 B\cos(G+\beta)

    Now, both [tex]\vec{E}_1[/tex] and [tex]\vec{E}_2[/tex] become real. So I can square the total field [tex]\vec{E} = \vec{E}_1 + \vec{E}_2[/tex] directly

    [tex]E^2 = E_1^2 + E_2^2 + 2E_1E_2 =
    4E_0^2 A^2\cos^2(F+\alpha) + 4E^2_0 B^2\cos^2(G+\beta) + 8E_0^2AB\cos(F+\alpha)\cos(G+\beta)

    But I remember the interference term should only contain the

  2. jcsd
  3. Dec 19, 2008 #2


    User Avatar
    Homework Helper

    What do you mean by "the condition for two-plane-wave interference"? They always interfere, regardless of any specific phases and whatnot.

    Are these waves supposed to be going in exactly the same direction? If so, this problem may be quite easy (depending on what "the condition for two-plane-wave interference" means.)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: E&M plane wave interference
  1. Wave interference (Replies: 2)

  2. E&M Charged disk (Replies: 1)