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Michelson Morley Experiment for Arbitrary Angle

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data

    The ether wind theory of the Michelson-Morley experiment is discussed in the text for the special case where the arms of the interferometer are parallel and perpendicular to the wind. Consider the general case for an angular setting θ. Prove that, for equal arms of length L, the time difference for the two paths is given to a good approximation by Δt=[v^2l.cos2θ]/c^3 where v is the velocity of the ether wind.

    2. Relevant equations

    relative velocity problem where t=distance/velocity

    3. The attempt at a solution

    I tried to work out the velocity of the light going through each arm and got
    t1=t2=L/(c^2+(c-v)^2)^1/2+L/(c^2+(c+v)^2)^1/2
    which is obviously wrong. I think I'm meant to split the velocity of the wind into vcosθ and vsinθ but I'm not sure how to apply this to the problem?
     
  2. jcsd
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