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Fabry-Perot Interferometer: Energy Conservation

  1. Dec 2, 2007 #1
    1. The problem statement, all variables and given/known data

    This is regarding a Fabry-Perot Interferometer with identical mirrors:

    If you shine a beam of light on a 99% reflecting mirror, 1% goes through and the other 99% is reflected. But if a second mirror is placed behind the first one, where there is only 1% of the light present, somehow 100% of the light appears. Explain this, also explain how energy is conserved.

    2. Relevant equations

    I_t = I_0 * {T^2 / (1-R^2)} * { 1 / (1 + F * sin^2([tex]\Delta[/tex]/2))}

    F = finesse = 4R / (1-R)^2

    I_t = transmitted intensity
    I_0 = original intensity

    T = transmittance
    R = reflectance

    [tex]\Delta[/tex] = [tex]\delta[/tex] + [tex]\delta[/tex]_r
    [tex]\delta[/tex] = phase difference per round trip between mirrors
    [tex]\delta[/tex]_r = phase difference due to reflection = 0 or pi

    3. The attempt at a solution

    I understand mathematically why it's true. If you set [tex]\Delta[/tex] to an integer multiple of pi, then sin [tex]\Delta[/tex] = 0 and then

    I_t/I_0 = {T^2 / (1-R^2)} * { 1 / (1 + F*(0)) }

    I_t/I_0 = T^2 / (1 - R^2) = 1

    so I_t = I_0, so 100% of the light appears.

    I really don't know how to explain this physically. Help?
     
    Last edited: Dec 2, 2007
  2. jcsd
  3. Dec 3, 2007 #2

    Gokul43201

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    Staff Emeritus
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    Gold Member

    Can you write down the question EXACTLY as it was given to you?

    I can't seem to make much sense of it. First of all, the interferometer set-up I'm familiar with has the mirrors facing each other, not one behind the other. Secondly, in this geometry, I expect that only about half the incident power is transmitted through in the forward direction, the rest is transmitted backwards.

    What does the question mean by "100% of the light appears"? Appears where?

    I may be completely off here, so it would help if someone else takes a look.
     
  4. Feb 7, 2009 #3
    "I really don't know how to explain this physically. Help?"

    Has anyone an answer to this question?

    That is the question of my life too.
     
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