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Relating Optical Depth and Extinction (τ(λ) and A(λ))

  1. Feb 4, 2009 #1
    Hey guys sorry my first post is a help request and not an introduction or anything but I'd really appreciate a helping hand here

    1. The problem statement, all variables and given/known data

    Show that the extinction A(λ) and optical depth τ(λ) are related by the linear relationship A(λ)=1.086*τ(λ)

    2. Relevant equations

    m(λ)=M(λ) + 5Log(d)-5 + A(λ)
    which I'd rearrage to

    Here in lies the problem, I have all the equations I can find in my notes and the slides but nothing that relates τ(λ) to anything other than:

    exp(-τ) = (I/I0) (sorry wasn't sure how to subscript the 0 in I0)

    and then nothing to relate intensities to magnitudes.

    3. The attempt at a solution

    I thought maybe I could use 2 stars where I new the apparent and absolute magnitudes ( the sun and vega, etc) and the distance obviously and then calculate how τ(λ) and A(λ) are related and show the 1.086 multiplier in both but I can't work out how to relate A(λ) to anything involving intensity.

    I hope you guys can help me out here since I'm stumped :) thanks for anything you can
  2. jcsd
  3. Feb 4, 2009 #2
    Start with the definition of a difference in apparent magnitudes. . .

    [tex] m_1 - m_2 = 2.5log(I_1/I_2) [/tex]

    extinction, A is defined as [tex] A = m^{'} - m [/tex]

    Now, how are I_1, I_2, and tau related. . .
  4. Feb 4, 2009 #3
    Souldn't it be [tex] m_1 - m_2 = 2.5log(I_2/I_1) [/tex] ?
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