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Star light extinction and optical extinction

  1. May 7, 2009 #1

    TFM

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

    The normalized extinction is defined as

    [tex] F(\lambda) = \frac{A_{\lambda}-A_v}{A_B - A_v} [/tex]

    where [tex] A_{\lambda} [/tex] is the extinction (in magnitudes) at wavelength [tex] \lambda [/tex]. B and V are wavelength bands but for the purposes of this question we will
    assume that they represent particular wavelengths with B = 420nm and V = 540 nm.

    (a)

    Show that if the optical depth is proportional to frequency (i.e. [tex] \tau = \frac{C}{\lambda} [/tex]), then [tex] F(\lambda) = \frac{c_1}{\lambda} + c_2 [/tex] where [tex]c_1[/tex] and [tex]c_2[/tex] are constants which should be evaluated in terms of C, V and B.

    (b)

    Hence sketch [tex] F(\lambda) [/tex] over the visible range, 300–800 nm.


    (c)

    Find the asymptotic value of [tex] F(\lambda) as \lambda \leftharpoondown \infty [/tex] (i.e. the numerical value of [tex]c_2[/tex]).

    2. Relevant equations

    The equation of radiative transfer:

    [tex] dI_{\nu} = (s_{\nu} - I_{\nu})d\tau_{\nu} [/tex]

    [tex] s_{\nu} = j_{\nu}/\alpha_{\nu} [/tex]

    [tex] \tau_{\nu} = \int \alpha_{\nu} ds [/tex]



    3. The attempt at a solution

    I am not quite sure where to start for part a). I know quite a few equations, which I have posted above. But could any tell me what is the best way to start this question?

    Many Thanks,

    TFM
     
    Last edited: May 7, 2009
  2. jcsd
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