Homework Help: Star light extinction and optical extinction

1. May 7, 2009

TFM

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

The normalized extinction is defined as

$$F(\lambda) = \frac{A_{\lambda}-A_v}{A_B - A_v}$$

where $$A_{\lambda}$$ is the extinction (in magnitudes) at wavelength $$\lambda$$. 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. $$\tau = \frac{C}{\lambda}$$), then $$F(\lambda) = \frac{c_1}{\lambda} + c_2$$ where $$c_1$$ and $$c_2$$ are constants which should be evaluated in terms of C, V and B.

(b)

Hence sketch $$F(\lambda)$$ over the visible range, 300–800 nm.

(c)

Find the asymptotic value of $$F(\lambda) as \lambda \leftharpoondown \infty$$ (i.e. the numerical value of $$c_2$$).

2. Relevant equations

$$dI_{\nu} = (s_{\nu} - I_{\nu})d\tau_{\nu}$$

$$s_{\nu} = j_{\nu}/\alpha_{\nu}$$

$$\tau_{\nu} = \int \alpha_{\nu} ds$$

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