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

[Mike89]

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

Homework Statement

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

Homework Equations

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

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.

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

 

[AstroRoyale]

Start with the definition of a difference in apparent magnitudes. . .

m_1 - m_2 = 2.5log(I_1/I_2)

extinction, A is defined as A = m^{'} - m

Now, how are I_1, I_2, and tau related. . .

 

[torehan]

m_1 - m_2 = 2.5log(I_1/I_2)

Souldn't it be m_1 - m_2 = 2.5log(I_2/I_1) ?