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

1. Feb 4, 2009

### 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

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
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.

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. Feb 4, 2009

### 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. . .

3. Feb 4, 2009

### torehan

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