Optical Path Length Problem in Astrophysics & Interstellar Medium

[Joeseye]

Problem:

My homework constantly refers to something called the optical path length, L - I'm not exactly sure what this is. It's in the equation below. This question is in relation to astrophysics and dust extinction in the Interstellar Medium.

Relevant equations:

Dust optical depth, τ_λ = N_g∏a²L

Solution:

My best guess is that it's something to do with the penetration distance into a cloud(?).

Thanks.

 

[gneill]

Hmm. Optical depth is something different from optical path length. Optical depth should be related to optical extinction (light absorption by a medium). Optical path length is usually the physical distance of the path that light follows through a system, multiplied by the index of refraction of the medium. L*n in other words.