What is the threshold for total extinction of light in a given medium?

[Tiberius47]

Homework Statement

I am given a distance at which a particular object is just discernible and am asked to find the opacity of the air.

Homework Equations

The Attempt at a Solution

I know that:

I(x)=I₀e^-kρx

but I don't know at what point you have total extinction. Obviously you would only have zero intensity with the density, opacity, or distance at infinity.

I'm using Foundations of Astrophysics by Ryden and I can't find a reference to what intensity of light is not visible.

 

[mfb]

A rough approximation might be sufficient. In that case, you can consider something like I(x)=1/e I_0 or I(x)=1/e^2 I_0.