Discovering Your Friend's Location in a Forest: Astrophysics Question Homework

[mpn17]

Homework Statement

You are lost in a forest. You have become separated from your friend. At your eye level, only tree
trunks block your view of distant parts of the forest (there are no leaves and branches at eye level to
block your view, only tree trunks). The trees are spread randomly throughout the forest, but with a
typical spacing of about 3 m, and the tree trunks have typical diameters of 20 cm. You can hear your
friend calling, but you can't see her. Approximately how close do you need to get to each other before
you will see your friend?

Homework Equations

Mean free path=1/n*sigma=1/n*pi*r^2
Optical Depth T=x/1/n*sigma=n*x*sigma
I/Io=e^-nxsigma

The Attempt at a Solution

Not really sure where to go with this to be honest... I don't see how I have enough information/what assumptions to make

Obviously we can solve for Sigma since we have the diamter, but then we don't know how big the forest area/volume is so we can't find n (make an assumption?)

Thanks for any help

 

[Simon Bridge]

You know the mean spacing of the trees... you don't need to know the overall size of the forest if you do it in terms of densities. Perhaps think this way: what is the average size the forest needs to be to block your view of the outside?