Solving Snell's Law Problem: Find Refractive Index at Height h

[zell99]

Homework Statement

A man, height h, can see a mirage at angles less than a known angle $\theta$ to the horizontal. The refractive index of air is at ground level is known. Find the refractive index of air at height h.

Homework Equations

Snell's law: $n1 sin(\theta 1)=n2 sin(\theta2)$ where angles are measured relative to the normal of the boundary.
I'm assuming it's a normal mirage, i.e. can see an image of the sky in the ground.

The Attempt at a Solution

My plan was to split the air up into infintesimal stips at constant height, find $d\theta$ as a function of $d(refractive index)$ and integrate to find $\theta$ as a function of refractive index. The problem I have is I don't know what the initial value of theta is, and I obviously need to include h somewhere.
If anyone could point me in the right direction I'd really appreciate it.
Thanks

 

[zell99]

Has anyone got any ideas? I should have said theta is very small, so small angle approximations are fine where appropriate.
Thanks