A man, height h, can see a mirage at angles less than a known angle [itex]\theta[/itex] to the horizontal. The refractive index of air is at ground level is known. Find the refractive index of air at height h.
Snell's law: [itex]n1 sin(\theta 1)=n2 sin(\theta2)[/itex] 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 [itex]d\theta[/itex] as a function of [itex]d(refractive index)[/itex] and integrate to find [itex]\theta[/itex] 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.