Snell's law problem

  • Thread starter zell99
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Homework Statement


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.

Homework Equations


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.
Thanks
 
Last edited:

Answers and Replies

  • #2
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Has anyone got any ideas? I should have said theta is very small, so small angle approximations are fine where appropriate.
Thanks
 

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