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Snell's law problem

  1. Mar 20, 2007 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant 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.

    3. 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: Mar 21, 2007
  2. jcsd
  3. Mar 24, 2007 #2
    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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