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Homework Help: Finding the index of refraction with respect to the vertical axis

  1. Dec 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Studying the mirage, we can assume that the index of refraction depends only on the vertical coordinate z. A ray of light starts from {0,0} with angle [tex]\beta\leq30[/tex]. It's trajectory fits on an ellipse with major axis a and minor axis b.

    a) Give [tex]n(z)=?[/tex]
    b) What is the trajectory of a ray of light that starts with angle [tex]2\beta[/tex] ?


    2. Relevant equations
    From functional analysis we derived that in this situation:
    [tex]\frac{n[z]}{\sqrt{1+z'[x]^2}}=\text{constant}[/tex]


    3. The attempt at a solution

    What I have problems with is expressing u and v in terms of beta,a and b. If I could do that then I could give the equation for the ellipse, order it for z[x] and insert it into the equation in 2. I was supposed to do this in an exam in about half an hour, so it has to have a simple solution that I cannot see even after looking at it for hours.

    I have made a drawing
     
    Last edited: Dec 31, 2009
  2. jcsd
  3. Dec 31, 2009 #2

    Redbelly98

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    Welcome to Physics Forums.

    Are u and v the (x,z) coordinates of the center of the ellipse? What about starting with the general equation for an ellipse, and setting z'=tan(β) at the origin?
     
  4. Dec 31, 2009 #3
    Last edited by a moderator: May 4, 2017
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