1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook