(adsbygoogle = window.adsbygoogle || []).push({}); 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 in2.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

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

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