- #1
avisha03
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Homework Statement
A duck is walking in a flat desert (yes, the proff. is creative...). According to atmospheric conditions the Refractive index is n(y)=1.0006-0.0003y. y in KM.
An observer is on the ground, 26.2 KM far. Where will he see the duck? Show the gragh of the ray path.
Homework Equations
d(ne)/ds= grad n
e- the ray path direction
The Attempt at a Solution
I used the eikonal equation, and some matematical manipulations to get the following equation:
dy/dx= sqrt((a-by)^2/c^2-1)
(a=1.0006, b=0.0003, c=1.0006*cos(theta_0))
In order to try and find y as a function of x, I tried to solve the latter eq. by seperating it, and using the variable replacment: m=a-by
I got:
ln(m+sqrt(m^2-c^2))=exp(-bx/c)
now I don't know wheather my way till now is correct, and how to display y as y(x).
Thanks for your help!