WackStr
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Homework Statement
This is from hand and finch. We proved in the previous problem that (using euler lagrange equation):
x=\int_0^y\frac{dy}{\sqrt{\left(\frac{n[y]}{n_0}\right)-1}}
where n_0 is the refractive index at y=0 and x=0. The ray enters horizontally.
As an actual computation the book says that assume n[y]=n_0e^{-\alpha y} and n_0=1.5. Aslo y(30)=-1.
We need to find \alpha
The Attempt at a Solution
From the information given it seems like the equation we need to solve is
30=\int_0^{-1}\frac{dy}{\sqrt{e^{-2\alpha y}-1}} for \alpha but it seems like this equation has no solution.
So I am stuck at this point.