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## Homework Statement

See the picture for the situation of the problem.

I'm told that any ray starting from S and getting through the "Cartesian Oval" reach point P.

I must show that the equation of the interface curve is [tex]l_0n_1+l_i n_2=K[/tex] where K is a constant.

So far I've showed that [tex]l_0=\sqrt {x^2+y^2}[/tex] and [tex]l_i=\sqrt {y^2+(s_0 + s_i -x)^2}[/tex]. But I remain stuck as how to proceed further.

Any idea is greatly appreciated.

## Homework Equations

Snell's law? I've tried something with it but didn't reach anything.

Maybe Fermat's principle?

## The Attempt at a Solution

See above.