The shape of the interface pictured in Fig. P.1 is known as a Cartesian oval after Rene Descartes who studied it in the early 1800s. It's the perfect configuration to carry any ray from S to the interface to P. Prove that the defining equation is
ℓ0n1 + ℓin2 = constant
Show that this is equivalent to
n1(x2+y2)1/2+n2[y2+(s0+si−x2)]1/2 = constant
Figure P.1
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