The shape of the interface pictured in Fig. P.5.1 is known as a Cartesian oval after Rene...

The shape of the interface pictured in Fig. P.5.1 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.5.1