Referring to Fig. 3.38, if I represents a perfect image of the point O, show that the equation of the refracting surface (separating two media of refractive indices n1 and n2) is given by
n1 [x2 + y2 + z2] ½ + n2 [x2 + y2 + (z2 – z)2] ½ = n1 z1 – n2 (z2 – z1) (97)
where the origin is assumed to be at the point O and the coordinates of P and I are assumed to be (0,0, z1) and (0,0, z2) respectively. The surface corresponding to Eq.(97) is known as a Cartesian oval.
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