/sci/ - Science & Math

given a refracting surface I have to show that to produce a perfect image that the surface must satisfy the general equation of a bivariate quadratic. I can understand the reasoning behind it as the light rays further from the middle must be compensated for their vertical dimension to have the same optical path length of the middle rays, but Im not exactly sure how I would take this and get to an equation exactly.

would i just set the optical path lengths equal to each other and it will get to that equation?