Feynman's Missing Equation in his Lectures(Optics)

[Thecla]

In volume I of Feynman's Lectures on Physics (Chapter 27) he solves the problem of the focal length of spherical surfaces.
He says we have to arrange the curved surface of the glass in a manner that every ray from O, which hits the surface at any point P, will be bent so as to proceed to O'. Their travel time will be equal if we consider the index of refraction for air=1 and for glass=n [see attachment].

"This condition supplies us with an equation for determining the surface(of the glass). The answer is that it is a very complicated fourth-degree curve" He wants the student to entertain himself by trying to solve for this curve by analytic geometry, but he proceeds to solve the simpler case of using nearly parallel light rays near the axis.

What is the fourth-degree curve that is missing from this Chapter?

 

[jedishrfu]

There's a discussion on Physics Stack Exchange about it:

http://physics.stackexchange.com/questions/66624/perfectly-focusing-refractive-surface

 

[Thecla]

thanks for the information