Proof that light rays take the same time to reach the focal point of a lens In a thin plano-convex lens, if the wave front is perpendicular to the lens axis, all of the rays are in phase and are focused at the focal point. Can we use the lens geometry to mathematically prove that all rays take the same time to reach the focal point?
 A: If you know how to use Snell's law and do a bit of trigonometry, you can calculate the distance a ray travels in glass and in air , starting at each point on the plane surface of the lens and ending at the focus. The time spent in the glass is the distance traveled in the glass, times the refractive index, divided by the speed of light. Same in the air, using distance and index in the air. Write a formula for the total time as a function of radial position on the lens, and you will find that the radial position cancels out, making time independent of radial position.
A: $\def\rP{{\rm P}}$
IMO there's need to clarify the matter, as I'm seeing different aspects superimposed.
1) You'd not confuse behaviour of a beam of rays parallel to optical
axis and that of a parallel beam at angle with optical axis. In former
case it happens what you found: in paraxial approximation all rays
converge to the focus, but if you consider rays too far away from axis
this is no longer true. Generally the distant rays intersect optical
axis before focus - the whole beam after traversing the lens traces a
figure known as "caustic". This phenomenon is known as "spherical
aberration".
2) Spherical aberration may be corrected if rear spherical surface is
replaced by an "aspherical" one. For your particular case -
plano-convex lens, source at infinity - this can be obtained with a
hyperbolic surface.
3) Once one succeeds - e.g. by aspherical surface - to get exact
convergence of all rays in one point, the propagation time is the
same along every ray. This can be seen observing equal-time
(equal-phase) surfaces.
4) It may look improper to speak of phase in geometrical optics - that's
why I wrote equal-time. Equal-time surfaces may be rigorously defined within geometrical optics as follows.
Consider a ray starting from source S and choose a time $t$. On that
ray mark the point P such that propagation time from S to P equals
$t$. Repeat the construction for all rays, keeping $t$ fixed. The set
of all points so obtained is a surface, which we'll call "equal-time
surface" for time $t$. The same construction may be repeated for
different $t$'s and we get a family of equal-time surfaces.
You may also view $t$ as a function of P, for fixed S. This function (usually multiplied by $c$) is called eikonal: 
$$c\,t = W(\rP).$$
Thus equal-time surfaces are the level surfaces of $W$. The value
of $W(\rP)$ is also called the optical path from S to P. It can be shown that the equal-time surface through P is orthogonal to the ray
through P.
5) Now we may give the proof of property 3). If all rays do pass
through one point Q, then an equal-time surface, being orthogonal to
all rays, is a sphere centred in Q. For any point P on a given sphere
the distance PQ is the same, so it's obvious that time from S to Q is
the same along any ray, qed.
6) If spherical aberration is present there is no point Q, equal-time
surfaces aren't spherical. Of course you may always choose a point P
at will, and there is always a ray passing through P, with a well
defined optical path. But generally such ray is unique or there are
only a few rays through P - it depends on P's position wrt caustic. In special cases (e.g. if P is on optical axis of your lens) it's clear by
symmetry that there are infinite rays through P. Infinite, but by no
means all.
7) About off-axis rays, the discourse is different. Even if spherical aberration was corrected, there still remain "extra-axial" aberrations, much harder both to treat theoretically and to correct in practice. Outgoing rays will behave in an asymmetrical way, the caustic will take a complicated shape. Reducing the width of incoming beam isn't so effective for extra-axial aberrations as it's for spherical aberration. That's why designing wide-angle optical systems is especially difficult.
