 Solution

For nonzero small $d$, stationarity of the travel time givesTo focus a bundle, this must hold for neighbouring off-axis rays, not merely for the automatically stationary axial ray $d=0$. Comparing with the thin lens equation, $1/a+1/b=1/f$, givesFor parallel incident rays $a\to \infty$, the image is at $b=f$. A centre-thick lens with $\alpha >0$ and $n>1$ is converging.