= Solution
For nonzero small $d$, stationarity of the travel time gives
$$
\frac{d(ct)}{dd}=d\left[\frac1a+\frac1b-2\alpha(n-1)\right]=0.
$$
To 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, $1/a+1/b=1/f$, gives
$$
\boxed{f=\frac1{2\alpha(n-1)}.}
$$
For parallel incident rays $a\to\infty$, the image is at $b=f$. A centre-thick lens with $\alpha>0$ and $n>1$ is converging.
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