= Solution
In the thin-lens approximation, the geometric <path length> is
$$
L_{\rm geom}(d)\simeq\sqrt{a^2+d^2}+\sqrt{b^2+d^2}
\simeq a+b+\frac{d^2}{2a}+\frac{d^2}{2b}.
$$
The glass replaces approximately length $s(d)$ of air, rather than adding a further geometric segment. Its excess <optical path length> is therefore $(n-1)s(d)$. With $s(d)=s_0-\alpha d^2$,
$$
\boxed{ct(d)\simeq a\left(1+\frac{d^2}{2a^2}\right)+b\left(1+\frac{d^2}{2b^2}\right)+(n-1)(s_0-\alpha d^2).}
$$
The approximations retain terms quadratic in the small ray height and neglect products of lens thickness with the squared ray slope. The distinction between geometric and <optical path length> explains why the glass contribution contains $n-1$, not $n$.
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