Past exam of the physics 2 paper of the University of Oxford / 2014 resit / 10 / 2 / Solution

In the thin-lens approximation, the geometric path length isThe 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 $s(d)=s_0-\alpha d^2$,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 $n$.