In order to workout the method for establishing the formula of thin lens, my teacher says that the optical path is:
$PA + AQ = PS1 + nS1S2 + S2Q$$PA + AQ = PS_1 + nS_1S_2 + S_2Q$ ($n$ is the refractive index of the lens)
Why is she multiplying $S1S2$$S_1S_2$ by $n$?
Also, she says that for spherical surface $S1$$S_1$, with centre of curvature $C1$$C_1$, we can write from geometry,
$h^2 = 2(S1C1 - OS1) OS1 $$h^2 = 2(S_1C_1 - OS_1) OS_1 $
How is she deriving this?