Derivation of the thin lens equation?

[Qubit12]

'm currently reading chapter 27 of the Feynman lectures, where he derives the thin lens equation for a single refracting surface. He arrives at the equation

h^2/2s + nh^2/s' = (n-1)h^2/2r

Where s is the object distance, s' is the image distance, n is the index of refraction of the second medium (the first is one), r is the radius of curvature, and h is the altitude of a triangle

Where does the (n-1) come from? Wouldn't it simply be n?

This is kind of vague, so please look at the second page of
http://student.fizika.org/~jsisko/Knjige/Opca%20Fizika/Feynman%20Lectures%20on%20Physics/Vol%201%20Ch%2027%20-%20Geometric%20Optics.pdf

I would be so grateful. Thanks.

 

[Borek]

All expressions in the equation are excess times as compared with the idea that light travels from O to Q in the air and then from Q to O' in the glass.

$(n-1)\frac{h^2}{2R}$ is about how much longer light travels between V and Q. $n\frac{h^2}{2R}$ is a total time of travel between V and Q, not excess time, for the excess time you have to subtract time it would take for the light to travel between V and Q in the air - which is just $\frac{h^2}{2R}$ (as we assumed the speed in air is just 1).