thin-lens equation

[twitch94301]

Hey. I understand the thin-lens equation and that it is 1/distance from lens to object + 1/distance from lens to image = 1/focal length. But, I was wondering how/why it works. If someone knows, I would appriciate the help. Thanks.

[krab]

The idea of a lens is to have a linear relationship between the distance a ray passes through off axis, and the amount the ray is kinked on passing through. Let us call the former quantity r and the latter \Delta\theta. The proportionality constant is f, the focal length. So we have
r=f\Delta\theta
If a ray comes from a point on axis a distance o upstream of the lens, and if \theta_o is the angle, then for small angles, \theta_o=r/o.
If this ray comes to a point on axis a distance i downstream of the lens, and if \theta_i is the angle, then for small angles, \theta_i=r/i.
Now, realize that
\Delta\theta=\theta_o+\theta_i
and you have your formula.

[twitch94301]

Thanks for the help.