Solve the Thin-Lens Equation: How & Why It Works

[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 appreciate 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.