Relating Image Distance and Image Height

[swooshfactory]

Regarding the thin lens equation,

1/s + 1/s' = 1/f

where s= distance of object from lens, s' = distance of image from lens, and f=focal length, can h and h' (h = height of object and h' = image height) be substituted from s and s'? I know the values are related through similar triangles, I am just not positive that they can be substituted in this equation. Could anyone shed some light on this being a valid substitution?

 

[Kurdt]

You can't replace image distances with image heights in the thin lens equation but they are related by transverse magnification.

M_T = \frac{y_i}{y_0} = -\frac{s_i}{s_0}

This occurs because in geometrical optics they both form sides of similar right triangles.