Similarity and Optics

It is purely geometry that we can determine properties of convex lenses and their images. In this case, it suffices to use congruency and similarity to show the relationship between object distance u, image distance v and focal length f. From there we can also determine the height of object h and height of image k .Consider the ray diagram below.

Triangles OCD and OBE are similar, hence h/k=u/v .
Also, triangles AOG and BEG are similar, hence f/(v-f)=h/k=u/v.

But h/k =u/v. Substitute this into the second equation will result in the neat formula:

1/f=1/u+1/v