"triangle "" EFO "" is similar to ""triangle "OIH
(bar (IH))/(bar (EF))=(bar(OI))/(bar(OF))
g:"image height"
c:"object height"
u:"distance between object and lens"
u^':"distance between image and lens"
color(red)(g/c)=u^'/u
"triangle "" EFC "" is similar to ""triangle "COG
(bar (OG))/(bar (EF))=(bar(OC))/(bar(FC))
color(red)(g/c)=f/(u-f)
u^'/u=f/(u-f)
u^'(u-f)=u f
u^' u-u^' f=u f
u f+u^' f=u^' u
f(u+u^')=u^' u
f=(u^' u)/(u+u^')
1/f=(u+u^')/(u^' u)
1/f=cancel(u)/(u^' cancel(u))+cancel(u)^'/(cancel(u)^' u)
1/f=1/u+1/u^'