##1/f=1/u+1/u^’##
##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^’##