Object distance, u=(50.1±0.5)cm and  image distance v=(20.1±0.2)cm, then focal length is

Focal length is given by 1f=1v+1u or f=uvu+v=(50.1)(20.1)(50.1)+(20.1)=14.3  cmAlso, Δff=±(Δuu+Δvv+Δu+Δvu+v)=±(0.550.1+0.220.1+0.5+0.250.1+20.1)=±[0.00998+0.00995+0.00997]=±[0.0299]∴  Δf=0.0299×14.3=0.428=0.4  cm∴f=(14.3±0.4)cmIn power If Z=An,  then  ΔZZ=nΔAAIn more general form if Z=AxByCq,  then the maximum fractional error in Z isΔZZ=xΔAA+yΔBB+qΔCC(Note that there is no negative sign)