If object distance u = (50.1 +-10.2) cm and image distance v = (20.1 +-0.2) cm, then find value of focal length with error.

If object distance u = (50.1 +-10.2) cm and image distance v = (20.1 +

1.	If object distance u = (50.1 +-10.2) cm and image distance v = (20.1 +-0.2) cm, then find value of focal length with error.
Answer» Solution :Focal length of SPHERICAL MIRROR, `(1)/(F)=(1)/(u)+(1)/(v)` `:.f=(uv)/(u+v)` `=((50.1(20.1))/(50.1+20.1))` `=(1007.01)/(70.2)` `=14.334` `14.3 CM` Relative ERROR, `(Deltaf)/(f)=(Deltau)/(u)+(Deltau)/(v)+(Delta(u+v))/(u+v)` `=(Deltau)/(u)+(Deltau)/(v)+(Deltau+Deltav)/(u+v)` `(Deltaf)/(14.3)=(0.2)/(50.1)+(0.2)/(20.1)+(0.2+0.2)/(50.1+20.1)` `=0.004+0.012+0.006` `=0.02` `:. Deltaf=0.02xx14.3` `=0.286` `=0.3` `:.`Focal length `f+-Deltaf=(14.3+-0.3) cm`