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.

Explanation

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`