Calculate focal length of a spherical mirror from the following observations : object distance, `u = (50.1 +- 0.5)cm` and image distance , `upsilon = (20.1 +- 0.2)cm.`

Explanation

Formula for local length of a spherical mirror
`(1)/(f)=(1)/(v)+(1)/(u)`
or `f=(uv)/(u+v)`
`=((50.1)(20.1))/((50.1)+(20.1))=14.3 cm`
Also, `(Deltaf)/(f)=pm[(Deltau)/(u)+(Deltav)/(v)+(Deltau+Deltav)/(u+v)]`
`=pm[(0.5)/(50.1)+(0.2)/(20.1)+(0.5+0.2)/(50.1+20.1)]`
= `[0.00998+0.00995+0.00997]`
`=pm(0.0299)`
`therefore` `Deltaf=0.0299xx14.3=0.428=0.4cm`
`therefore` `f=(14.3pm0.4)cm`