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.`

Options

A. `(0.04pm14.3)`
B. `(14.3pm0.4)`
C. `(14.3pm0.04)`
D. None of these

Answer

B

Explanation

Formula forfocal length of a spherical mirror `(1)/f=(1)/(v)+(1)/(u)`
`or f=(uv)/(u+v)`
`=((50.1)(20.1))/((50.1+20.1))=14.3cm`
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)`
`:.Deltaf=0.0299xx14.3=0.428=0.4cm`
`:.f=(14.3pm0.4)cm`
`(DeltaT)/Txx100=pm((1)/(2)xx(Deltal)/(l)xx100+(1)/(2)xx(Deltag)/(g)xx100)`
`=pm((1)/(2)xx1+(1)/(2)xx2)=pm1.5%`