To measure radus of curvature of a convex mirror unsing a spherometer, it was found that `I = (4.4+-0.1)` cm and h =(0.085 +- 0.001)` cm. Calculate the maximum possible error in the radius of curvature.

Answer

`+-2.5cm`

Explanation

Here, `I =(4.4 +-0.1)cm`
`h = (0.085 +- 0.001)cm.`
From `R = (I^2)/(6h) +(h)/(2)`
`R = ((4.4)^2)/(6xx0.085) +(0.085)/(2)`
`=37.96 +0.042 = 38.002 =38cm`
(rounded to have two significant figures)
`(DeltaR)/(R ) =+-[2((DeltaI)/(l)) +(Deltah)/(h) +(Deltah)/(h)]`
`=+-[(2xx0.1)/(4.4) +(0.001)/(0.085) +(0.001)/(0/0.085)]`
`(DeltaR)/( r) = +-0.067`
`DeltaR = +- 0.067 R= +-0.067x38 = +-2.546`
`Delta R= +- 2.5cm`
(rounded to have two significant figures)