In `u-v` method to find focal length of a concave mirror, if object distance is found to be `10.0 cm` and image distance was also found to be `10.0 cm`, then find maximum permissible error in f.

Options

A. `5+-0.002 cm`
B. `5+-0.01 cm`
C. `5+-0.02 cm`
D. `5+-0.05 cm`

Answer

D

Explanation

`(1)/(u)+(1)/(v)=(1)/(f)`
`implies(1)/((-10))+(1)/((-10))=(1)/(f)"`
`implies|f|=5cm`
`(df)_(max)=((Deltau)/(u^(2))+(Deltav)/(v^(2)))xxf^(2)`
`(df)_(max)=((0.1)/(10^(2))+(0.1)/(10^(2)))xx5^(2)=0.05cm`
so, `f=(5+-0.05)cm`