In an optical bench experiment to measure the focal length of a concave mirror random error in focal length will be

Options

A. minimum when `u = f` and maximum when `u= infty`
B. minimum when `u = infty` and minimum when `u = f`
C. minimum when `u= 0` and maximum when `u= 2f`
D. minimum when `u = 2f` and maximum when `u =0`

Answer

D

Explanation

`(Deltaf)/f^(2)=(Deltau)/u^(2)+(Deltav)/v^(2) Deltau=Deltav` for optical bench
` Rightarrow 1/(f^(2))xxd(Deltaf)=Deltau[-2/u^(3)-2/v^(3)xx(dv)/(du)]_(for min error)=0`
` (dv)/(du)=-v^(3)/u^(3)=-v^(2)/u^(2)Rightarrow v=u`
` for `u = 2f`, error is min