The focal f to a mirror is given by `(1)/(f) = (1)/(u) + (1)/(v)` where u and v represent object and image distance respectively then

Options

A. `(Delta f)/(f) = (Delta u)/(u) + (Delta v)/(v)`
B. `(Delta f)/(f) = (Delta u)/(v) + (Delta v)/(u)`
C. `(Delta f)/(f) = (Delta u)/(u) + (Delta v)/(v)- (Delta(u +v))/(u +v)`
D. `(Delta f)/(f) = (Delta u)/(u) + (Delta v)/(v)+ (Delta u)/(u + v) +(Delta v)/(u+v)`

Answer

D

Explanation

`f = (uv)/(u+v),(Delta f)/(f) = (Delta u)/(u)+(Delta v)/(v) +(Delta(u+v))/(u+v)`
`= (Delta u)/(u) +(Delta v)/(v) +(Delta u)/(u+v)+ (Deltav)/(u+v)`