A short linear object of length b lies along the axis of a concave mirror of focal length f at a distanee u from the pole of the mirror. The size of the image is approximately equal to

Options

A. `b((u-f)/(f))^(1//2)`
B. `b((u-f)/(f))^(2)`
C. `b((f)/(u-f))^(1//2)`
D. `b((f)/(u-f))^(2)`

Answer

D

Explanation

From mirrorr formula `(1)/(f)=(1)/(v)+(1)/(u)` …(i)
Differentiating equation `(i)` we obtain
`0=-(1)/(v^(2))dv-(1)/(u^(2))du`
`impliesdv=-((v)/(u))^(2)du` ...`(ii)`
Also from equation `(i) (v)/(u)=(f)/(u-f) ....`(iii)
From equations (ii) and (iii) we get
`dv=-((f)/(u-f))^(2).b`
Therefore size of image is `((f)/(u-f))^(2)b`