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

Answer

D

Explanation

As `(1)/(u) + (1)/(v)=(1)/(f)`, differentiating we get
`-(1)/(u^2)(du)/(dt) - (1)/(v^2) (dv)/(dt) = 0` or `(dv)/(du) = -(v^2)/(u^2)`
`m = (h_2)/(h_1) = -(dv)/(du) = (v^2)/(u^2)`
or `m = (h_2)/(b) = (v^2)/(u^2)` or `h_2 = b((v^2)/(u^2))`
`h_2 = b((f)/(u - f))^2` `[as m = (v)/(u) = (f)/(u - f)]`.