A pin of small length 'a' is placed along the axis of a concave mirror of focal length f, at the distance u $$(u > f)$$ from its pole. The length of its image is 'b'. If the same object is placed perpendicular to its axis at the same distance u and the length of its image is now 'c', then

A

$$b = a\frac{f^2}{(u - f)^2}$$

B

$$c = \sqrt{ab}$$

C

$$c = b\frac{u - f}{f}$$

D

$$bc = \frac{a^2f^3}{(u - f)^3}$$