A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. What is the length of the image?

5 cm

\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)

The end of the rod nearest to the mirror is at a distance of 20cm hence its at the centre of the mirror. Image of this point will be at the same point hence at a distance of 20cm.

Other end is at a distance of 30cm from the mirror.

u = -30cm , f = -10 cm $\Rightarrow v = -15cm$

Hence length of image rod is 5cm.