Question

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 the end closer to the pole is $20 \,cm$ away from it. Find the length of the image.

• A. 2 cm
• B. 4 cm
• C. 5 cm
• D. 6 cm

Answer 1

Answer: (C)

Since, point $A$ is centre of curvature, image of $A$ is formed on $A$ itself.
Image of $B, u=-30 \,cm , f=-10\, cm , v=?$
$\frac{1}{v}+\frac{1}{u} =\frac{1}{f} $
$\frac{1}{v}+\frac{1}{-30} = \frac{1}{-10} $
$\Rightarrow \frac{1}{v} =-\frac{1}{10}+\frac{1}{30} =\frac{-3+1}{30} $
$\Rightarrow v =-15 \,cm $

Length of image
$A' B'=20-15=5 \,cm$