Question

A rod of length $10cm$ lies along the principal axis of a concave mirror of focal length $10cm$ in such a way that the end closer to the pole is $20cm$ 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 $B,u=-30cm,f=-10cm,v=?$
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-30}=\frac{1}{-10}$
$\Rightarrow \frac{1}{v}=-\frac{1}{10}+\frac{1}{30}=\frac{-3+1}{30}$
$\Rightarrow v=-15cm$

Length of image
$A^{\prime }{B}^{\prime }=20-15=5cm$