Question

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

• A. 10 cm
• B. 15 cm
• C. 2.5 cm
• D. 5 cm

Answer 1

Answer: (D)

The position of image of nearer end to mirror can be found out using mirror equation,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v_1}=\frac{1}{-20}-\frac{1}{-10}$
$\Rightarrow v_2=-20$
Similarly position of image of farther end to mirror can be found out as
$=\frac{1}{v_2}=\frac{1}{-(10+20)}-\frac{1}{-10}$
$\Rightarrow v_2=-15$
Hence the length of the image
$=20cm-15cm=5cm$