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

Answer 1

The correct option is D $5cm$

The position of image of nearer end to mirror can be found out using mirror equation,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v_1}=\frac{1}{-20}-\frac{1}{-10}$

$⟹v_2=-20$

Similarly position of image of farther end to mirror can be found out as

$=\frac{1}{v_2}=\frac{1}{-(10+20)}-\frac{1}{-10}$

$⟹v_2=-15$

Hence the length of the image $=20cm-15cm=5cm$