Question

A rod of length $10cm$ lies along the principal axis of 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. $15cm$
• B. $2.5cm$
• C. $5cm$
• D. $10cm$

Answer 1

The correct option is C $5cm$

Rod $AB$ of length $10cm$ lies on the axis in front of concave mirror such that end A lies at a distance of $20cm$ from the mirror.
Using mirror formula :
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Case A : $u=-20cm$ $f=-10cm$
$\therefore$ $\frac{1}{v_A}+\frac{1}{-20}=\frac{1}{-10}$
$⟹v_A=-20cm$
Case B : $u=-30cm$ $f=-10cm$
$\therefore$ $\frac{1}{v_B}+\frac{1}{-30}=\frac{1}{-10}$
$⟹v_B=-15cm$
Thus length of image $L=20-15=5cm$