Question

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

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

Answer 1

Answer: (C)

5 cm

Given for the concave mirror :
Focal Length, $f=-10cm$
Length of the rod, $L_{AB}=10cm$
Closer end distance of rod, $u_A=-20cm$
Far end distance of rod, $u_B=u_A+L_{AB}$
$u_B=-20-10=-30cm$
By using mirror formula for end $A$:

$\frac{1}{V_A}+\frac{1}{-20}=\frac{1}{-10}$
$V_A=-20cm$ [Image position of the end A]
$\frac{1}{V_B}+\frac{1}{-30}=\frac{1}{-10}$
$\frac{1}{V_B}=\frac{1}{15}$
$v_B=-15cm$
Length of the image can be given as:
$L_{A^{\prime }{B}^{\prime }}=\left|V_A\right|-\left|V_B\right|=20-15=5cm$