Question

Two objects $A$ and $B$ when placed in turns in front of a concave mirror, give images of equal size. The focal length of the concave mirror is $7.5cm$ and size of object $A$ is three times the size of object $B$. The distance of $B$ from the mirror, if $A$ is placed $30cm$ from the mirror, is

• A. 18 cm
• B. 15 cm
• C. 20 cm
• D. 25 cm

Answer 1

Answer: (B)

Let $m_A=\frac{I_A}{O_A}$ and $m_B=\frac{I_B}{O_B}$
Here, $I_A=I_B$ and $O_A=3O_B$
$\frac{m_A}{m_B}=\frac{I_A}{O_A}\times \frac{O_B}{I_B}=\frac{I_A}{I_B}\times \frac{O_B}{O_A}=\frac{1}{3}$
Also, $m_A=\frac{f}{f-u_A}$ and $m_B=\frac{f}{f-u_B}$
$\therefore \frac{m_A}{m_B}=\left(\frac{f-u_B}{f-u_A}\right)$
or $\frac{1}{3}=\frac{-7.5-u_B}{-7.5-(-30)}$
or $u_B=-15cm$