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 $7.5 cm$ and size of object $A$ is three times the size of object $B$. The distance of $B$ from the mirror, if $A$ is placed $30 cm$ 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 $O_{A}=3 O_{B}$
$\frac{m_{A}}{m_{B}}=\frac{I_{A}}{O_{A}} \times \frac{O_{B}}{I_{B}}=\frac{I_{A}}{I_{B}} \times \frac{O_{B}}{O_{A}}=\frac{1}{3}$
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 $u_{B}=-15\, cm$