Two objects A and B are placed at 15cm and 25cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is

To find the distance between the images formed by a concave mirror for two objects placed at different distances from the pole, we will first calculate the image distances for both objects using the mirror equation. Then, we'll find the distance between the two images.

Mirror formula: 
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}$
Concave mirror$\mathrm{f}=\frac{-\mathrm{R}}{2}=\frac{-40}{2}=-20\mathrm{cm}$
For objects kept at 15cm
$\begin{array}{l}\frac{1}{-20}=\frac{-1}{15}+\frac{1}{{\mathrm{v}}_1}\Rightarrow \frac{1}{{\mathrm{v}}_1}=\frac{1}{15}-\frac{1}{20}=\frac{1}{60}\\ {\mathrm{v}}_1=60\mathrm{cm}\end{array}$
For object kept at 25cm
$\begin{array}{l}\frac{1}{-20}=\frac{-1}{25}+\frac{1}{{\mathrm{v}}_2}\Rightarrow \frac{1}{{\mathrm{v}}_2}=\frac{1}{25}-\frac{1}{20}=\frac{-1}{100}\\ {\mathrm{v}}_2=-100\mathrm{cm}\end{array}$
distance between two images ${\mathrm{v}}_1-{\mathrm{v}}_2=60-(-100)=160\mathrm{cm}$