A concave mirror has a focal length 20cm. The distance between the two positions of the object for which the image size is double of the object size is

$\text{u}={\text{u}}_{\text{1}}\text{v}=-2{\text{u}}_{\text{1}}\text{f}=2\text{0cm}$

$\frac{\text{1}}{\text{f}}=\frac{\text{1}}{\text{v}}+\frac{1}{\text{u}}$

Then we get

$\frac{1}{-2{\text{u}}_1}-\frac{1}{{\text{u}}_1}=\frac{-1}{20}$

${\text{u}}_{\text{1}}=30\text{cm}$

For virtual image

$\text{u}=-{\text{u}}_2;\text{v}={\text{2u}}_{\text{2}}$

$\text{f}=-20\text{cm}$

${\text{u}}_2=10\text{cm}$

Distance between position$={\text{u}}_1-{\text{u}}_{\text{2}}$

$=30-10$

$=20\text{cm}$