A concave mirror of focal length 20cm is cut into two parts from the middle and the two parts are moved perpendicularly by a distance 1cm from the previous principle axis AB. The distance between the images formed by the two parts, if the object is kept at a distance of 10cm from the pole of the original principal axis is  

The focal length of mirror does not change due to the cutting. ${\mathrm{A}}_1{\mathrm{A}}_2\text{ and }{\mathrm{B}}_1{\mathrm{B}}_2$ are principal axes of upper and lower parts of mirror pieces. If we consider lower piece, height of object A above its principal axis will be 1 cm.
$\mathrm{u}=-10\mathrm{cm},\mathrm{V}=?,\mathrm{f}=-20\mathrm{cm}$
$\frac{1}{\mathrm{V}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\Rightarrow \frac{1}{\mathrm{V}}+\frac{1}{-10}=\frac{1}{-20}\Rightarrow \mathrm{V}=+20\mathrm{cm}$

$\frac{{\mathrm{y}}_{\mathrm{i}}}{{\mathrm{y}}_0}=\frac{-\mathrm{V}}{\mathrm{u}}\Rightarrow \frac{{\mathrm{y}}_{\mathrm{i}}}{1}=-\frac{(+20)}{-10}\Rightarrow {\mathrm{y}}_{\mathrm{i}}=+2\mathrm{cm}$
i.e. image (I_L)formed by lower mirror piece will be on the principal axis A₁A₂ . Similarly image (I_U)due to upper piece will be on B₁B₂ . The distance between the images is 2 cm