Question

Find out the image position formed by concave mirror, considering the image formed by plane mirror as an object for concave mirror.

Answer 1

The object distance from the plane mirror is $10\text{cm}$, so the image will form $10\text{cm}$ behind the plane mirror. Now given that image will be considered as the object for the concave mirror.
So the distance of object from the concave mirror will now become,$u=40+20=60\text{cm}$
Given,
focal length, $f=20\text{cm}$

Sign conventions for concave mirror are:
u = -ve ( Left side of the mirror)
f = -ve
Using Mirror Formula:
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-60}=\frac{-1}{20}$

$\frac{1}{v}=\frac{1-3}{60}$

$⟹v=-30\text{cm}$

i.e. $30\text{cm}$ from the pole (left side of the mirror)