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# A point object is placed in front of a thin lens of focal length $f= 0.50\;m$ at a distance of $1.0\;m$ . A flat mirror is placed 2 m behind the lens. What is the distance between the lens and the final image formed.

$(a)\;1.0\;m \\ (b)\;0.5\;m \\ (c)\;0.6\;m \\ (d)\;0.2 \;m$

Since object is at 1 m in front of lens of focal length 0.5 m it is at 2 f from lens 10 image $I_1$ is formed at 1m on the other side of lens.
$I_1$ forms object for mirror which is 1 m in front .
$\therefore I_2$ is formed 1 m behind mirror.
Now final image $I_3$ is formed
Using lens formula
$\large\frac{1}{v}- \frac{1}{u} =\frac{1}{f}$
$u= 3m$
$f= 0.5 m$
$\large\frac{1}{v} -\frac{1}{-3}=\frac{1}{.5}$
$\large\frac{1}{v} =\frac{1}{.5} -\frac{1}{3}$
$\large\frac{1}{v}$$=2 -\large\frac{1}{3}$
$\large\frac{1}{v} =\frac{5}{3}$
$v= \large\frac{3}{5}$
$\quad= 0.6 \;m$ from lens
Hence c is the correct answer.