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Figure shows the setup of forming image on object itself using convex lens and plane mirror .

Let us consider that object is at a distance d from lens and plane mirror is at 25 cm from lens at other side of lens as shown in figure..

The path length of ray after first refraction from lens to form image is  ( 25 + 25 + d ) cm = ( 50 + d ) cm as shown in figure.

Lens equation is

(1/v) - (1/u) = 1/f

where v = ( 50+d ) cm is the lens-to-image distance  and u = - d is the lens-to-object distance.

Focal length f = + 10 cm ( given )

(Cartesian sign convention is followed )

Hence Lens equation becomes

[ 1 / ( 50+d) ] + (1/d) = 1/10

By solving above equation, we get d = 11.9 cm .