A thin convex lens of focal length 'f' is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance a/3 in front of the combination. The value of 'a' is?

The first image will be formed from refraction from lens, its position can be determined by lens formulasThe lens formulas is given as1v𕒵u=1f.. (i)whereu=−a,f=+f, substituting values in equation (i)1v𕒵−a=1f⇒v=afa−fThe image formed will be left side of lens providea>fThe mirror will form the image at right side of the lens with distance equal toafa−fNow the third image will be formed by lens again for which the coordinate system will be reversed of earlier as the rays are traveling from left to right:u=afa−f,f=+fandv=a3applying lens formulas1v𕒵u=1f.. (i)3a−a−faf=1f.. (ii) multiplying and dividing by f3faf−a−faf=aaf3f−a+f=a⇒a=2fHence, correct answer is option A