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 $\large\frac{a}{3}$ in front of the combination. The value of 'a' is :

Question

$\begin{array}{1 1} f \\ 2f \\ 3f \\ \frac{3}{2}f \end{array} $