A thin convex lens L (refractive index =1.5 ) is placed on a plane mirror M. When a pin is placed at A, such that OA =18 cm, its real inverted image…

A thin convex lens L (refractive index $\displaystyle =1.5$ ) is placed on a plane mirror M. When a pin is placed at A, such that $\displaystyle \mathrm{OA}=18 \mathrm{~cm}$, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index $\displaystyle \mu_l$ is put between the lens and the mirror, the pin has to be moved to A', such that $\displaystyle \mathrm{OA}^{\prime}=27 \mathrm{~cm}$, to get its inverted real image at A' itself. The value of $\displaystyle \mu_l$ will be :