An optical arrangement consists of two concave mirrors  $M_1 and M_2$, and a convex lens L with a common principal axis, as shown in the figure. The focal length of L is 10 cm. The radii of curvature of $M_1 and M_2$, are 20 cm and 24 cm, respectively. The distance between L and  $M_2$ is 20 cm. A point object S is placed at the mid-point between L and $M_2$ on the axis. When the distance between L and  $M_1$, is n/ 7 cm, the image formed after refraction from lens then reflection from $M_1$  and again refraction from lens and finally reflection from $M_2$ coincides with S. The value of n is ____