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 $\mathrm{M}_2$ 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 $n / 7 \mathrm{~cm}$, one of the images coincides with S . The value of $n$ is $\_\_\_\_$ .