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 \( 10 \, \text{cm} \). The radii of curvature of \( M_1 \) and \( M_2 \) are \( 20 \, \text{cm} \) and \( 24 \, \text{cm} \), respectively. The distance between \( L \) and \( M_2 \) is \( 20 \, \text{cm} \). 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 \( n/7 \, \text{cm} \), one of the images coincides with \( S \). The value of \( n \) is _______.
