An optical arrangement consists of two concave mirrors \(M_1\) and \(M_2\), and a convex lens \(....

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