Geometrical Optics

A thin cylindrical rod of length \(10 \mathrm{~cm}\) is placed horizontally on the principle axis of a concave mirror of focal length \(20 \mathrm{~cm}\). The rod is placed in a such a way that mid point of the rod is at \(40 \mathrm{~cm}\) from the pole of mirror. The length of the image formed by the mirror will be \(\frac{x}{3} \mathrm{~cm}\). The value of \(x\) is _____________.