A laser beam of 10 mm beam diameter is focused onto an optical fiber using a thin biconvex lens as shown in the figure. The refractive index of the lens is $1.5$. The refractive indices of the core and cladding of the fiber are $1.55 \;and \;1.54$ respectively. The minimum value of the focal length of the lens to attain he maximum coupling to the fiber $\text{(in mm, rounded off to one decimal place)}$ is ______
