Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of air of height h=1/3 cm, and the second and third layers are of equal thickness d=(√3−1)/2 cm, and refractive indices μ₁=√(3/2) and μ₂=√3, respectively. A light source O is placed on the top of the first unit, as shown. A ray of light from O is incident on the second layer of the first unit at an angle θ=60° to the normal. For a specific value of n, the ray emerges from the bottom at a distance l=8/√3 cm, as shown. The value of n is ____.