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Consider a configuration of \( n \) identical units, each consisting of three layers. The first layer is a column of air of height \( h=\frac{1}{3} \mathrm{~cm} \), and the second and third layers are of equal thickness \( d=\frac{\sqrt{3-1}}{2} \mathrm{~cm} \), and refractive indices \( \mu_{1}=\sqrt{\frac{3}{2}} \) and \( \mu_{2}=\sqrt{3} \), respectively. A light source \( O \) is placed on the top of the first unit, as shown in the figure. A ray of light from \( O \) is incident on the second layer of the first unit at an angle of \( \theta=60^{\circ} \) to the normal. For a specific value of \( n \), the ray of light emerges from the bottom of the configuration at a distance \( l=\frac{8}{\sqrt{3}} \mathrm{~cm} \), as shown in the figure. The value of \( n \) is
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