Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $\frac{\mathrm{\alpha }}{4} \mathrm{cm}.$ The value of $\mathrm{\alpha }$ is ______.