Two light beams fall on a transparent material block at point 1 and 2 with angle $\mathrm{\theta }$₁ and $\mathrm{\theta }$₂, respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, d = 4$\sqrt{3}$ cm and ${\mathrm{\theta }}_1={\mathrm{\theta }}_2={\cos }^{-1}\left(\frac{{\mathrm{n}}_2}{2{\mathrm{n}}_1}\right)$, where refractive index of the block n₂ > refractive index of the outside medium n₁, then the thickness of the block is ________ cm.