Two light beams fall on a transparent material block at point 1 and 2 with angle ${\theta_1}$ and ${\theta_2}$, 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, ${\rm{d}} = 4\sqrt 3 \;{\rm{cm}}$ and ${\theta _1} = {\theta _2} = {\cos ^{ - 1}}\left( {\frac{{{n_2}}}{{2{n_1}}}} \right)$, where refractive index of the block ${n_2}>$ refractive index of the outside medium ${n_1}$, then the thickness of the block is _______ cm .