Two light beams fall on a transparent material block at point 1 and 2 with angle θ_1 and θ_2, respectively, as shown in figure. After refraction, the…

Two light beams fall on a transparent material block at point $\displaystyle 1$ and $\displaystyle 2$ with angle $\displaystyle \theta_1$ and $\displaystyle \theta_2$, respectively, as shown in figure. After refraction, the beams intersect at point $\displaystyle 3$ which is exactly on the interface at other end of the block. Given : the distance between $\displaystyle 1$ and $\displaystyle 2$, $\displaystyle \mathrm{d}=4 \sqrt{3} \mathrm{~cm}$ and $\displaystyle \theta_1=\theta_2=\cos ^{-1}\left(\frac{n_2}{2 n_1}\right)$, where refractive index of the block $\displaystyle n_2>$ refractive index of the outside medium $\displaystyle \mathrm{n}_1$, then the thickness of the block is $\displaystyle \_\_\_\_$ cm.