Physics Question from JEE Main 2025 · 29 January, Shift 1

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 the figure. After refraction, the beams intersect at point $3$ which is exactly on the interface at the other end of the block. Given: the distance between $1$ and $2$, $d = 4\sqrt{3} \, \text{cm}$ and $\theta_1 = \theta_2 = \cos^{-1} \left( \frac{n_2}{2n_1} \right)$, where $n_2$ is the refractive index of the block and $n_1$ is the refractive index of the outside medium, then the thickness of the block is _____ cm.