JEE Main 2025 — Ray Optics Question with Solution

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