Two identical glass rods S _ 1 and S _ 2 (refractive index = 1.5)...

Two identical glass rods ${S}_{1}$ and ${S}_{2}$ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod ${S}_{1}$ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside ${S}_{2}$ . The distance $d$ is