Two identical glass rods  $S_1$ and  $S_2$ (refractive index =1.5) have one convex end of radius of curvature 10cm. They are placed with the curved surfaces at a distance  d as shown in the figure, with their axis (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 50cm 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