The plane face of a plano convex lens is silvered. If be the refractive index and R , the radius of curvature of curved surface, then system will behave like a concave mirror of curvature

Step-by-step solution

When an object is placed in front of such a lens,the rays first of all refracted from the convex surface, then refract from the polished plane surface and again refracts from convex surface. If f_l and f_m be the focal lengths of lens (convex surface) and mirror (plane polished surface) respectively, then effective focal length F is given by aligned & 1 F = 1 f_l + 1 f_m + 1 f_l = 2 f_l + 1 f_m = 2 f_l ( f_m= R 2 = ) & 1 f_l =( -1) ( 1 R ) & 1 F = 2( -1) R or F= R 2( -1) or R=2 F= R ( -1) aligned