An equiconvex lens is cut two halves along (i) XOX' and (ii) YOY' as shown in the figure. Let f, f^ , f^ be the focal length of the complete lens, of each half in case (i) and each half in case (ii), respectively. Choose the correct statement from the following:

Step-by-step solution

Since the lens is equiconvex, the radius of curvature of each half is same. Using lens maker formula 1 f =( -1) ( 1 R₁ - 1 R₂ ) Here R₁=RR₂=-R by convection 1 f =( -1) 2 R ( -1) 1 R = 1 2 f ( i ) If we cut the lens along XOX ^ then two halves of the lens will be having the same radii of curvalur and aligned & R₁=R, R₂=-R & 1 f^ =( -1) ( 2 R ) & 1 f^ = 2 2 f = 1 f aligned From (i) it is clear that f^ =f But when we cut along YOY ' then aligned & R₁=R and R₂= & 1 f^ =( -1) ( 1 R - 1 ) & =( -1) 1 R = 1 2 f & f^ =2 f a