A convex lens has its radii of curvature equal. The focal length of the lens is f . If it is divided vertically into two identical plano-convex lenses by cutting it, then the focal length of the plano-convex lens is ( = the refractive index of the material of the lens)

Step-by-step solution

The given, R₁=R, R₂=-R f=F Lens Maker's formula aligned 1 F & =( -1) [ 1 R₁ - 1 R₂ ] 1 f & =( -1) [ 1 R + 1 R ] f & = R 2( -1) R & =2 f( -1) aligned Now, it is divided vertically into two identical plano convex lens aligned & 1 f^ =( -1) [ 1 R₁ - 1 R₂ ] & 1 f₁ =( -1) [ 1 R - 1 ] [ R₁=R, R₂= ] & f₁= R ( -1) & f₁= 2 f( -1) ( -1) & f₁=2 f aligned