When a lens is cut into two halves along X O X^ , then focal length of each half lens

Step-by-step solution

If R be the magnitude of radius of curvature of equiconvex lens, then its focal length f is given by aligned 1 f & =( -1) ( 1 R₁ - 1 R₂ ) & =( -1) ( 1 R - 1 -R )= 2( -1) R 1 f & = 2( -1) R ...(i) aligned When equiconvex lens is cut into two halves along X O X^ , then R₁=R, R₂=-R Focal length f^ is given as aligned 1 f^ & =( -1) ( 1 R - 1 -R )= 2( -1) R = 1 f [ from (i) ] f^ & =f aligned