A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4 D , the power of a cut lens will be

Step-by-step solution

Biconvex lens is cut perpendicularly to the principal axis, it will become a plano-convex lens. Focal length of biconvex lens gathered 1 f =(n-1) ( 1 R₁ - 1 R₂ ) 1 f =(n-1) 2 R ( R₁=R, R₂=-R ) gathered f= R 2(n-1) (i) For plano-convex lens gathered 1 f₁ =(n-1) ( 1 R - 1 ) f₁= R (n-1) (ii) gathered Comparing Eqs. (i) and (ii), we see that focal length becomes double. As power of lens P 1 focal length Hence, power will become half. New power = 4 2 =2 D