A symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the difference between the powers of the original lens and the cut lens is

Step-by-step solution

The power P of a thin lens is given by the lens maker formula P = ( - 1) ( 1 R₁ - 1 R₂ ) . For a symmetric double convex lens, R₁ = R and R₂ = -R . Thus, P = ( - 1) ( 1 R - 1 -R ) = ( - 1) 2 R = 4 D. When the lens is cut into two equal parts by a plane perpendicular to the principal axis, each part becomes a plano-convex lens. For a plano-convex lens, one surface has radius R and the other is flat, meaning R₁ = R and R₂ = . The power of each cut lens P' is P' = ( - 1) ( 1 R - 1 ) = - 1 R . Comparing P and P' , we s