An equiconvex lens of focal length f is cut into two identical halves by a plane perpendicular to the principal axis. The plane surface of one of the resulting plano-convex lenses is then silvered. The magnitude of the equivalent focal length of this new optical system is

Step-by-step solution

For the original equiconvex lens, the focal length f is given by 1 f = ( - 1) ( 2 R ) . When cut perpendicular to the principal axis, the resulting plano-convex lens has a focal length f_l given by 1 f_l = ( - 1) ( 1 R ) . Thus, f_l = 2f . When the plane surface is silvered, the system behaves as an equivalent mirror. Light passes through the lens, reflects from the mirror, and passes through the lens again. The equivalent power is P_ eq = 2P_l + P_m . The power of the lens is P_l = 1 f_l = 1 2f and the power of th