A plano-convex lens of refractive index 1.5 has a radius of curvature of 20 cm for its curved surface. If its plane surface is silvered, what will be the effective focal length of the resulting system?

Step-by-step solution

The silvered lens acts as an equivalent mirror. The power of the equivalent mirror is given by: P_ eq = 2P_ l + P_ m The focal length of the plano-convex lens f_ l is: 1 f_ l = ( - 1) ( 1 R - 1 ) 1 f_ l = (1.5 - 1) ( 1 20 - 0 ) = 0.5 20 = 1 40 cm ⁻¹ The power of the lens is P_ l = 1 f_ l = 1 40 cm ⁻¹ . Since the plane surface is silvered, it acts as a plane mirror with an infinite radius of curvature. Its focal length f_ m = , so its power P_ m = 0 . The equivalent power of the system is: P_ eq = 2 ( 1 40 ) + 0 = 1