Two lenses, A and B, are made of the same transparent material. Lens A is an equiconvex lens, while lens B is a plano-convex lens. If the curved surfaces of both lenses have the same radius of curvature, what is the ratio of the power of lens A to the power of lens B?

Step-by-step solution

Let the radius of curvature of the curved surfaces be R and the refractive index of the material be . For the equiconvex lens A, the radii of curvature are R₁ = R and R₂ = -R . The power of lens A is: P_ A = ( - 1) ( 1 R - 1 -R ) = ( - 1) ( 2 R ) For the plano-convex lens B, the radii of curvature are R₁ = R and R₂ = . The power of lens B is: P_ B = ( - 1) ( 1 R - 1 ) = ( - 1) ( 1 R ) The ratio of their powers is: P_ A P_ B = 2( - 1)/R ( - 1)/R = 2 1 Thus, the ratio is 2:1 . Answer: 2:1