A plano-convex lens made of a material with refractive index 1.5 has a radius of curvature R for its curved surface and an optical power P₀ . It is placed in contact with a plano-concave lens of an unknown refractive index and radius of curvature R for its curved surface. If the power of the combination is - P₀ 2 , the value of is :

Step-by-step solution

For the plano-convex lens, the radii of curvature are R₁ = R and R₂ = . Using the lens maker's formula, its power P₀ is: P₀ = (1.5 - 1) ( 1 R - 1 ) = 0.5 R For the plano-concave lens, the radii of curvature are R₁ = and R₂ = R (or R₁ = -R and R₂ = ). In either case, its power P₂ is: P₂ = ( - 1) ( 1 - 1 R ) = - ( - 1) R When placed in contact, the equivalent power of the combination is the sum of the individual powers: P_ eq = P₀ + P₂ We are given that P_ eq = - P₀ 2 . Substituting the expressions: - 1 2 ( 0.5 R ) =