The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index =1.7 ) are same. If the curvature of planoconcave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is _ _ _ _ .

Step-by-step solution

Let R₁ and R₂ be the radii of the front and back surfaces of the biconvex lens. The power of the biconvex lens is P₁ = (1.5 - 1) ( 1 R₁ + 1 R₂ ) = 0.5 ( 1 R₁ + 1 R₂ ) . The plano-concave lens has a flat surface and a concave surface of radius R₂ (matching the back surface of the biconvex lens). Its power is P₂ = (1.7 - 1) ( 1 R₂ ) = 0.7 R₂ . Since the magnitudes of power are equal: 0.5 ( 1 R₁ + 1 R₂ ) = 0.7 R₂ Simplifying: 0.5 R₁ + 0.5 R₂ = 0.7 R₂ , which gives 0.5 R₁ = 0.2 R₂ Therefore: R₁ R₂ = 0.5 0.2 = 5 2