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 plano-concave 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 i $s ______.$
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Question

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 plano-concave 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 i $s ______.$

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G1 Physics · Accepted Answer

Let the radii of curvature of the front and back surfaces of the biconvex lens be R₁ and R₂ in magnitude. For the biconvex lens in air, the magnitude of power is |P₁| = (1.5-1) (1/R₁ + 1/R₂) = 0.5(1/R₁+1/R₂). For the plano-concave lens of refractive index 1.7, one surface is plane and the curved surface has radius R₂. Therefore its power magnitude is |P₂| = (1.7-1)/R₂ = 0.7/R₂. The power magnitudes are equal: 0.5(1/R₁+1/R₂) = 0.7/R₂. Therefore, 0.5/R₁ = 0.2/R₂. Hence, R₁/R₂ = 0.5/0.2 = 5/2. Thu…