Two lenses, A and B, are made of the same transparent material. Lens A is an equiconvex lens with both surfaces having a radius of curvature R . Lens B is a biconvex lens with surfaces having radii of curvature R and 2R . The ratio of the power of lens A to the power of lens B ( P_A : P_B ) is:

Step-by-step solution

The power of a lens is given by the Lens Maker's formula: P = 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) For lens A (equiconvex), R₁ = R and R₂ = -R : P_A = ( - 1) ( 1 R - (- 1 R ) ) = ( - 1) ( 2 R ) For lens B (biconvex), R₁ = R and R₂ = -2R : P_B = ( - 1) ( 1 R - (- 1 2R ) ) = ( - 1) ( 1 R + 1 2R ) = ( - 1) ( 3 2R ) Taking the ratio of their powers: P_A P_B = ( - 1) ( 2 R ) ( - 1) ( 3 2R ) = 2 3/2 = 4 3 Thus, the ratio P_A : P_B is 4:3 . Answer: 4:3