A double convex lens has a focal length of 25 cm . The radius of curvature of one of its surfaces is twice that of the other. Determine the radii, given that the refractive index of the lens material is 1.5 .

Step-by-step solution

Given f = 25 cm and = 1.5 . Let the radii of curvature of the double convex lens be R₁ = R and R₂ = -2R . Using the lens maker's formula: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) Substituting the given values: 1 25 = (1.5 - 1) ( 1 R - 1 -2R ) 1 25 = 0.5 ( 1 R + 1 2R ) 1 25 = 1 2 ( 3 2R ) 1 25 = 3 4R 4R = 75 R = 18.75 cm The other radius is 2R = 2 18.75 = 37.5 cm . The radii of curvature are 18.75 cm and 37.5 cm .