Lenses are fabricated from a material having a refractive index of 1.50 . The magnitudes of the radii of curvature are 20 cm and 30 cm . Determine the focal lengths of all the possible lenses that can be formed with these specifications.

Step-by-step solution

Using the lens maker's formula: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) Given = 1.50 , the term ( - 1) = 0.5 = 1 2 . The magnitudes of the radii of curvature are 20 cm and 30 cm . Depending on the type of lens (biconvex, biconcave, concavo-convex, or convexo-concave), the signs of R₁ and R₂ can be positive or negative. The possible values for the term ( 1 R₁ - 1 R₂ ) are: Case 1: R₁ and R₂ have opposite signs. 1 R₁ - 1 R₂ = ( 1 20 + 1 30 ) = ( 3 + 2 60 ) = 1 12 cm ⁻¹ Substituting into the formula: 1 f = 1 2 ( 1 12 ) = 1 24 cm