Practice question

**Combination of lenses in contact** effective power P = P₁+P₂, effective focal length 1/F = 1/f₁ + 1/f₂, for thin lenses in contact. If separated by d, 1/F =1/f₁+1/f₂ - d/(f₁ f₂). Power adds algebraically, converging + with diverging - can cancel, used to correct aberrations and design achromatic doublets. Refractive index: n = (sin ( (A + D_m/2) )/sin ( (A/2) )) . A = 60° , D_m = 40° . n = (sin ( (60 + 40/2) )/sin ( (60/2) )) = (sin 50°/sin 30°) . sin 50° ≈ 0.766 , sin 30° = 0.5 . n = (0.766/0.5) ≈ 1.53 . Substituting