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. f₁ = 60 cm , f₂ = -30 cm . (1/f) = (1/f₁) + (1/f₂) = (1/60) + (1/-30) = (1/60) - (2/60) = (1 - 2/60) = (-1/60) . f = -60 cm (diverging system). Substituting values gives -60 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v -